# V3R1T4S known unknowns: 1116 open problems, built 2026-11-06T20:25:41Z from https://v3r1t4s.org. Tab-separated: id, category, kind, compute, path, title. Pages: https://github.com/elder-plinius/V3R1T4S/blob/main/<path>
id	category	kind	compute	path	title
aiice-arctic-sea-ice-forecast-leaderboard	Earth and sky	harvest	laptop-hours	known-unknowns/earth-and-sky/aiice-arctic-sea-ice-forecast-leaderboard.md	AIICE Arctic sea-ice concentration forecasting benchmark: beat every leaderboard model in a sea and scenario
short-binary-multiple-deletion-code-records	Record tables	harvest	laptop-hours to laptop-…	known-unknowns/record-tables/short-binary-multiple-deletion-code-records.md	Binary deletion codes: improve the best size at length 15 or 16, correcting two or three deletions
pycox-metabric-gbsg-breast-cancer-survival	Disease research	harvest	laptop-minutes	known-unknowns/disease-research/pycox-metabric-gbsg-breast-cancer-survival.md	Breast-cancer prognosis benchmark: beat the published time-dependent concordance on METABRIC and Rotterdam/GBSG
graph-automata-max-period	Graphs, games and automata	harvest	laptop-hours	known-unknowns/graphs-games-automata/graph-automata-max-period.md	Cellular automata on graphs: the next maximum period for Life on simple graphs (A384209) and for totalistic or outer-totalistic rules on connected graphs (A357951-A357953)
crus-riesel-sierpinski-k-elimination	Number hunts	harvest	laptop-hours	known-unknowns/number-hunts/crus-riesel-sierpinski-k-elimination.md	Conjectures 'R Us: eliminate a remaining k from a Riesel or Sierpinski base conjecture
laminar-ef1-four-agent-key-matroids	Graphs, games and automata	standard	laptop-hours to laptop-…	known-unknowns/graphs-games-automata/laminar-ef1-four-agent-key-matroids.md	Cookson–Shah four-agent key matroids: EF1 with ordered no-envy on 8 or 12 goods
crim-partition-game-even-rank-conjectures	Graphs, games and automata	standard	laptop-hours to pure th…	known-unknowns/graphs-games-automata/crim-partition-game-even-rank-conjectures.md	CRIM on integer partitions: prove or refute the Bašić-Gottlieb-Krnc normal-play P-position conjectures or characterize 4-part P-positions (arXiv:2606.16828)
divisor-poset-game-p-positions-a393927	Graphs, games and automata	harvest	laptop-hours	known-unknowns/graphs-games-automata/divisor-poset-game-p-positions-a393927.md	Divisor takeaway poset game on {2, 3, ..., k}: second-player winning sizes beyond k = 125 (OEIS A393927)
fjssp-w-worker-flexibility-bks	Optimization benchmarks	harvest	laptop-hours	known-unknowns/optimization-benchmarks/fjssp-w-worker-flexibility-bks.md	Flexible job shop with worker flexibility (FJSSP-W benchmark, 402 instances): lower a best known makespan
gauss-kuzmin-wirsing-certified-digits	Number hunts	standard	laptop-hours	known-unknowns/number-hunts/gauss-kuzmin-wirsing-certified-digits.md	Gauss-Kuzmin-Wirsing constant (C_83): more than Nisoli's 175 certified decimals of |lambda_2|
nplb-generalized-cullen-woodall-first-prime	Number hunts	harvest	laptop-hours	known-unknowns/number-hunts/nplb-generalized-cullen-woodall-first-prime.md	Generalized Cullen and Woodall primes: first prime for a base with none known
immrep22-tcr-epitope-microauc	Disease research	harvest	laptop-hours	known-unknowns/disease-research/immrep22-tcr-epitope-microauc.md	IMMREP22 TCR-epitope specificity: beat the best published per-epitope micro-AUC on the public paired-chain benchmark
coin-basket-adversarial-games	Graphs, games and automata	harvest	laptop-hours	known-unknowns/graphs-games-automata/coin-basket-adversarial-games.md	Jehn's adversarial coin-basket games: 'Fill your basket' fair compensation beyond n = 16 (OEIS A392305) and the 3-basket guaranteed win beyond n = 14 (A391538, conjectured formula)
coin-basket-random-expected-values	Graphs, games and automata	harvest	laptop-hours to laptop-…	known-unknowns/graphs-games-automata/coin-basket-random-expected-values.md	Jehn's random-basket coin game: exact optimal expected win for 2 baskets beyond n = 22 (OEIS A391791) and 3 baskets beyond n = 18 (A391792)
cubic-graphs-graceful-knuth-beyond-14	Graphs, games and automata	harvest	laptop-hours	known-unknowns/graphs-games-automata/cubic-graphs-graceful-knuth-beyond-14.md	Knuth's cubic graceful conjecture: extend the verification past 14 vertices (16, 18, 20, 22), or a connected cubic graph that is not graceful
langton-ant-ft-minimal-seed	Graphs, games and automata	standard	laptop-minutes to lapto…	known-unknowns/graphs-games-automata/langton-ant-ft-minimal-seed.md	Langton's ant: the least highway onset g(k) from starts with at most k black cells, k = 0..11, with proof of minimality
least-qnr-prescribed-quadratic-character-next-terms	Number hunts	harvest	laptop-hours	known-unknowns/number-hunts/least-qnr-prescribed-quadratic-character-next-terms.md	Least quadratic non-residue records: the next term of A000229 (least prime whose least QNR is the 39th prime, 167) or of a sibling prescribed-character sequence
mint-linear-ooa-depth-2-to-8	Record tables	harvest	laptop-minutes to lapto…	known-unknowns/record-tables/mint-linear-ooa-depth-2-to-8.md	Linear ordered orthogonal arrays of depth 2-8: higher strength than MinT's best known (MinT 'Advanced' tables)
median-selection-network-size-records	Record tables	harvest	laptop-hours to laptop-…	known-unknowns/record-tables/median-selection-network-size-records.md	Median selection networks: reduce a current comparator count for 10–25 inputs
kamada-near-repdigit-wanted-composites	Number hunts	harvest	laptop-days	known-unknowns/number-hunts/kamada-near-repdigit-wanted-composites.md	Near-repdigit factor tables (Kamada): factor a composite on the 'hoped to be factored' lists
new-periodic-variables-not-in-vsx	Sky archives	harvest	laptop-hours	known-unknowns/sky-archives/new-periodic-variables-not-in-vsx.md	New periodic variable stars / eclipsing binaries absent from VSX, confirmed in two independent surveys
no-three-collinear-cube-a399138	Graphs, games and automata	harvest	laptop-hours	known-unknowns/graphs-games-automata/no-three-collinear-cube-a399138.md	No three collinear in the n x n x n grid (OEIS A399138): beat a(7) >= 73, a(8) >= 94, a(9) >= 116, a(10) >= 138 or a(11) >= 164
node-kayles-lattices-petersen-a316632-a316533	Graphs, games and automata	harvest	laptop-hours	known-unknowns/graphs-games-automata/node-kayles-lattices-petersen-a316632-a316533.md	Node-Kayles on 3 x n lattices, m x n grids, and generalized Petersen graphs GP(n,2): open outcomes and nimbers (OEIS A316632, A316533)
oberwolfach-problem-orders-61-64	Graphs, games and automata	standard	laptop-days	known-unknowns/graphs-games-automata/oberwolfach-problem-orders-61-64.md	Oberwolfach problem: solve every instance OP(F) of order 61 to 64 (verified so far for all orders up to 60)
iedb-mhci-bd2009-blind-auc	Disease research	harvest	laptop-hours	known-unknowns/disease-research/iedb-mhci-bd2009-blind-auc.md	Peptide-MHC class I binding: beat NetMHCpan's blind-set AUC on the frozen public IEDB BD2009-to-Blind benchmark
percolation-3d-higher-d-low-precision-rows	Physics	harvest	laptop-hours per lattice	known-unknowns/physics/percolation-3d-higher-d-low-precision-rows.md	Percolation thresholds still at 3-4 digits: stacked 2D lattices, van der Marck duals, d-dimensional bcc/diamond (d = 4-6) and extended neighbourhoods in Wikipedia's 3D and higher-…
physlib-restricted-lorentz-connected	Formal proofs	standard	laptop-hours	known-unknowns/formal-proofs/physlib-restricted-lorentz-connected.md	Physlib semiformal result FXNL5: the restricted Lorentz group SO+(1,d) is connected
polaris-moleculeace-activity-cliff-mse	Drug discovery	harvest	laptop-hours	known-unknowns/drug-discovery/polaris-moleculeace-activity-cliff-mse.md	Polaris MoleculeACE (30 activity-cliff QSAR leaderboards): beat the single listed MSE on an official cliff split
proteingym-cancer-dms-supervised-5fold	Disease research	harvest	laptop-hours	known-unknowns/disease-research/proteingym-cancer-dms-supervised-5fold.md	ProteinGym supervised benchmark: beat the public best 5-fold Spearman on a cancer-gene DMS assay
proteingym-cancer-dms-zero-shot	Disease research	harvest	laptop-hours	known-unknowns/disease-research/proteingym-cancer-dms-zero-shot.md	ProteinGym zero-shot: beat the best public Spearman on a cancer-gene deep-mutational-scanning assay
qoblib-birkhoff-small-exact-records	Optimization benchmarks	harvest	laptop-hours to laptop-…	known-unknowns/optimization-benchmarks/qoblib-birkhoff-small-exact-records.md	QOBLIB minimum Birkhoff decomposition: an exact decomposition of B5_25_2 with at most 13 terms or B6_36_10 with at most 18
qoblib-steiner-tree-packing-records	Optimization benchmarks	harvest	laptop-hours	known-unknowns/optimization-benchmarks/qoblib-steiner-tree-packing-records.md	QOBLIB node-disjoint Steiner tree packing (multi-layer switchbox routing): a cheaper packing for an instance without a proved optimum
qoblib-portfolio-ten-assets-exact	Optimization benchmarks	standard	laptop-hours to laptop-…	known-unknowns/optimization-benchmarks/qoblib-portfolio-ten-assets-exact.md	QOBLIB ten-asset portfolio: close the exact optimum gap for a010_t10_orig_b004_l1e-03
reversed-zeckendorf-game-p-positions-a389618	Graphs, games and automata	harvest	laptop-minutes to lapto…	known-unknowns/graphs-games-automata/reversed-zeckendorf-game-p-positions-a389618.md	Reversed Zeckendorf game: second-player winning starting numbers beyond n = 129 (OEIS A389618) and the Batterman et al. infinite P-position conjecture
risk-or-safety-exact-optimal-play	Graphs, games and automata	harvest	laptop-hours to laptop-…	known-unknowns/graphs-games-automata/risk-or-safety-exact-optimal-play.md	Risk or Safety: exact optimal-play win probabilities beyond n = 30 (OEIS A387261/A387262)
site-percolation-2-uniform-lattices-thresholds	Physics	harvest	laptop-hours	known-unknowns/physics/site-percolation-2-uniform-lattices-thresholds.md	Site percolation thresholds of the 20 two-uniform lattices: beat the 4-digit values of Neher, Mecke and Wagner (2008) listed on Wikipedia's percolation-threshold tables
lifelike-rules-still-life-counts	Graphs, games and automata	harvest	laptop-hours	known-unknowns/graphs-games-automata/lifelike-rules-still-life-counts.md	Still-life counts in other Life-like rules: HighLife a(14) (A175000), 2x2 a(11) (A166476), Move a(11) (A175001), Maze a(10) (A175002)
benzel-stones-and-bones-next-terms	Graphs, games and automata	harvest	laptop-hours	known-unknowns/graphs-games-automata/benzel-stones-and-bones-next-terms.md	Stones-and-bones tilings of benzels (Propp's Problems 15-18): the next terms of A364416 and A364417, or of the weighted A364418 and A364438
subtraction-game-max-period-terms	Graphs, games and automata	harvest	laptop-hours to laptop-…	known-unknowns/graphs-games-automata/subtraction-game-max-period-terms.md	Subtraction games: longest eventual period for largest move n (OEIS A389689 at n = 25 and from n = 30, A389690 beyond n = 22)
super-edge-magic-trees-beyond-17	Graphs, games and automata	harvest	laptop-hours	known-unknowns/graphs-games-automata/super-edge-magic-trees-beyond-17.md	Super edge-magic tree conjecture (Enomoto-Llado-Nakamigawa-Ringel): extend the verification past 17 vertices, or a tree that is not super edge-magic
tdc-drugcomb-synergy-four-endpoints	Disease research	harvest	laptop-hours	known-unknowns/disease-research/tdc-drugcomb-synergy-four-endpoints.md	TDC DrugComb HSA/Loewe/Bliss/ZIP: lower the leaderboard MAE on a cancer drug-synergy endpoint
tdc-drugcomb-css-mae	Disease research	harvest	laptop-hours	known-unknowns/disease-research/tdc-drugcomb-css-mae.md	TDC DrugComb_CSS: lower the leaderboard MAE for drug-combination sensitivity in cancer cell lines
tser-beat-reference-30-resample-best-rmse	Machine learning	harvest	laptop-hours	known-unknowns/machine-learning/tser-beat-reference-30-resample-best-rmse.md	Time series extrinsic regression (TSER archive): beat the best reference regressor's 30-resample mean RMSE on a dataset
tiny-tag-busy-beaver-exact	Graphs, games and automata	harvest	laptop-minutes to lapto…	known-unknowns/graphs-games-automata/tiny-tag-busy-beaver-exact.md	Tiny Tag busy beaver: the first exact value beyond n = 10 (all 2,048 length-11 strings classified)
tsasm-a005164-order-51-exact	Recreational math	standard	laptop-hours	known-unknowns/recreational-math/tsasm-a005164-order-51-exact.md	Totally symmetric alternating sign matrices: a rigorous count A005164(25) (order 51), and an exact-enumeration check of the terms that rest on a conjectured formula
schutte-multiple-tournament-dice-bounds	Graphs, games and automata	harvest	laptop-hours to laptop-…	known-unknowns/graphs-games-automata/schutte-multiple-tournament-dice-bounds.md	Unfair dice games: improve a small Schütte multiple-tournament construction bound
pg2q-nr-arcs-ball-braun-tables	Record tables	harvest	laptop-hours	known-unknowns/record-tables/pg2q-nr-arcs-ball-braun-tables.md	(n,r)-arcs in PG(2,q), 11 <= q <= 31: raise a lower bound on m_r(2,q) in Ball's table or Braun's q = 23..31 table
three-player-jamfold-sng-epsilon	Graphs, games and automata	standard	laptop-hours to laptop-…	known-unknowns/graphs-games-automata/three-player-jamfold-sng-epsilon.md	3-handed no-limit hold'em jam/fold sit-and-go endgame (Ganzfried-Sandholm): a certified epsilon-equilibrium well below $0.0488
adderboard-smallest-adder-transformer	Algorithms	harvest	laptop-hours	known-unknowns/algorithms/adderboard-smallest-adder-transformer.md	AdderBoard: smallest transformer (fewest unique parameters) adding two 10-digit numbers
amr-patric-folds-beat-published-f1	Disease research	harvest	laptop-hours	known-unknowns/disease-research/amr-patric-folds-beat-published-f1.md	AMR genotype-to-phenotype: beat the published benchmark F1 on the frozen PATRIC species-antibiotic folds
anagol-per-language-shortest	Compression and code golf	harvest	laptop-minutes	known-unknowns/compression-and-golf/anagol-per-language-shortest.md	Anarchy Golf: a strictly shorter solution than the best-ranked one in some language on a post-mortem problem
arch-comp-ainncs-docking-full-initial-set	ML robustness	standard	laptop-hours	known-unknowns/ml-robustness/arch-comp-ainncs-docking-full-initial-set.md	ARCH-COMP AINNCS 2D Spacecraft Docking: verify or falsify the neural controller on the full initial set (unsolved since ARCH-COMP22)
go3-event4-synthetic-best-scores	Optimization benchmarks	harvest	laptop-hours	known-unknowns/optimization-benchmarks/go3-event4-synthetic-best-scores.md	ARPA-E GO Competition Challenge 3 (multi-period AC unit commitment): beat the best Event 4 score on a public synthetic scenario
atom3d-rsr-rna-model-ranking	Biology	standard	laptop-hours	known-unknowns/biology/atom3d-rsr-rna-model-ranking.md	ATOM3D RSR: beat the published Spearman for ranking RNA structural models by RMSD
bamboo-slip-rejoining-wisepanda	Ancient texts and fragments	harvest	laptop-hours	known-unknowns/ancient-texts/bamboo-slip-rejoining-wisepanda.md	Bamboo-slip fragment rejoining: beat WisePanda's Top-10 and Top-50 on the released Bamboo1350 fracture-curve benchmark without using real pairs
beacon-rna-benchmark-unsaturated-tasks	Biology	harvest	laptop-hours	known-unknowns/biology/beacon-rna-benchmark-unsaturated-tasks.md	BEACON RNA benchmark: beat the best listed score on an unsaturated task (CRISPR off-target, structure-score imputation, splice sites, APA, RNA switches)
beans-animal-datasets-per-task-best	Ecology and bioacoustics	harvest	laptop-hours to laptop-…	known-unknowns/ecology/beans-animal-datasets-per-task-best.md	BEANS animal-sound benchmark: beat the best published test score on one of seven freely downloadable animal classification or detection datasets
bhh-tsp-constant-c12-bounds	Erdős problems and proofs	standard	laptop-hours to laptop-…	known-unknowns/erdos-and-proofs/bhh-tsp-constant-c12-bounds.md	Beardwood-Halton-Hammersley TSP constant (C_12): a certified bound beating 0.6421 <= beta_2 <= 0.861715646305
bernstein-constant-digits	Number hunts	standard	laptop-days	known-unknowns/number-hunts/bernstein-constant-digits.md	Bernstein's constant beta = lim 2n E_2n(|x|): more than the 50 decimals of Varga and Carpenter (1985)
bilateral-trade-best-offer-vs-second-best	Graphs, games and automata	standard	laptop-hours	known-unknowns/graphs-games-automata/bilateral-trade-best-offer-vs-second-best.md	Bilateral trade: an instance where the better of seller-offering and buyer-offering earns less than 3/4 of second-best gains from trade (open gap [1/2, 3/4], Babaioff-Dobzinski-Ku…
codetables-binary-linear	Record tables	harvest	laptop-hours	known-unknowns/record-tables/codetables-binary-linear.md	Binary (or small-q) linear codes beating codetables.de lower bounds
single-transposition-codes-length-12	Record tables	harvest	laptop-hours to laptop-…	known-unknowns/record-tables/single-transposition-codes-length-12.md	Binary codes correcting one adjacent transposition at length 12: first unknown terms of OEIS A057608 and A057657 (Sloane's 1tc/1et graphs)
constant-weight-codes	Record tables	harvest	laptop-hours	known-unknowns/record-tables/constant-weight-codes.md	Binary constant-weight codes A(n,d,w): new lower bounds in Brouwer's table
binary-minimal-code-length-records	Record tables	harvest	laptop-hours to laptop-…	known-unknowns/record-tables/binary-minimal-code-length-records.md	Binary minimal codes for secret sharing: shorten the dimension 10–13 records
binary-polynomial-multiplication-gates	Algorithms	harvest	laptop-hours	known-unknowns/algorithms/binary-polynomial-multiplication-gates.md	Binary polynomial multiplication M(n): fewer AND/XOR gates than the best known circuit for n-term polynomials over GF(2)
bivariate-bicycle-exact-distance-360-756	Physics	standard	laptop-days	known-unknowns/physics/bivariate-bicycle-exact-distance-360-756.md	Bivariate bicycle codes: prove the exact distance of IBM's [[360,12,<=24]] or [[756,16,<=34]] code (only upper bounds are published)
bohr-radius-bidisc-k2-bounds	Erdős problems and proofs	standard	laptop-hours	known-unknowns/erdos-and-proofs/bohr-radius-bidisc-k2-bounds.md	Bohr radius of the bidisc K_2 (C_59): an explicit Schur function beating the 0.302825279492 upper bound, or a certified lower bound above Knese's 0.3006
book-ramsey-small-off-diagonal	Record tables	harvest	laptop-hours	known-unknowns/record-tables/book-ramsey-small-off-diagonal.md	Book Ramsey numbers off the n-1,n diagonal: close a gap in DS1 Table IXa (R(B4,B7) 22-23, R(B4,B9) 27-28, R(B5,B9) 28-30, R(B7,B11) 37-38) or a lower-only cell of Table VII (books…
brainfuck-constants-shorter	Compression and code golf	harvest	laptop-hours	known-unknowns/compression-and-golf/brainfuck-constants-shorter.md	Brainfuck constants: a shorter BF program producing a constant than the esolangs table
brownian-motion-project-sorries	Formal proofs	harvest	laptop-hours	known-unknowns/formal-proofs/brownian-motion-project-sorries.md	Brownian Motion Lean project: close an unclaimed sorry (uniform integrability of stopped submartingales, UI martingale convergence, reflection principle)
burnt-pancake-even-n-exact-flips	Biology	standard	laptop-hours	known-unknowns/biology/burnt-pancake-even-n-exact-flips.md	Burnt pancake sorting: settle T(n) for an even n by finding a flipping sequence that attains the lower bound
reversible-tm-busy-beaver-bbrev6	Graphs, games and automata	harvest	laptop-hours	known-unknowns/graphs-games-automata/reversible-tm-busy-beaver-bbrev6.md	Busy Beaver for reversible Turing machines: decide BBrev(6)'s 388 holdouts or beat the 537,556-step champion
ski-calculus-busy-beaver-small	Graphs, games and automata	harvest	laptop-hours	known-unknowns/graphs-games-automata/ski-calculus-busy-beaver-small.md	Busy Beaver for SKI combinator calculus: beat a listed lower bound for size 7..11, or settle Xi_0(7) exactly
wang-tiles-busy-beaver-bbwt	Graphs, games and automata	harvest	laptop-hours	known-unknowns/graphs-games-automata/wang-tiles-busy-beaver-bbwt.md	Busy Beaver for Wang tiles: exact BBWT(5), or n Wang tiles that tile a larger largest square than the n = 5..10 records
cami2-taxonomic-binning-species-f1	Genomes	standard	laptop-days	known-unknowns/genomics/cami2-taxonomic-binning-species-f1.md	CAMI II taxonomic binning of reads at species rank: beat ganon2's per-bin F1 on the plant-associated samples without losing accuracy
cami2-taxonomic-profiling-species-f1	Genomes	harvest	laptop-days	known-unknowns/genomics/cami2-taxonomic-profiling-species-f1.md	CAMI II taxonomic profiling at species rank: beat ganon2's F1 on the plant-associated samples in the CAMI Benchmarking Portal
card-guessing-yes-no-feedback-exact	Graphs, games and automata	harvest	laptop-hours to laptop-…	known-unknowns/graphs-games-automata/card-guessing-yes-no-feedback-exact.md	Card guessing with yes/no feedback: exact optimal expected scores for two-copy decks beyond n = 10
cath42-inverse-folding-recovery-record	Biology	harvest	laptop-hours to laptop-…	known-unknowns/biology/cath42-inverse-folding-recovery-record.md	CATH 4.2 inverse folding: beat the best published sequence recovery (0.63, Refold) on the standard test split
chaocipher-single-message-and-extended-kpa	Unbroken ciphers	harvest	laptop-hours	known-unknowns/unbroken-ciphers/chaocipher-single-message-and-extended-kpa.md	Chaocipher: break a single ciphertext-only message, and known-plaintext attack on the Extended variant (open per the Chaocipher Clearing House)
circulant-weighing-matrices-open	Record tables	harvest	laptop-hours	known-unknowns/record-tables/circulant-weighing-matrices-open.md	Circulant weighing matrices: settle an 'Open' CW(n,k) in Gordon's La Jolla repository
climatebench-total-nrmse-cpu	Earth and sky	harvest	laptop-hours	known-unknowns/earth-and-sky/climatebench-total-nrmse-cpu.md	ClimateBench: beat the best published total NRMSE for climate-model emulation on the SSP2-4.5 test scenario, on CPU
h3-collinear-benchmark-pec-ecg-energies	Physics	harvest	laptop-days	known-unknowns/physics/h3-collinear-benchmark-pec-ecg-energies.md	Collinear H3 benchmark potential energy curve: a lower variational Born-Oppenheimer energy than Ferenc and Matyus (2022) at the van der Waals minimum or at any of their 114 tabula…
condorcet-domains	Record tables	harvest	laptop-hours	known-unknowns/record-tables/condorcet-domains.md	Condorcet domains: a larger domain than the best published one for some n in 9..25
connect-four-w-plus-h-17	Graphs, games and automata	harvest	laptop-days	known-unknowns/graphs-games-automata/connect-four-w-plus-h-17.md	Connect Four on a board with width + height = 17 (9x8, 10x7, 11x6, 12x5, 13x4): the first unsolved sizes
connected-still-life-max-population	Graphs, games and automata	harvest	laptop-hours	known-unknowns/graphs-games-automata/connected-still-life-max-population.md	Connected maximum-density still lifes: close a gap in Mahajan's n = 26..50 table (OEIS A398723), starting with 349 <= a(26) <= 352
constant-dimension-subspace-codes-table	Record tables	harvest	laptop-hours	known-unknowns/record-tables/constant-dimension-subspace-codes-table.md	Constant dimension subspace codes A_q(n,d;k): beat a best known lower bound in the Bayreuth subspace code tables (q = 2..9, n <= 19)
overlapping-hyperspheres-percolation-d6-11	Physics	harvest	laptop-days	known-unknowns/physics/overlapping-hyperspheres-percolation-d6-11.md	Continuum percolation of overlapping hyperspheres in d = 6-11: beat the Torquato-Jiao (2012) thresholds, still the most precise published values
covering-codes-q2-q4-upper-bounds	Record tables	harvest	laptop-hours to laptop-…	known-unknowns/record-tables/covering-codes-q2-q4-upper-bounds.md	Covering codes K_q(n,R) for q = 2, 3, 4 (hypercube domination, football pool): beat an upper bound in Kéri's tables
covering-designs-record	Record tables	harvest	laptop-hours	known-unknowns/record-tables/covering-designs-record.md	Covering designs C(v,k,t): beat a repository entry
cram-open-nimbers	Graphs, games and automata	harvest	laptop-hours to laptop-…	known-unknowns/graphs-games-automata/cram-open-nimbers.md	Cram: compute a missing nimber in Beling's normal-play table (5x13, 6x11, 7x10, ...) or a missing misère value (5x8, 5x9, 6x7, 6x8, 6x9)
hypercube-crossing-number-drawings	Graphs, games and automata	harvest	laptop-hours	known-unknowns/graphs-games-automata/hypercube-crossing-number-drawings.md	Crossing number of the hypercube Q_n: a drawing with fewer crossings than Yang-Wang-Wang-Zhou's records (n = 5..13), or a certified lower bound for cr(Q_5)
cuneiform-language-identification-cli2019	Ancient texts and fragments	harvest	laptop-hours	known-unknowns/ancient-texts/cuneiform-language-identification-cli2019.md	Cuneiform language and dialect identification (VarDial 2019 CLI): beat NRC-CNRC's macro-F1 0.7695 on the released test set, closed track
ebl-unidentified-fragment-overlaps	Ancient texts and fragments	harvest	laptop-hours	known-unknowns/ancient-texts/ebl-unidentified-fragment-overlaps.md	Cuneiform: fragment-to-fragment overlaps among UNIDENTIFIED eBL fragments (new witnesses of unknown compositions, 'indirect joins')
ebl-fragment-identification	Undeciphered scripts	harvest	laptop-hours	known-unknowns/undeciphered-scripts/ebl-fragment-identification.md	Cuneiform: identify unplaced transliterated fragments as witnesses of known compositions (electronic Babylonian Library)
manypoints-curves-finite-fields-lower-bounds	Number hunts	harvest	laptop-hours	known-unknowns/number-hunts/manypoints-curves-finite-fields-lower-bounds.md	Curves over finite fields with many points: raise a lower bound on manYPoints
deepsomatic-hcc1395-chr1-heldout-f1	Genomes	harvest	laptop-hours per cell	known-unknowns/genomics/deepsomatic-hcc1395-chr1-heldout-f1.md	DeepSomatic on held-out HCC1395 chr1: beat DeepSomatic 1.10's somatic F1, especially ONT (SNV 0.858, indel 0.737) and tumor-only modes
degree-diameter-planar-table	Record tables	harvest	laptop-hours	known-unknowns/record-tables/degree-diameter-planar-table.md	Degree-diameter problem for planar graphs: a larger planar graph than the Combinatorics Wiki table
dengue-2015-open-challenge-beat-published-skill	Disease research	harvest	laptop-hours	known-unknowns/disease-research/dengue-2015-open-challenge-beat-published-skill.md	Dengue Forecasting Project (San Juan and Iquitos): beat the published forecast skill on the frozen 2015 challenge targets
designs-in-classical-polar-spaces	Record tables	harvest	laptop-hours	known-unknowns/record-tables/designs-in-classical-polar-spaces.md	Designs in finite classical polar spaces: a new realizable 2-(r,k,lambda)_Q design (or the first one in a Hermitian polar space)
dimer-constant-cubic-lattice-rigorous-bounds	Physics	standard	laptop-days	known-unknowns/physics/dimer-constant-cubic-lattice-rigorous-bounds.md	Dimer constant of the cubic lattice Z^3: a certified upper bound below He's 0.452130 (2026) or a lower bound above Csikvari's 0.441075
golomb-square-grid-distinct-distances	Record tables	harvest	laptop-hours	known-unknowns/record-tables/golomb-square-grid-distinct-distances.md	Distinct distances in a lattice square (Erdős-Guy 'Golomb square'): n points with all distances distinct in a smaller k x k grid than known, n = 15..26
dominant-transversal-order-3-mod-4	Record tables	standard	laptop-hours	known-unknowns/record-tables/dominant-transversal-order-3-mod-4.md	Dominant transversals: a Latin square of order 11 (or 15, 19, ...) with a transversal that meets every other transversal (Ghafari-Wanless Question 1)
dreval-cross-study-ctrpv2-to-gdsc2	Disease research	harvest	laptop-hours	known-unknowns/disease-research/dreval-cross-study-ctrpv2-to-gdsc2.md	DrEval cross-study generalisation: beat the public best CTRPv2-to-GDSC2 (and CCLE/GDSC1/CTRPv1) transfer numbers
dreval-lco-ctrpv2-normalized-r2	Disease research	harvest	laptop-hours	known-unknowns/disease-research/dreval-lco-ctrpv2-normalized-r2.md	DrEval leave-cell-line-out: beat the public best normalized R^2 / Pearson for cancer drug-response prediction on CTRPv2
dreval-ldo-beat-naive-mean-effects	Disease research	harvest	laptop-hours	known-unknowns/disease-research/dreval-ldo-beat-naive-mean-effects.md	DrEval leave-drug-out: the open question of beating the naive mean-effects baseline for unseen cancer drugs
driams-maldi-amr-beat-published-auroc	Disease research	harvest	laptop-hours	known-unknowns/disease-research/driams-maldi-amr-beat-published-auroc.md	DRIAMS MALDI-TOF resistance prediction: beat the published per-species-drug AUROC on the public spectra
eca-rule30-rule110-cyclic-max-period	Graphs, games and automata	harvest	laptop-days	known-unknowns/graphs-games-automata/eca-rule30-rule110-cyclic-max-period.md	Elementary CA on rings: the maximum cycle length of Rule 30 (A334497) and Rule 110 (A204371) on a cyclic width of 37
codetables-eaqecc-qubit-gaps	Record tables	harvest	laptop-hours	known-unknowns/record-tables/codetables-eaqecc-qubit-gaps.md	Entanglement-assisted qubit codes [[n,k,d;c]]: raise a lower bound in Grassl's EAQECC table
erdos-1055-erdos-selfridge-class-a20	Erdős problems and proofs	harvest	laptop-days	known-unknowns/erdos-and-proofs/erdos-1055-erdos-selfridge-class-a20.md	Erdos #1055 (Erdos-Selfridge prime classes): determine a(20) of OEIS A005113, or find a class-20 prime below 764276710625653
erdos-1204-narrow-admissible-tuples	Erdős problems and proofs	harvest	laptop-hours to laptop-…	known-unknowns/erdos-and-proofs/erdos-1204-narrow-admissible-tuples.md	Erdos #1204 (Elliott): a narrower admissible k-tuple than Sutherland's table for some 343 <= k <= 5000, or exact minimal sums B(k) beyond k = 147
erdos-583-gallai-path-decomposition	Erdős problems and proofs	standard	laptop-days	known-unknowns/erdos-and-proofs/erdos-583-gallai-path-decomposition.md	Erdos #583 (Gallai path decomposition): a connected graph needing more than ceil(n/2) paths, or the exhaustive n = 12 check
erdos-628-double-critical-order-14	Erdős problems and proofs	harvest	laptop-days for order 1…	known-unknowns/erdos-and-proofs/erdos-628-double-critical-order-14.md	Erdos #628 (Erdos-Lovasz Tihany, a = 2 branch): a noncomplete double-critical graph, or the order-14 census
erdos757-sidon-in-45-sets	Record tables	harvest	laptop-hours	known-unknowns/record-tables/erdos757-sidon-in-45-sets.md	Erdos #757: (4,5)-set with Sidon density below 4/7
erdos-1023-union-free-n8	Erdős problems and proofs	standard	laptop-hours	known-unknowns/erdos-and-proofs/erdos-1023-union-free-n8.md	Erdős #1023 small cases: 80 subsets of an 8-set with no member a union of others (OEIS A347025; best known 79, upper bound 89)
erdos-302-unit-fraction-free-upper-constant	Erdős problems and proofs	standard	laptop-hours	known-unknowns/erdos-and-proofs/erdos-302-unit-fraction-free-upper-constant.md	Erdős #302: a certified upper constant below 0.84617 for the largest set in [1,N] with no 1/a = 1/b + 1/c
erdos-703-forbidden-intersection-row9	Erdős problems and proofs	harvest	laptop-days	known-unknowns/erdos-and-proofs/erdos-703-forbidden-intersection-row9.md	Erdős #703 small cases: T(9,2) and T(9,3), the largest family of subsets of a 9-set with no two members meeting in exactly 2 (or 3) elements (OEIS A390645 row 9)
erdos-discrepancy-c3-longest-sequence	Erdős problems and proofs	standard	laptop-hours	known-unknowns/erdos-and-proofs/erdos-discrepancy-c3-longest-sequence.md	Erdős discrepancy, C = 3: a +-1 sequence longer than 130,000 with discrepancy at most 3
distinct-subset-sums-small-n	Record tables	harvest	laptop-hours	known-unknowns/record-tables/distinct-subset-sums-small-n.md	Erdős distinct subset sums: an n-element set with distinct subset sums and smaller maximum than the best known
egz-constant-even-nonpower2-exponent	Number hunts	harvest	laptop-hours	known-unknowns/number-hunts/egz-constant-even-nonpower2-exponent.md	Erdős–Ginzburg–Ziv constants s(C_n^r) for even n that is not a power of two: beat s(C_6^4) >= 85, s(C_6^5) >= 177, s(C_10^4) >= 153 or s(C_6^3) >= 41
eterna100-v2-vienna2-algorithmic-solve	Biology	harvest	laptop-hours	known-unknowns/biology/eterna100-v2-vienna2-algorithmic-solve.md	Eterna100-V2 under ViennaRNA 2: an automated RNA design algorithm that solves a puzzle no benchmarked algorithm has solved
covid19-hub-europe-archive-beat-eurocovidhub-ensemble	Disease research	harvest	laptop-hours	known-unknowns/disease-research/covid19-hub-europe-archive-beat-eurocovidhub-ensemble.md	European COVID-19 Forecast Hub archive: beat EuroCOVIDhub-ensemble's WIS on the hub's own published scores
respicast-ili-ari-europe-beat-hub-ensemble	Disease research	harvest	laptop-hours	known-unknowns/disease-research/respicast-ili-ari-europe-beat-hub-ensemble.md	European RespiCast hub: beat the hub ensemble's WIS for influenza-like illness or acute respiratory infection incidence across EU/EEA countries
fmm-catalogue-small-format-rank	Algorithms	harvest	laptop-hours	known-unknowns/algorithms/fmm-catalogue-small-format-rank.md	Fast matrix multiplication: beat a best-known rank in the Lille FMM catalogue for a small format
fmm-ternary-integer-ring-upgrade	Algorithms	harvest	laptop-hours	known-unknowns/algorithms/fmm-ternary-integer-ring-upgrade.md	Fast matrix multiplication: best-known rank with ternary/integer coefficients where only rational or complex schemes are known
fmm-additive-complexity-records	Algorithms	harvest	laptop-hours	known-unknowns/algorithms/fmm-additive-complexity-records.md	Fast matrix multiplication: fewer additions for a fixed best-known rank (straight-line program records)
fev-bench-beat-best-task-sql	Machine learning	harvest	laptop-hours	known-unknowns/machine-learning/fev-bench-beat-best-task-sql.md	fev-bench forecasting: beat the best posted scaled quantile loss on a task with locally run open-weight models
rectangular-box-sudoku-min-clue-records	Recreational math	harvest	laptop-hours	known-unknowns/recreational-math/rectangular-box-sudoku-min-clue-records.md	Fewest clues for Sudoku with other box shapes: beat ton's records (10x10 2x5: 22, 12x12 2x6: 32, 12x12 3x4: 30, 15x15 3x5: 48, 20x20 4x5: 88, 25x25 5x5: 146)
fewest-squares-rectangle-scaling-counterexample	Recreational math	standard	laptop-days	known-unknowns/recreational-math/fewest-squares-rectangle-scaling-counterexample.md	Fewest squares tiling a rectangle: a counterexample to h(dn,dm) = h(n,m) beyond the 388 x 388 table, or new exact rows of OEIS A219158
latin-min-transversals-odd-orders	Record tables	harvest	laptop-hours	known-unknowns/record-tables/latin-min-transversals-odd-orders.md	Fewest transversals in a Latin square of odd order: beat 778 (n=11), 11744 (n=13), 165289 (n=15) or a larger-order record (OEIS A091323)
finite-lattices-next-terms	Wildcard	harvest	laptop-days	known-unknowns/wildcard/finite-lattices-next-terms.md	Finite lattices: the next count of unlabeled lattices (A006966, n = 21), semimodular (A229202, n = 26), modular (A006981, n = 36) or distributive lattices (A006982, n = 61)
star-discrepancy-finite-point-sets-2d-3d	Record tables	harvest	laptop-hours	known-unknowns/record-tables/star-discrepancy-finite-point-sets-2d-3d.md	Finite point sets with record-low L-infinity star discrepancy in [0,1]^2 (n = 22..1020) or [0,1]^3 (n = 9..5000)
archive-mr-mass-planet-first-dynamical-mass	Sky archives	harvest	laptop-hours	known-unknowns/sky-archives/archive-mr-mass-planet-first-dynamical-mass.md	First measured mass (TTV or RV, public data only) for a transiting planet whose NASA Exoplanet Archive mass still comes from a mass-radius relation
hgca-rv-true-mass-unmeasured-companion	Sky archives	harvest	laptop-hours	known-unknowns/sky-archives/hgca-rv-true-mass-unmeasured-companion.md	First true (dynamical) mass for an RV-detected companion from Hipparcos-Gaia accelerations plus public radial velocities
fisbe-flylight-neuron-instance-segmentation	Neuroscience	standard	laptop-days	known-unknowns/neuroscience/fisbe-flylight-neuron-instance-segmentation.md	FISBe (FlyLight) 3D neuron instance segmentation: beat PatchPerPix's benchmark score S = 0.35 on the combined test set
flab-antibody-developability-zero-shot	Biology	standard	laptop-hours	known-unknowns/biology/flab-antibody-developability-zero-shot.md	FLAb antibody developability: beat the released zero-shot scores on a therapeutic-property category
flip-gb1-plmfit-scoreboard-spearman	Biology	harvest	laptop-hours	known-unknowns/biology/flip-gb1-plmfit-scoreboard-spearman.md	FLIP GB1 fitness landscape: beat the PLMFit scoreboard Spearman on the one-vs-rest or three-vs-rest split
fc-textbook-category-sorries	Formal proofs	harvest	laptop-hours	known-unknowns/formal-proofs/fc-textbook-category-sorries.md	Formal Conjectures `textbook` sorries: formalise a known textbook-level result
freek-100-isabelle-hol-light-rocq-metamath-gaps	Formal proofs	harvest	pure thought plus lapto…	known-unknowns/formal-proofs/freek-100-isabelle-hol-light-rocq-metamath-gaps.md	Freek Wiedijk's 100 theorems: fill a gap in Isabelle, HOL Light, Rocq, Metamath or Mizar (Lean is complete)
catagolue-glider-synthesis-cost-records	Graphs, games and automata	harvest	laptop-hours	known-unknowns/graphs-games-automata/catagolue-glider-synthesis-cost-records.md	Game of Life: a cheaper glider synthesis than Catagolue's best-known cost for a still life or oscillator
game-of-sloanes-complex-line-packings	Physics	harvest	laptop-hours	known-unknowns/physics/game-of-sloanes-complex-line-packings.md	Game of Sloanes: a packing of n lines in C^d (d = 3..7) with lower coherence than the live leaderboard
llrl-ant-minimal-seed	Graphs, games and automata	standard	laptop-hours to laptop-…	known-unknowns/graphs-games-automata/llrl-ant-minimal-seed.md	Generalised ant LLRL: the least onset of the period-384 highway g(k) from starts with at most k non-zero cells, k = 0..K0, with proof of minimality
genomic-benchmarks-gresova-hard-datasets-accuracy	Biology	harvest	laptop-hours	known-unknowns/biology/genomic-benchmarks-gresova-hard-datasets-accuracy.md	Genomic Benchmarks (Gresova et al.): beat the best published test accuracy on Human Enhancers Cohn, Human OCR Ensembl or Drosophila Enhancers Stark
german-hospitalization-nowcast-hub-beat-ensemble-wis	Disease research	harvest	laptop-hours	known-unknowns/disease-research/german-hospitalization-nowcast-hub-beat-ensemble-wis.md	German COVID-19 hospitalization nowcast hub: beat the hub ensemble's WIS on the published real-time nowcasts
gilbreath-conjecture-verification-beyond-1-5e15	Number hunts	standard	laptop-days	known-unknowns/number-hunts/gilbreath-conjecture-verification-beyond-1-5e15.md	Gilbreath's conjecture: extend the verification beyond Colonna's x = 1.5 x 10^15 (2026)
windmill-kn2-harmonious-graham-sloane	Graphs, games and automata	standard	laptop-hours	known-unknowns/graphs-games-automata/windmill-kn2-harmonious-graham-sloane.md	Graham-Sloane windmill conjecture: is K_8^(2) (two K_8 sharing a vertex) harmonious? (first open case of 'K_n^(2) harmonious iff n = 4')
cohn-grassmannian-packings-table	Packings and physics	harvest	laptop-hours	known-unknowns/packings-physics/cohn-grassmannian-packings-table.md	Grassmannian packings: N subspaces of R^m (m <= 16) with larger minimal squared chordal distance than Cohn's table
gravity-spy-v1-official-split-accuracy	Earth and sky	standard	laptop-hours	known-unknowns/earth-and-sky/gravity-spy-v1-official-split-accuracy.md	Gravity Spy v1.0 LIGO glitch classification: beat the best published test accuracy on the official 22-class split
greenberg-p3-real-quadratic-beyond-1e5	Number hunts	harvest	laptop-days	known-unknowns/number-hunts/greenberg-p3-real-quadratic-beyond-1e5.md	Greenberg's conjecture for p = 3: extend the Mercuri-Paoluzi-Schoof verification for real quadratic fields beyond discriminant 100,000
potts-antiferromagnet-colouring-entropy-bounds	Physics	standard	laptop-days	known-unknowns/physics/potts-antiferromagnet-colouring-entropy-bounds.md	Ground-state entropy of Potts antiferromagnets (proper colourings): tighten the certified bounds of Lundow and Markstrom (2008) for 4- and 5-colourings of the square grid or 3- an…
gset-max-k-cut-records	Optimization benchmarks	harvest	laptop-hours to laptop-…	known-unknowns/optimization-benchmarks/gset-max-k-cut-records.md	Gset Max-k-Cut (k = 3, 4): a better k-partition than the best published for a Gset graph
metagenomics-nonneoplastic-disease-classification	Disease research	harvest	laptop-hours	known-unknowns/disease-research/metagenomics-nonneoplastic-disease-classification.md	Gut-microbiome disease classification: beat the published cross-validated AUC on public non-cancer disease cohorts
guts-weenie-rule-strong-equilibrium	Graphs, games and automata	standard	laptop-hours to laptop-…	known-unknowns/graphs-games-automata/guts-weenie-rule-strong-equilibrium.md	Guts with the Weenie rule: does the symmetric threshold resist every coalition for n >= 4?
ghr-sum-difference-c3a	Erdős problems and proofs	harvest	laptop-hours	known-unknowns/erdos-and-proofs/ghr-sum-difference-c3a.md	Gyarmati-Hennecart-Ruzsa sum-difference constant C_3a: beat 1.19519192 (finite-certified record 1.19102809)
hadamard-maxdet-records	Record tables	harvest	laptop-hours	known-unknowns/record-tables/hadamard-maxdet-records.md	Hadamard maximal determinant: new record determinants for orders n not divisible by 4
hard-core-entropy-square-honeycomb-digits	Physics	harvest	laptop-hours	known-unknowns/physics/hard-core-entropy-square-honeycomb-digits.md	Hard-core lattice gas at unit activity: more correct digits of the hard-square entropy constant (OEIS A085850) or the honeycomb constant than Baxter's corner-transfer-matrix values
cohn-harmonic-energy-spheres-dim4-32	Packings and physics	harvest	laptop-hours	known-unknowns/packings-physics/cohn-harmonic-energy-spheres-dim4-32.md	Harmonic energy on spheres in 4 to 32 dimensions: lower the best known energy in the Ballinger-Blekherman-Cohn-Giansiracusa-Kelly-Schurmann table
hest-bench-cancer-expression-from-morphology	Disease research	harvest	laptop-hours	known-unknowns/disease-research/hest-bench-cancer-expression-from-morphology.md	HEST-Benchmark: beat the best published Pearson for predicting spatial gene expression from tumour histology
chime-frb-cat2-hidden-repeater	Sky archives	harvest	laptop-hours	known-unknowns/sky-archives/chime-frb-cat2-hidden-repeater.md	Hidden repeating FRB source among apparently one-off bursts in CHIME/FRB Catalog 2
dujella-torsion-rank-records-quadratic-fields	Number hunts	harvest	laptop-hours	known-unknowns/number-hunts/dujella-torsion-rank-records-quadratic-fields.md	High-rank elliptic curves with prescribed torsion over quadratic fields: beat or certify a cell
limit-tori-3d-polynomial-hilbert-numbers	Wildcard	harvest	laptop-hours	known-unknowns/wildcard/limit-tori-3d-polynomial-hilbert-numbers.md	Hilbert's 16th problem for invariant tori in 3D: more normally hyperbolic limit tori than N_h(2) >= 3, N_h(3) >= 5, N_h(4) >= 7, N_h(5) >= 13
iea37-cs1-circular-wind-farm-layout	Engineering and chips	harvest	laptop-hours	known-unknowns/engineering/iea37-cs1-circular-wind-farm-layout.md	IEA Wind Task 37 case study 1: a feasible 16-, 36- or 64-turbine circular-farm layout with higher AEP than every published or posted layout
ieantn-awaiting-solution-nodes	Formal proofs	harvest	laptop-hours	known-unknowns/formal-proofs/ieantn-awaiting-solution-nodes.md	IEANTN (explicit analytic number theory network): a Comparator-verified solution for an unclaimed node (e.g. the cotangent zeta-value expansion)
ihtp-ihtc2024-hidden-m-instances-upper-bounds	Optimization benchmarks	harvest	laptop-hours	known-unknowns/optimization-benchmarks/ihtp-ihtc2024-hidden-m-instances-upper-bounds.md	IHTC-2024 competition (m01-m30) instances: lower a best known integrated surgery-admission-nurse schedule cost below the post-competition table
induced-forest-planar-ratio-25-52	Graphs, games and automata	standard	laptop-hours for gadget…	known-unknowns/graphs-games-automata/induced-forest-planar-ratio-25-52.md	Induced forests in planar graphs after the Albertson-Berman refutation: a planar graph with largest induced forest below 25/52 of its vertices
indus-temporal-heldout-structure	Undeciphered scripts	harvest	laptop-hours	known-unknowns/undeciphered-scripts/indus-temporal-heldout-structure.md	Indus script: structural model trained on the 1977 corpus that predicts later-excavated inscriptions
khipu-heldout-cord-value-prediction	Undeciphered scripts	harvest	laptop-hours	known-unknowns/undeciphered-scripts/khipu-heldout-cord-value-prediction.md	Inka khipus: frozen structural model that predicts masked cord values on khipus outside khipu.db (Open Khipu Repository)
integer-chebyshev-constant-unit-interval	Number hunts	standard	laptop-hours	known-unknowns/number-hunts/integer-chebyshev-constant-unit-interval.md	Integer Chebyshev constant of [0,1]: a certified bound beating Niedbala Giraudin's 2026 bracket 0.422228600019 <= t_Z([0,1]) <= 0.422684697505
ihtp-ihtc2024-upper-bounds	Optimization benchmarks	harvest	laptop-hours	known-unknowns/optimization-benchmarks/ihtp-ihtc2024-upper-bounds.md	Integrated Healthcare Timetabling (IHTC-2024): lower the best known cost of a public (i01-i30) or competition (m01-m30) hospital instance
invrs-leaderboard-photonic-pareto	Engineering and chips	harvest	laptop-hours	known-unknowns/engineering/invrs-leaderboard-photonic-pareto.md	invrs-gym photonic inverse design: a manufacturable design beating the frozen invrs leaderboard's efficiency-vs-length-scale front
isic2018-task2-attribute-detection-jaccard	Disease research	standard	laptop-hours	known-unknowns/disease-research/isic2018-task2-attribute-detection-jaccard.md	ISIC 2018 Task 2 (dermoscopic attribute segmentation): beat the challenge-best mean Jaccard of 0.307 on the public test masks
isic2019-diagnosis-balanced-accuracy-with-unknown	Disease research	harvest	laptop-hours	known-unknowns/disease-research/isic2019-diagnosis-balanced-accuracy-with-unknown.md	ISIC 2019 skin-lesion diagnosis with an 'unknown' class: beat the best balanced accuracy (0.636; 0.607 without external data) on the public test labels
jarvis-agra-tinnet-adsorption-energy-mae	Chemistry and materials	harvest	laptop-hours	known-unknowns/chemistry-materials/jarvis-agra-tinnet-adsorption-energy-mae.md	JARVIS-Leaderboard catalysis adsorption energies (AGRA O, OH, CO, CHO, COOH and TinNet O, OH, N): beat the best listed test MAE
jarvis-supercon-tc-snumat-hse-gap-mae	Physics	harvest	laptop-hours	known-unknowns/physics/jarvis-supercon-tc-snumat-hse-gap-mae.md	JARVIS-Leaderboard frozen mid-size tasks: experimental superconducting Tc from composition (SuperCon, 16,414) or HSE06 band gap from structure (SNUMAT, 10,386): beat the best list…
jarvis-mlearn-mlff-force-mae	Physics	harvest	laptop-hours	known-unknowns/physics/jarvis-mlearn-mlff-force-mae.md	JARVIS-Leaderboard mlearn force fields (Cu, Ge, Li, Mo, Ni, Si): beat the best listed test force MAE with a model trained on a laptop
jarvis-mof-hmof-co2-qmof-bandgap-mae	Physics	harvest	laptop-hours	known-unknowns/physics/jarvis-mof-hmof-co2-qmof-bandgap-mae.md	JARVIS-Leaderboard MOF tasks: beat the best test MAE for GCMC CO2 uptake in hypothetical MOFs (0.01 and 2.5 bar) or for the PBE band gap of QMOF frameworks
jarvis-qm9-std-jctc-property-mae	Chemistry and materials	harvest	laptop-days	known-unknowns/chemistry-materials/jarvis-qm9-std-jctc-property-mae.md	JARVIS-Leaderboard QM9 (qm9_std_jctc, 130,829 molecules): beat ALIGNN's test MAE on one of 11 quantum-chemical properties (R2 excluded)
jarvis-small-data-exfoliation-tc-mae	Physics	harvest	laptop-hours	known-unknowns/physics/jarvis-small-data-exfoliation-tc-mae.md	JARVIS-Leaderboard small-data materials properties (exfoliation energy, superconducting Tc): beat the best listed test MAE
kakeya-sum-difference-c3b-c3c-entropy	Erdős problems and proofs	harvest	laptop-hours	known-unknowns/erdos-and-proofs/kakeya-sum-difference-c3b-c3c-entropy.md	Kakeya-type sum-difference constants C_3b and C_3c: beat the entropy-certificate lower bounds
kissing-number-dims-25-48	Record tables	harvest	laptop-hours	known-unknowns/record-tables/kissing-number-dims-25-48.md	Kissing number lower bounds in dimensions 25-48 (beat the max over ALL sources, not Cohn's table)
knight-covering-large-boards	Graphs, games and automata	harvest	laptop-hours	known-unknowns/graphs-games-automata/knight-covering-large-boards.md	Knight covering (domination) of the n x n board: fewer knights than Frank Rubin's records for n = 22..50
knotinfo-crosscap-number-bounds	Wildcard	harvest	laptop-hours	known-unknowns/wildcard/knotinfo-crosscap-number-bounds.md	KnotInfo crosscap numbers: a nonorientable spanning surface beating the best upper bound for an 11- or 12-crossing knot (573 intervals)
knotinfo-nakanishi-index-unknown	Wildcard	harvest	laptop-hours	known-unknowns/wildcard/knotinfo-nakanishi-index-unknown.md	KnotInfo Nakanishi index: prove the Alexander module cyclic (index 1) for one of the 229 11- and 12-crossing knots listed [1;2]
knotinfo-stick-number-bounds	Wildcard	harvest	laptop-hours	known-unknowns/wildcard/knotinfo-stick-number-bounds.md	KnotInfo stick numbers: a polygon with fewer edges than the best known for a prime knot up to 13 crossings, or a 9-stick realisation of a knot listed [9,10]
ccd-kob-andersen-crystal-ground-states	Packings and physics	standard	laptop-hours	known-unknowns/packings-physics/ccd-kob-andersen-crystal-ground-states.md	Kob-Andersen binary Lennard-Jones crystals: a periodic 80:20 structure with lower zero-pressure energy than the Cambridge Cluster Database records (-7.4903 per atom at N = 60, -7.…
kobon-triangles-open-cells	Record tables	harvest	laptop-hours	known-unknowns/record-tables/kobon-triangles-open-cells.md	Kobon triangles: more triangular faces from n straight lines than the best known, for an n where the record is below the upper bound
latin-largest-critical-sets	Record tables	harvest	laptop-hours	known-unknowns/record-tables/latin-largest-critical-sets.md	Largest critical sets lcs(n) of Latin squares: a critical set larger than the A063437 records for n = 8..17 (Bean's 2026 searches, n = 9..15 and 17)
evalatin2026-latin-dependency-parsing	Ancient texts and fragments	standard	laptop-hours	known-unknowns/ancient-texts/evalatin2026-latin-dependency-parsing.md	Latin dependency parsing (EvaLatin 2026): beat the best CLAS on Seneca's Phoenissae (74.03) and Aquinas's Summa (83.14) under the official scorer
evalatin2026-latin-ner	Ancient texts and fragments	standard	laptop-hours	known-unknowns/ancient-texts/evalatin2026-latin-ner.md	Latin named entity recognition (EvaLatin 2026, Ovid, Pliny, Tacitus): beat uOttawa's strict micro-F1 (0.908 coarse, 0.865 fine)
carmichael-least-62-prime-factors	Number hunts	standard	laptop-days	known-unknowns/number-hunts/carmichael-least-62-prime-factors.md	Least Carmichael number with exactly 62 prime factors: the next term a(62) of OEIS A006931
chess-no-promotion-diagrams-upper-bound	Recreational math	standard	laptop-hours to laptop-…	known-unknowns/recreational-math/chess-no-promotion-diagrams-upper-bound.md	Legal chess diagrams without promotion: beat Gourion's upper bound of 3.7422e37
go-legal-positions-beyond-tromp-tables	Graphs, games and automata	harvest	laptop-hours to laptop-…	known-unknowns/graphs-games-automata/go-legal-positions-beyond-tromp-tables.md	Legal Go positions: 20x20 (OEIS A094777 a(20)) and the first unknown cells of Tromp's rectangular m x n tables
levine-hat-n-player-records	Graphs, games and automata	harvest	laptop-hours to laptop-…	known-unknowns/graphs-games-automata/levine-hat-n-player-records.md	Levine's hat puzzle with 3 to 12 players: beat a best-known success probability in the Buhler et al. record table (or lower V3 <= 89/256)
leyland-smallest-unproven-prp	Number hunts	standard	laptop-days	known-unknowns/number-hunts/leyland-smallest-unproven-prp.md	Leyland primes: prove the smallest unproven Leyland PRP (x^y+y^x: 13 749 digits; x^y-y^x: 10 483 digits)
linear-a-morphology-heldout	Undeciphered scripts	harvest	laptop-hours	known-unknowns/undeciphered-scripts/linear-a-morphology-heldout.md	Linear A: pre-registered morphological alternations that predict held-out contexts
loda-oeis-shorter-or-new-programs	Compression and code golf	harvest	laptop-hours	known-unknowns/compression-and-golf/loda-oeis-shorter-or-new-programs.md	LODA: a new verified LODA program for an OEIS sequence that has none
cayley-graphs-order-144-hamiltonian	Graphs, games and automata	standard	laptop-days	known-unknowns/graphs-games-automata/cayley-graphs-order-144-hamiltonian.md	Lovász conjecture, smallest open order: is every connected Cayley graph on a group of order 144 Hamiltonian?
madry-mnist-challenge-whitebox-below-leader	ML robustness	harvest	laptop-hours	known-unknowns/ml-robustness/madry-mnist-challenge-whitebox-below-leader.md	MadryLab MNIST challenge (white-box, Linf 0.3): push the secret model's accuracy below the leaderboard's best attack
magnet-dst-private-test-rmse	Earth and sky	harvest	laptop-hours	known-unknowns/earth-and-sky/magnet-dst-private-test-rmse.md	MagNet geomagnetic-storm challenge: beat the winning RMSE for real-time Dst forecasting on the released private test set
matrix-1-to-n2-extremal-det-perm	Record tables	harvest	laptop-hours	known-unknowns/record-tables/matrix-1-to-n2-extremal-det-perm.md	Matrices filled with 1..n^2 (Pfoertner's OEIS family): beat a best-known maximal determinant or extremal permanent
womersley-maxdet-points-s2	Packings and physics	harvest	laptop-hours	known-unknowns/packings-physics/womersley-maxdet-points-s2.md	Maximum-determinant (Fekete-type interpolation) points on S^2: a larger log det than Womersley's table for some degree n <= 100
maxsat-evaluation-best-known-cost	Optimization benchmarks	harvest	laptop-hours per instan…	known-unknowns/optimization-benchmarks/maxsat-evaluation-best-known-cost.md	MaxSAT Evaluation benchmarks: beat the best known cost of an instance whose optimum is unknown
clamm2017-medieval-manuscript-dating	Ancient texts and fragments	harvest	laptop-days	known-unknowns/ancient-texts/clamm2017-medieval-manuscript-dating.md	Medieval manuscript dating (ICDAR 2017 CLaMM tasks 3 and 4): beat 59.0% and 49.9% date-class accuracy on the released test sets
medmnist-pathmnist-breastmnist-accuracy	Disease research	harvest	laptop-hours	known-unknowns/disease-research/medmnist-pathmnist-breastmnist-accuracy.md	MedMNIST v2: beat the best published accuracy/AUC on the colorectal-histology (PathMNIST) or breast-ultrasound (BreastMNIST) benchmark
metamath-pmproofs-shorter-d-proof	Compression and code golf	harvest	laptop-hours to laptop-…	known-unknowns/compression-and-golf/metamath-pmproofs-shorter-d-proof.md	Metamath pmproofs.txt: a strictly shorter condensed-detachment proof of a Principia Mathematica theorem
mfass-splice-disruption-beat-pangolin-ap	Disease research	harvest	laptop-hours	known-unknowns/disease-research/mfass-splice-disruption-beat-pangolin-ap.md	MFASS splice-disruption prediction: beat Pangolin's published average precision on the 27,733-variant functional set
minimizer-density-record-tables	Biology	harvest	laptop-hours	known-unknowns/biology/minimizer-density-record-tables.md	Minimizer schemes: beat the lowest published DNA density for a (w, k) pair in the public minimizer density tables
minimum-broadcast-graphs-23-25	Graphs, games and automata	standard	laptop-hours to laptop-…	known-unknowns/graphs-games-automata/minimum-broadcast-graphs-23-25.md	Minimum broadcast graphs on 23–25 vertices: improve the remaining edge bounds
selection-min-comparisons-n16-n17	Algorithms	harvest	laptop-hours to laptop-…	known-unknowns/algorithms/selection-min-comparisons-n16-n17.md	Minimum-comparison selection: settle V8(16) in {28, 29}, or beat the new n = 17 upper bounds (V6..V9 of 17)
seismic-missed-events-vs-comcat	Earth and sky	harvest	laptop-hours	known-unknowns/earth-and-sky/seismic-missed-events-vs-comcat.md	Missed local earthquakes in open EarthScope/IRIS waveforms, above the regional completeness magnitude, absent from USGS ComCat
brouwer-mixed-binary-ternary-codes	Record tables	harvest	laptop-hours	known-unknowns/record-tables/brouwer-mixed-binary-ternary-codes.md	Mixed binary/ternary codes N(m,n,d): new lower bound in Brouwer's mixed-code tables
mixed-dimension-subspace-codes-binary	Record tables	harvest	laptop-hours	known-unknowns/record-tables/mixed-dimension-subspace-codes-binary.md	Mixed dimension binary subspace codes A_2(n,d), n = 6..8: improve a bound in Kurz's Table 8.1 (A_2(6,3) 108-117, A_2(7,3) 614-776, A_2(8,5) 263-326, ...)
mmlib-multimode-rcpsp-ub	Optimization benchmarks	harvest	laptop-hours	known-unknowns/optimization-benchmarks/mmlib-multimode-rcpsp-ub.md	MMLIB / Boctor multi-mode resource-constrained project scheduling: shorter makespan for an open instance
mms-impossibility-small-instances	Wildcard	standard	laptop-hours	known-unknowns/wildcard/mms-impossibility-small-instances.md	MMS impossibility: an additive instance where no allocation gives every agent more than 20/21 of her maximin share (or chores above 31/30)
monomer-dimer-square-lattice-constant-digits	Physics	harvest	laptop-hours	known-unknowns/physics/monomer-dimer-square-lattice-constant-digits.md	Monomer-dimer constant of the square lattice: more than the 11-12 decimals published by Kong (2006)
latin-max-intercalates	Record tables	harvest	laptop-minutes to lapto…	known-unknowns/record-tables/latin-max-intercalates.md	Most intercalates (2x2 subsquares) in a Latin square of order n = 10..28: beat the A092237 / A307164 records
motif-scaffolding-24-task-unique-successes	Biology	harvest	needs cluster	known-unknowns/biology/motif-scaffolding-24-task-unique-successes.md	Motif scaffolding benchmark (24 tasks): more unique in-silico successes than the published best on a task
matsp-multi-activity-shift-scheduling	Optimization benchmarks	harvest	laptop-hours	known-unknowns/optimization-benchmarks/matsp-multi-activity-shift-scheduling.md	Multi-activity multi-day shift scheduling (Curtois-Qu MATSP instances 1-225): beat a best known penalty
multiperfect-new-k-perfect	Number hunts	harvest	laptop-hours	known-unknowns/number-hunts/multiperfect-new-k-perfect.md	Multiply perfect numbers: find a new 9-, 10- or 11-perfect number
muonic-molecular-ions-weakly-bound-states-energies	Physics	harvest	laptop-hours to laptop-…	known-unknowns/physics/muonic-molecular-ions-weakly-bound-states-energies.md	Muonic molecular ions dd-mu and dt-mu: a lower variational energy for the weakly bound (J,v) = (1,1) states than Frolov's 2025 values (the (2,0) states of dd-mu, dt-mu and tt-mu a…
mtc3-hutton-cipher-part-5	Unbroken ciphers	harvest	laptop-hours	known-unknowns/unbroken-ciphers/mtc3-hutton-cipher-part-5.md	MysteryTwister 'The Hutton Cipher – Part 5' (4,250-letter ciphertext-only, 0 solvers since 2023)
qrac-n-to-1-shared-randomness-optimality	Physics	standard	laptop-hours	known-unknowns/physics/qrac-n-to-1-shared-randomness-optimality.md	n-to-1 qubit random access codes with shared randomness: prove the 4-to-1 code (p = 0.741481) optimal, or beat a numerical optimum for n = 4..9
hls-multitemporal-crop-cdl-miou	Earth and sky	standard	laptop-hours	known-unknowns/earth-and-sky/hls-multitemporal-crop-cdl-miou.md	NASA/IBM HLS multi-temporal crop segmentation (US, CDL 2022): beat 55.1 mIoU (InstaGeo's fine-tuned Prithvi-EO-2.0-300M) on the official validation split
ncbi-pathogen-ast-ecoli-genotype-phenotype-f1	Disease research	harvest	laptop-hours	known-unknowns/disease-research/ncbi-pathogen-ast-ecoli-genotype-phenotype-f1.md	NCBI Pathogen Detection AST: beat the published antibiotic-specific genotype-phenotype F1 for Escherichia coli/Shigella
nceas-disdat-presence-only-sdm-auc	Ecology and bioacoustics	standard	laptop-hours	known-unknowns/ecology/nceas-disdat-presence-only-sdm-auc.md	NCEAS/disdat species distribution benchmark: beat the best published presence-absence AUC for presence-only models in six regions
catwise-cold-brown-dwarf-candidate-uncatalogued	Sky archives	harvest	laptop-hours	known-unknowns/sky-archives/catwise-cold-brown-dwarf-candidate-uncatalogued.md	New cold (late-T or Y) brown dwarf candidate with significant motion in CatWISE2020 and unTimely, absent from SIMBAD and the ultracool-dwarf compilations
tess-eb-etv-new-hierarchical-triple	Sky archives	harvest	laptop-hours	known-unknowns/sky-archives/tess-eb-etv-new-hierarchical-triple.md	New hierarchical triple from eclipse-timing variations of a TESS eclipsing binary
lunar-pit-candidate-not-in-lroc-atlas	Planets and moons	harvest	laptop-hours	known-unknowns/planetary-science/lunar-pit-candidate-not-in-lroc-atlas.md	New lunar pit (steep-walled collapse feature) in public LROC NAC images, absent from the LROC Pits Atlas
iau-mdc-new-meteor-shower-gmn	Earth and sky	harvest	laptop-hours	known-unknowns/earth-and-sky/iau-mdc-new-meteor-shower-gmn.md	New meteor shower in public Global Meteor Network orbits, absent from the live IAU MDC shower list
ztf-microlensing-event-uncatalogued	Sky archives	harvest	laptop-hours to overnig…	known-unknowns/sky-archives/ztf-microlensing-event-uncatalogued.md	New microlensing event in public ZTF light curves absent from published ZTF, Gaia and OGLE/KMTNet microlensing catalogues
gaia-dr3-open-cluster-not-in-ucc	Sky archives	harvest	laptop-hours per field	known-unknowns/sky-archives/gaia-dr3-open-cluster-not-in-ucc.md	New open cluster in Gaia DR3 absent from the Unified Cluster Catalogue (UCC 260615) and the Hunt and Reffert census
kepler-k2-new-vetted-transit-candidate	Sky archives	harvest	laptop-hours	known-unknowns/sky-archives/kepler-k2-new-vetted-transit-candidate.md	New vetted transit candidate in archival Kepler or K2 light curves (not in KOI/K2 candidate tables)
tess-new-vetted-transit-candidate	Sky archives	harvest	laptop-hours	known-unknowns/sky-archives/tess-new-vetted-transit-candidate.md	New vetted transiting-planet candidate in public TESS light curves (not in TOI/CTOI/Archive)
nieuwland-constant-lower-bounds-gosain-tables	Recreational math	harvest	laptop-hours per solid	known-unknowns/recreational-math/nieuwland-constant-lower-bounds-gosain-tables.md	Nieuwland constants of the Platonic, Archimedean, Catalan and Johnson solids: a Rupert passage with a larger scale than Gosain-Grimmer's tables
nih-thin-smear-malaria-patient-grouped-sensitivity	Disease research	harvest	laptop-hours	known-unknowns/disease-research/nih-thin-smear-malaria-patient-grouped-sensitivity.md	NIH/NLM thin-smear malaria cells: beat the published sensitivity at matched specificity, and under a patient-grouped split
nist-aes-circuit-records	Algorithms	harvest	laptop-days for the sea…	known-unknowns/algorithms/nist-aes-circuit-records.md	NIST Circuit Complexity AES tables: a smaller or shallower {AND, XOR, XNOR} circuit for the AES S-box, inverse S-box, MixColumns or InvMixColumns
no-four-in-plane-cubic-grid	Record tables	harvest	laptop-hours	known-unknowns/record-tables/no-four-in-plane-cubic-grid.md	No four in a plane: more points in the n x n x n grid with no four coplanar than the best known (OEIS A280537, AZsPCs 2016)
non-attacking-queens-game-nimbers-a344227	Graphs, games and automata	standard	laptop-hours for toroid…	known-unknowns/graphs-games-automata/non-attacking-queens-game-nimbers-a344227.md	Non-Attacking Queens game (Node-Kayles on the n-queens graph): exact nimber a(18), the 20x20 outcome, and toroidal Conjecture T1 (OEIS A344227)
nucleotide-transformer-benchmark-mcc	Biology	standard	laptop-hours	known-unknowns/biology/nucleotide-transformer-benchmark-mcc.md	Nucleotide Transformer benchmark: beat the best published MCC on a genomic regulatory task
chess-endgame-nulp-nine-pieces	Recreational math	standard	laptop-days with a comb…	known-unknowns/recreational-math/chess-endgame-nulp-nine-pieces.md	Number of unique legal chess positions with 9 pieces (next term of OEIS A318266, Kryukov's NULP)
opn-roadblock-composites	Number hunts	harvest	laptop-hours	known-unknowns/number-hunts/opn-roadblock-composites.md	Odd perfect number proof tree: factor a 'most wanted roadblock' composite on Ochem's lists
oeis-keyword-more-new-terms	Recreational math	harvest	laptop-hours	known-unknowns/recreational-math/oeis-keyword-more-new-terms.md	OEIS 'keyword:more' sequences: compute the next term(s) beyond the live entry and b-file
openproblems-batch-integration-hard-metrics	Biology	standard	laptop-hours	known-unknowns/biology/openproblems-batch-integration-hard-metrics.md	Open Problems batch integration: beat every listed method on the metrics where single-cell integration still fails
openproblems-label-projection-cross-dataset	Biology	harvest	laptop-hours	known-unknowns/biology/openproblems-label-projection-cross-dataset.md	Open Problems label projection: beat the best listed accuracy/macro-F1 for transferring cell-type labels on the hardest datasets
openproblems-spatially-variable-genes-correlation	Biology	harvest	laptop-hours	known-unknowns/biology/openproblems-spatially-variable-genes-correlation.md	Open Problems spatially variable genes: beat the best ranking correlation on the hardest simulated spatial datasets
openood-v15-cifar-posthoc-near-ood-auroc	Machine learning	standard	laptop-hours	known-unknowns/machine-learning/openood-v15-cifar-posthoc-near-ood-auroc.md	OpenOOD v1.5 CIFAR-10/100: a post-hoc OOD detector on the official cross-entropy ResNet-18 checkpoints beating the best near-OOD AUROC
bitcoin-selfish-mining-revenue-bounds	Graphs, games and automata	standard	laptop-hours	known-unknowns/graphs-games-automata/bitcoin-selfish-mining-revenue-bounds.md	Optimal selfish mining in Bitcoin (Sapirshtein-Sompolinsky-Zohar model, gamma = 0): certify an upper bound on the optimal relative revenue below 0.70109 at alpha = 0.45 or below 0…
optiwindnet-routesets-cable-routing-records	Optimization benchmarks	harvest	laptop-hours	known-unknowns/optimization-benchmarks/optiwindnet-routesets-cable-routing-records.md	OptiWindNet RouteSets: a shorter offshore wind-farm array-cable network than the best stored for a real site
othello-perft-and-positions-next-terms	Graphs, games and automata	harvest	laptop-days for A124005…	known-unknowns/graphs-games-automata/othello-perft-and-positions-next-terms.md	Othello from the start: games after 22 plies (OEIS A124004) and distinct positions after 14 plies (A124005)
packing-density-4-point-patterns	Recreational math	harvest	laptop-hours for lower…	known-unknowns/recreational-math/packing-density-4-point-patterns.md	Packing densities of 2413, 1342 and 1324: beat a Sliacan-Stromquist or Presutti-Stromquist bound with an explicit permuton or a flag-algebra certificate
packomania-scu-spheres-in-cube	Packings and physics	harvest	laptop-hours	known-unknowns/packings-physics/packomania-scu-spheres-in-cube.md	Packomania: equal spheres in a cube (scu), beat a per-N record radius
pmms-impossibility-factors	Wildcard	standard	laptop-minutes to lapto…	known-unknowns/wildcard/pmms-impossibility-factors.md	Pairwise maximin share (PMMS): an additive instance whose best PMMS factor is below Gölz's 78/79 (goods) or above 1.102065 (chores)
grid-compositions-polyomino-tilings-a145835-n13	Graphs, games and automata	standard	laptop-days	known-unknowns/graphs-games-automata/grid-compositions-polyomino-tilings-a145835-n13.md	Partitions of the n x n grid into connected pieces (polyomino tilings of the square): the next term A145835(13), or the symmetric count A291807(13) as a partial win
peaceable-queens-torus-and-a16	Graphs, games and automata	harvest	laptop-hours	known-unknowns/graphs-games-automata/peaceable-queens-torus-and-a16.md	Peaceable queens: beat Clinch-Drescher-Huynh-Saffidine's odd-torus records (n = 19..63), or determine a(16)
peer-fold-classification-superfamily-holdout	Biology	harvest	laptop-hours	known-unknowns/biology/peer-fold-classification-superfamily-holdout.md	PEER fold classification: beat the leaderboard's 32.1% accuracy on held-out SCOP superfamilies
peg-solitaire-9x9-central-game	Graphs, games and automata	standard	laptop-days	known-unknowns/graphs-games-automata/peg-solitaire-9x9-central-game.md	Peg solitaire on the 9x9 square board: a central-game solution shorter than Alain Maye's 34 moves
pentagonal-geometries-pent4-pent5-exceptions	Record tables	harvest	laptop-hours	known-unknowns/record-tables/pentagonal-geometries-pent4-pent5-exceptions.md	Pentagonal geometries: construct PENT(4,r) for r in {8,12,16,28,32,36,44,48,56,64,72} or PENT(5,r) for r in {11,16,66,96,116}
perfect-squared-square-smallest-side-records	Recreational math	harvest	laptop-hours	known-unknowns/recreational-math/perfect-squared-square-smallest-side-records.md	Perfect squared squares: smaller side than the best known for an order 38..59 (OEIS A217148 table and squaring.net listings), or a nicer or more odd-sided record square
penney-permutations-rotation-conjecture	Graphs, games and automata	standard	laptop-hours to laptop-…	known-unknowns/graphs-games-automata/penney-permutations-rotation-conjecture.md	Permutation Penney: a pattern that its right rotation does not beat (counterexample to Elizalde-Lin Conjecture 6.1), or certified k = 4, 5
perturbench-frangieh21-melanoma-transfer	Disease research	harvest	laptop-hours	known-unknowns/disease-research/perturbench-frangieh21-melanoma-transfer.md	PerturBench Frangieh21: beat the published best covariate-transfer metrics for Perturb-seq in melanoma cells
perturbench-jiang24-cancer-lines-transfer	Disease research	harvest	laptop-days	known-unknowns/disease-research/perturbench-jiang24-cancer-lines-transfer.md	PerturBench Jiang24: beat the published best cytokine-perturbation transfer metrics across cancer cell lines
perturbench-norman19-combo-prediction	Disease research	harvest	laptop-hours	known-unknowns/disease-research/perturbench-norman19-combo-prediction.md	PerturBench Norman19: beat the published best combination-perturbation prediction metrics (CRISPR Perturb-seq in a leukemia line)
perturbench-srivatsan20-cell-line-transfer	Disease research	harvest	laptop-hours	known-unknowns/disease-research/perturbench-srivatsan20-cell-line-transfer.md	PerturBench Srivatsan20: beat the published best cross-cell-line chemical-perturbation transfer in three cancer cell lines
polaris-adme-fang-biogen-endpoints	Drug discovery	harvest	laptop-hours	known-unknowns/drug-discovery/polaris-adme-fang-biogen-endpoints.md	Polaris ADME-Fang (Biogen 3,521-compound DMPK set): beat the top listed score on an endpoint's public fold
polycube-tree-edge-unzipping	Recreational math	standard	laptop-hours	known-unknowns/recreational-math/polycube-tree-edge-unzipping.md	Polycube trees and edge-unzipping: a polycube tree with no edge zipper unfolding, or certified unzippings of all small ones (Demaine-Demaine-Eppstein-O'Rourke Question 1)
polyform-compatibility-open-pairs	Graphs, games and automata	harvest	laptop-hours	known-unknowns/graphs-games-automata/polyform-compatibility-open-pairs.md	Polyform compatibility: solve an open ('?') pair or shrink a smallest-known common figure on George Sicherman's tables
asteroid-precovery-arc-extension	Sky archives	harvest	laptop-hours	known-unknowns/sky-archives/asteroid-precovery-arc-extension.md	Precovery of known asteroids in public ZTF / Pan-STARRS / DECam images, extending the observed arc
shapley-network-design-pos-three-players	Graphs, games and automata	standard	laptop-hours to laptop-…	known-unknowns/graphs-games-automata/shapley-network-design-pos-three-players.md	Price of stability of undirected Shapley network design with three players: an instance above 1769/1126 (upper bound 286/175)
pnt-plus-unassigned-open-issues	Formal proofs	harvest	laptop-hours	known-unknowns/formal-proofs/pnt-plus-unassigned-open-issues.md	PrimeNumberTheoremAnd (PNT+): close an unassigned open formalisation issue (IK identities, Rosser-Schoenfeld prime sums, Dusart table bounds)
primes-in-ap-records-ap28	Number hunts	harvest	laptop-days	known-unknowns/number-hunts/primes-in-ap-records-ap28.md	Primes in arithmetic progression: beat a largest-known or smallest-known AP-k record (k = 3..27), or find the first AP28
proteinbench-apo-holo-multistate-tmens	Biology	standard	needs cluster	known-unknowns/biology/proteinbench-apo-holo-multistate-tmens.md	ProteinBench apo-holo: beat TMens 0.873 for predicting both states of 91 conformational-change proteins
proteingym-clinical-indels-auc	Disease research	harvest	laptop-hours	known-unknowns/disease-research/proteingym-clinical-indels-auc.md	ProteinGym clinical indels: beat the leaderboard's best average AUC on insertion/deletion clinical variants
proteingym-dms-indels-zeroshot-spearman	Disease research	harvest	laptop-hours	known-unknowns/disease-research/proteingym-dms-indels-zeroshot-spearman.md	ProteinGym indel benchmark (zero-shot): beat the best average Spearman on insertion/deletion DMS assays
proto-elamite-accounting-balance	Undeciphered scripts	harvest	laptop-hours	known-unknowns/undeciphered-scripts/proto-elamite-accounting-balance.md	Proto-Elamite: numeral-system and commodity assignments checked by tablet arithmetic
luhn-repunit-family-prp-primality-proofs	Number hunts	harvest	laptop-days	known-unknowns/number-hunts/luhn-repunit-family-prp-primality-proofs.md	Prove a listed PRP prime in Luhn's generalized repunit, generalized Wagstaff or generalized Mersenne tables (at least 10 000 digits)
qplib-better-solution-point	Optimization benchmarks	harvest	laptop-hours	known-unknowns/optimization-benchmarks/qplib-better-solution-point.md	QPLIB: better solution point for a quadratic (including QAP-type and Max-Cut-type binary) instance
quantum-latin-square-cardinalities-7-9-11-23	Record tables	harvest	laptop-hours	known-unknowns/record-tables/quantum-latin-square-cardinalities-7-9-11-23.md	Quantum Latin squares: realise an 'uncertain' cardinality for order 7, 9, 11 or 23 (Zhang-Lv-Cao Table 6)
ccd-quantum-lj-zpe-rare-gas-clusters	Chemistry and materials	harvest	laptop-hours	known-unknowns/chemistry-materials/ccd-quantum-lj-zpe-rare-gas-clusters.md	Quantum-corrected Lennard-Jones clusters (Xe, Ar, Ne with harmonic zero-point energy): lower a global minimum in the Calvo-Doye-Wales table (N < 100)
quaternary-legendre-pairs-open-lengths	Record tables	harvest	laptop-hours to laptop-…	known-unknowns/record-tables/quaternary-legendre-pairs-open-lengths.md	Quaternary Legendre pairs: settle an open even length up to 100 (70, 76, 88, 92, 94 or 100)
codetables-qubit-upper-bounds-n101-256	Physics	harvest	laptop-hours	known-unknowns/physics/codetables-qubit-upper-bounds-n101-256.md	Qubit stabilizer codes n = 101..256: lower a weak UPPER bound in Grassl's codetables.de qubit table with an exact LP/shadow certificate
codetables-qudit-quantum-codes-q3-q8	Record tables	harvest	laptop-hours	known-unknowns/record-tables/codetables-qudit-quantum-codes-q3-q8.md	Qudit stabilizer codes [[n,k,d]]_q for q = 3, 4, 5, 7, 8: raise a lower bound in Grassl's extended tables
ramsey-kk-minus-e-table-gaps	Record tables	harvest	laptop-hours	known-unknowns/record-tables/ramsey-kk-minus-e-table-gaps.md	Ramsey numbers with K_k - e: close a gap in Radziszowski's Table IIIa/IIIb (e.g. R(K4-e,K8-e) 30-32, R(K6,K5-e) 43-51, R(K8,K4-e) 36-39)
lattice-rsa-jamming-coverage-square-lattice	Physics	standard	laptop-days	known-unknowns/physics/lattice-rsa-jamming-coverage-square-lattice.md	Random sequential adsorption on the square lattice: more digits of the NN-exclusion jamming coverage 0.3641323(1), and the dimer value (0.906820 vs 0.906823)
phenopacket-store-rare-disease-gene-prioritization	Disease research	harvest	laptop-hours	known-unknowns/disease-research/phenopacket-store-rare-disease-gene-prioritization.md	Rare-disease gene prioritisation: beat published ranking performance on a frozen phenopacket-store release
raredis-corpus-rare-disease-ner-f1	Disease research	harvest	laptop-hours	known-unknowns/disease-research/raredis-corpus-rare-disease-ner-f1.md	RareDis corpus: beat the published BioBERT F1 for rare-disease and sign entity recognition on the fixed test split
rcplib-rg300-dc2-rcpsp-ub	Optimization benchmarks	harvest	laptop-hours	known-unknowns/optimization-benchmarks/rcplib-rg300-dc2-rcpsp-ub.md	RCPLIB (Vanhoucke-Coelho) RG300 and DC2 resource-constrained project scheduling: shorter makespan for an open instance
cryptocellar-enigma-1941-remaining	Unbroken ciphers	harvest	laptop-hours	known-unknowns/unbroken-ciphers/cryptocellar-enigma-1941-remaining.md	Remaining unbroken 1941 German Army Enigma messages (CryptoCellar list)
respicast-covid19-hub-beat-ensemble-wis	Disease research	harvest	laptop-hours	known-unknowns/disease-research/respicast-covid19-hub-beat-ensemble-wis.md	RespiCast COVID-19 hub: beat the hub ensemble's season WIS for COVID-19 hospital admissions in EU/EEA countries
rhombic-zonotopal-tilings-a006245-n17	Graphs, games and automata	harvest	laptop-days	known-unknowns/graphs-games-automata/rhombic-zonotopal-tilings-a006245-n17.md	Rhombic tilings of the 2n-gon (primitive sorting networks, A006245): the count for n = 17, or the next term of a higher-dimensional zonotopal-tiling column A060595-A060601
archiveii-interfamily-secondary-structure-f1	Biology	standard	laptop-hours	known-unknowns/biology/archiveii-interfamily-secondary-structure-f1.md	RNA secondary structure across families: beat the best published family-fold F1 on ArchiveII, especially telomerase RNA
robustbench-cifar100-linf-beat-autoattack	ML robustness	harvest	laptop-hours	known-unknowns/ml-robustness/robustbench-cifar100-linf-beat-autoattack.md	RobustBench CIFAR-100 Linf (eps 8/255): lower a listed model's robust accuracy below the best published value with a stronger attack
rongorongo-graphemes-parallels	Undeciphered scripts	harvest	laptop-hours	known-unknowns/undeciphered-scripts/rongorongo-graphemes-parallels.md	Rongorongo: graphemic inventory and new parallel passages found by alignment
rsv-hub-retrospective-beat-ensemble-wis	Disease research	harvest	laptop-hours	known-unknowns/disease-research/rsv-hub-retrospective-beat-ensemble-wis.md	RSV forecast hub: beat the hub ensemble's season-average WIS retrospectively on a completed RSV season
vesuvius-ct-codec-random-access	Herculaneum scrolls	harvest	laptop-hours	known-unknowns/herculaneum-scrolls/vesuvius-ct-codec-random-access.md	Scroll CT compression with random access: beat volcomp's rate-distortion on its 54 held-out PHerc. Paris 4 2.4 µm 128³ chunks while every chunk stays independently decodable
ecc-inversion-addition-chains	Algorithms	harvest	laptop-hours	known-unknowns/algorithms/ecc-inversion-addition-chains.md	Shorter addition chains for elliptic-curve field and scalar inversion exponents (Curve25519, P-256, P-384, secp256k1)
myerson-vs-anonymous-reserve-gap	Graphs, games and automata	standard	laptop-hours	known-unknowns/graphs-games-automata/myerson-vs-anonymous-reserve-gap.md	Single-item auctions: an asymmetric regular instance where Myerson's revenue exceeds second price with the best anonymous reserve by a factor above 2.1596 (JLTX four-buyer record)
hypergraph-ramsey-small-lower-bounds	Record tables	harvest	laptop-hours	known-unknowns/record-tables/hypergraph-ramsey-small-lower-bounds.md	Small hypergraph Ramsey numbers: beat R(4,5;3) >= 35, R(4,6;3) >= 63, R(5,5;3) >= 88, R(4,4,4;3) >= 79 or R(5,5;4) >= 35, or settle R(K4-t,K5;3) in 14-16
small-symmetric-function-circuit-size	Algorithms	harvest	laptop-hours to laptop-…	known-unknowns/algorithms/small-symmetric-function-circuit-size.md	Small symmetric Boolean functions over the full binary basis: smaller circuits for SUM_n (sideways sum), MAJ_n, SORT_n, or exact values such as Knuth's MOD3 n = 6 cases
folkman-numbers-small-table	Record tables	harvest	laptop-hours	known-unknowns/record-tables/folkman-numbers-small-table.md	Small vertex and edge Folkman numbers: improve a bound in the Hassan-Radziszowski-Van Overberghe 2026 tables
cage-upper-bounds	Graphs, games and automata	harvest	laptop-hours	known-unknowns/graphs-games-automata/cage-upper-bounds.md	Smaller (k,g)-graph than the cage record
smallest-mnist-99-percent-network	Machine learning	harvest	laptop-hours	known-unknowns/machine-learning/smallest-mnist-99-percent-network.md	Smallest neural network reaching 99% test accuracy on MNIST (record: 697 parameters)
oeis-a046057-moa-33	Wildcard	standard	laptop-days	known-unknowns/wildcard/oeis-a046057-moa-33.md	Smallest order with exactly 33 groups (OEIS A046057 a(33), the first unknown moa)
smt2026-p4-dfa-unknown-certificates	Optimization benchmarks	harvest	laptop-hours to laptop-…	known-unknowns/optimization-benchmarks/smt2026-p4-dfa-unknown-certificates.md	SMT-COMP 2026 P4/DFA bit-vector holdouts: one exact SAT model or UNSAT certificate
snake-coil-in-the-box	Record tables	harvest	laptop-hours	known-unknowns/record-tables/snake-coil-in-the-box.md	Snake-in-the-box / coil-in-the-box records in dimensions 9-13
moews-aliquot-cycles-new	Number hunts	harvest	laptop-hours	known-unknowns/number-hunts/moews-aliquot-cycles-new.md	Sociable numbers: find an aliquot cycle not on Moews' list
sorting-network-size-records	Record tables	harvest	laptop-hours	known-unknowns/record-tables/sorting-network-size-records.md	Sorting networks: fewer comparators than the best known for n = 16..32
spencer-discrepancy-c10c-lower-bound	Erdős problems and proofs	harvest	laptop-hours	known-unknowns/erdos-and-proofs/spencer-discrepancy-c10c-lower-bound.md	Spencer discrepancy constant C_10c: an n x n matrix in [-1,1] whose discrepancy beats the record ratio disc(A)/sqrt(n)
spherical-designs-s3-fewest-points	Packings and physics	harvest	laptop-days	known-unknowns/packings-physics/spherical-designs-s3-fewest-points.md	Spherical t-designs on S^3 (including SO(3) Chebyshev rules) with fewer points: beat the smallest known N for a degree t
spikeforest-paired-hybrid-sorter-accuracy	Neuroscience	harvest	laptop-hours per study	known-unknowns/neuroscience/spikeforest-paired-hybrid-sorter-accuracy.md	SpikeForest ground-truth spike sorting: beat the best average accuracy in the SpikeForest table on the paired Boyden recordings (and the hybrid Janelia studies)
spock-stability-auc-cleaned-dataset	Planets and moons	standard	laptop-days	known-unknowns/planetary-science/spock-stability-auc-cleaned-dataset.md	SPOCK orbital-stability benchmark (Thadhani et al. 2025 cleaned data): beat SPOCK 2.0's holdout AUC for 10^9-orbit stability of compact three-planet systems
srbench-2025-blackbox-dominate-leader	Machine learning	harvest	laptop-hours	known-unknowns/machine-learning/srbench-2025-blackbox-dominate-leader.md	SRBench 2025 black-box: a symbolic regressor that Pareto-dominates the best-accuracy method on a dataset
stable-marriage-max-stable-matchings	Record tables	harvest	laptop-hours	known-unknowns/record-tables/stable-marriage-max-stable-matchings.md	Stable marriage: an instance of size n with more stable matchings than the best known (OEIS A357271 and the Ong et al. 2025 instances)
av1324-growth-upper-bound-shuffle-automata	Recreational math	standard	laptop-hours to laptop-…	known-unknowns/recreational-math/av1324-growth-upper-bound-shuffle-automata.md	Stanley-Wilf limit of 1324: a certified upper bound below Brignall's 13.167248 (shuffle-automaton certificates)
steiner-2-designs-block-6-undecided	Record tables	harvest	laptop-hours to laptop-…	known-unknowns/record-tables/steiner-2-designs-block-6-undecided.md	Steiner systems S(2,6,v): settle one of the 27 undecided admissible v (smallest 51), or an undecided case with block size 7, 8 or 9
steinlib-puc-i640-open-upper-bounds	Optimization benchmarks	harvest	laptop-hours to laptop-…	known-unknowns/optimization-benchmarks/steinlib-puc-i640-open-upper-bounds.md	SteinLib PUC and I640: a cheaper Steiner tree for one of the 32 unsolved instances (hypercube, code-covering, bipartite, incidence graphs)
svcomp-2026-never-solved-validated-witness	Formal proofs	harvest	laptop-hours per task	known-unknowns/formal-proofs/svcomp-2026-never-solved-validated-witness.md	SV-COMP 2026: a doubly validated witness for a verification task that no participating verifier answered correctly
tcga-multiomics-survival-cindex-herrmann	Disease research	harvest	laptop-hours	known-unknowns/disease-research/tcga-multiomics-survival-cindex-herrmann.md	TCGA multi-omics survival: beat the best published C-index or integrated Brier score for a cancer cohort in the Herrmann benchmark
tdc-admet-regression-mae-caco2-ppbr-ld50	Drug discovery	harvest	laptop-hours	known-unknowns/drug-discovery/tdc-admet-regression-mae-caco2-ppbr-ld50.md	TDC ADMET Benchmark Group, MAE regression leaderboards (Caco2_Wang, PPBR_AZ, LD50_Zhu): beat rank 1 on the official scaffold split
tdc-admet-cyp-inhibition-auprc	Drug discovery	harvest	laptop-hours	known-unknowns/drug-discovery/tdc-admet-cyp-inhibition-auprc.md	TDC ADMET CYP inhibition leaderboards (CYP2C9/CYP2D6/CYP3A4_Veith, 12-13k molecules, AUPRC): beat MapLight+GNN
tdc-admet-small-classification-auprc-auroc	Drug discovery	harvest	laptop-hours	known-unknowns/drug-discovery/tdc-admet-small-classification-auprc-auroc.md	TDC ADMET small classification leaderboards (CYP substrates, hERG, DILI, Bioavailability): beat rank 1 on the official scaffold split
tdc-admet-excretion-spearman-leaderboards	Drug discovery	harvest	laptop-hours	known-unknowns/drug-discovery/tdc-admet-excretion-spearman-leaderboards.md	TDC ADMET Spearman leaderboards (Half_Life_Obach, Clearance_Hepatocyte_AZ, Clearance_Microsome_AZ, VDss_Lombardo): beat rank 1
tdc-dti-dg-bindingdb-patent-pcc	Drug discovery	harvest	laptop-hours	known-unknowns/drug-discovery/tdc-dti-dg-bindingdb-patent-pcc.md	TDC DTI Domain-Generalization (BindingDB patent-year split): beat the listed Pearson correlation
tgb-dynamic-node-affinity-ndcg-leaderboards	Machine learning	harvest	laptop-minutes for tgbn…	known-unknowns/machine-learning/tgb-dynamic-node-affinity-ndcg-leaderboards.md	TGB dynamic node affinity (tgbn-trade, genre, reddit, token): beat NAVIS's top test NDCG@10
three-body-equal-mass-rigorous-stability-beyond-eight	Physics	standard	laptop-hours to laptop-…	known-unknowns/physics/three-body-equal-mass-rigorous-stability-beyond-eight.md	Three-body problem: a computer-assisted proof of KAM (or linear) stability for an equal-mass periodic orbit other than the figure-eight, from the Hristov-Hristova-Tanikawa list of…
polytof-toffoli-tcount-benchmark-tensors	Physics	harvest	laptop-hours	known-unknowns/physics/polytof-toffoli-tcount-benchmark-tensors.md	Toffoli-count and T-count records: fewer non-Clifford gates for a benchmark circuit tensor than the Khoruzhii-Gelss-Pokutta (polytof) table
henon-topological-entropy-rigorous-bounds	Physics	standard	laptop-days	known-unknowns/physics/henon-topological-entropy-rigorous-bounds.md	Topological entropy of the classical Henon map: a rigorous lower bound above 0.46469, a certified upper bound below ln 2, or periodic-orbit counts beyond period 30
tourism-competition-beat-best-published-mape	Machine learning	standard	laptop-hours	known-unknowns/machine-learning/tourism-competition-beat-best-published-mape.md	Tourism forecasting competition (1,311 series): an out-of-sample average MAPE below N-BEATS-G's 18.47
trades-mnist-smallcnn-whitebox-below-leader	ML robustness	harvest	laptop-hours	known-unknowns/ml-robustness/trades-mnist-smallcnn-whitebox-below-leader.md	TRADES MNIST white-box leaderboard (Linf 0.3): push the TRADES SmallCNN's robust accuracy below 92.46%
traitgym-complex-traits-auprc	Biology	standard	laptop-hours	known-unknowns/biology/traitgym-complex-traits-auprc.md	TraitGym complex traits: beat the best AUPRC for picking the causal regulatory variant among matched controls
traitgym-mendelian-zero-shot-auprc	Biology	harvest	laptop-hours	known-unknowns/biology/traitgym-mendelian-zero-shot-auprc.md	TraitGym Mendelian traits: beat CADD zero-shot AUPRC on causal non-coding variants for rare disease
tsunami-tide-gauge-signal-not-in-ncei	Earth and sky	harvest	laptop-hours	known-unknowns/earth-and-sky/tsunami-tide-gauge-signal-not-in-ncei.md	Tsunami recorded on open tide-gauge data but absent (as an event or at that gauge) from the NCEI Global Historical Tsunami Database
cryptic-tb-resistance-beat-who-catalogue	Disease research	harvest	laptop-hours	known-unknowns/disease-research/cryptic-tb-resistance-beat-who-catalogue.md	Tuberculosis drug resistance from genotype: beat the WHO catalogue head-to-head on the public CRyPTIC compendium
turan-cycle-free-afzaly-mckay	Record tables	harvest	laptop-hours	known-unknowns/record-tables/turan-cycle-free-afzaly-mckay.md	Turan numbers for forbidden cycles: beat an 'at least' entry in the Afzaly-McKay extremal graph tables
auction-deterministic-threshold-monotonicity	Algorithms	standard	laptop-hours to laptop-…	known-unknowns/algorithms/auction-deterministic-threshold-monotonicity.md	Two-item auction determinism threshold: a density pair for which Thirumulanathan's c2*(c1) strictly decreases
ucr-tsc-beat-reference-30-resample-best	Machine learning	harvest	laptop-hours	known-unknowns/machine-learning/ucr-tsc-beat-reference-30-resample-best.md	UCR univariate time series classification: beat the best reference classifier's 30-resample mean accuracy on a dataset
uea-multivariate-tsc-beat-published-30-resample-best	Machine learning	harvest	laptop-hours	known-unknowns/machine-learning/uea-multivariate-tsc-beat-published-30-resample-best.md	UEA multivariate time series classification: beat the best published 30-resample mean accuracy on a dataset
nonogram-unique-count-7x7	Recreational math	harvest	laptop-days	known-unknowns/recreational-math/nonogram-unique-count-7x7.md	Uniquely solvable nonograms: count the 7 x 7 case (OEIS A242876 a(7)) or a new n x m cell beyond n*m = 44 (A384764)
dasch-unreported-historical-outburst	Sky archives	harvest	laptop-hours	known-unknowns/sky-archives/dasch-unreported-historical-outburst.md	Unreported historical outburst (nova, dwarf nova or large-amplitude event) in DASCH DR7 century-long plate light curves
brouwer-qary-unrestricted-a3-a4-a5	Record tables	harvest	laptop-hours	known-unknowns/record-tables/brouwer-qary-unrestricted-a3-a4-a5.md	Unrestricted ternary, quaternary and 5-ary codes A_q(n,d): new lower bound in Brouwer's small q-ary tables
linear-baseline-perturbation-replogle-k562	Disease research	harvest	laptop-hours	known-unknowns/disease-research/linear-baseline-perturbation-replogle-k562.md	Unseen single-gene perturbations in leukaemia cells: beat the linear baseline that currently matches every foundation model
covid19-forecast-hub-retrospective-beat-ensemble-wis	Disease research	harvest	laptop-hours	known-unknowns/disease-research/covid19-forecast-hub-retrospective-beat-ensemble-wis.md	US COVID-19 Forecast Hub: beat the hub ensemble's season-average WIS for hospital admissions in a vintage-honest retrospective
vdw-small-lower-bounds	Record tables	harvest	laptop-hours	known-unknowns/record-tables/vdw-small-lower-bounds.md	Van der Waerden numbers: beat a small-parameter lower bound W(r,k) or w(2;k1,k2)
vnncomp-2026-unsolved-instance-counterexample	ML robustness	harvest	laptop-hours	known-unknowns/ml-robustness/vnncomp-2026-unsolved-instance-counterexample.md	VNN-COMP 2026: a validated counterexample for a benchmark instance that no participating verifier solved
quartering-chessboard-a006067-n29	Recreational math	standard	laptop-days	known-unknowns/recreational-math/quartering-chessboard-a006067-n29.md	Ways to quarter an n x n chessboard into four congruent connected pieces: the next term A006067(29) or A006067(30), open since Howroyd's n = 28 in 2016
wieferich-other-bases-fischer-table	Number hunts	harvest	laptop-hours	known-unknowns/number-hunts/wieferich-other-bases-fischer-table.md	Wieferich primes to other bases: a new p with b^(p-1) == 1 (mod p^2) beyond Richard Fischer's searched limits (incl. Mirimanoff base 3)
xhstt-2014-high-school-timetabling-bks	Optimization benchmarks	harvest	laptop-hours	known-unknowns/optimization-benchmarks/xhstt-2014-high-school-timetabling-bks.md	XHSTT high school timetabling (Post archive): beat a best known solution cost on an open XHSTT-2014 instance
zapbench-whole-brain-forecast-mae	Neuroscience	standard	laptop-days	known-unknowns/neuroscience/zapbench-whole-brain-forecast-mae.md	ZAPBench whole-brain zebrafish activity forecasting: beat the best released long-context (C=256) test MAE at every horizon
ccd-c60-molecular-clusters	Packings and physics	harvest	laptop-hours	known-unknowns/packings-physics/ccd-c60-molecular-clusters.md	(C60)_N molecular clusters (Pacheco-Prates-Ramalho N <= 105, Girifalco N < 81): lower a putative global minimum in the Doye-Wales tables
ks-sat-threshold-f5-unsat-5cnf	Record tables	standard	laptop-days	known-unknowns/record-tables/ks-sat-threshold-f5-unsat-5cnf.md	(k,s)-SAT threshold: an unsatisfiable 5-CNF in which every variable occurs at most 7 times, proving f(5) <= 6
ccd-nacl-cluster-anions-born-mayer	Packings and physics	harvest	laptop-hours	known-unknowns/packings-physics/ccd-nacl-cluster-anions-born-mayer.md	(NaCl)_N Cl- cluster anions (N <= 35, Tosi-Fumi Coulomb plus Born-Mayer and Welch potentials): lower a putative global minimum in the Doye-Wales table
mint-ts-sequences-small-gaps	Record tables	standard	pure thought plus lapto…	known-unknowns/record-tables/mint-ts-sequences-small-gaps.md	(t,s)-sequences in base 2 or 3: close a MinT gap between the best known t and the lower bound (smallest: is there a (4,8)-sequence in base 2?)
orlib-mkp-chu-beasley-30-500-and-gk	Optimization benchmarks	harvest	laptop-hours	known-unknowns/optimization-benchmarks/orlib-mkp-chu-beasley-30-500-and-gk.md	0-1 multidimensional knapsack: beat a best known value on an OR-Library 30.500 (Chu-Beasley) or MK_GK (Glover-Kochenberger) instance
sudoku-16x16-fewer-than-55-clues	Recreational math	standard	laptop-days	known-unknowns/recreational-math/sudoku-16x16-fewer-than-55-clues.md	16 x 16 Sudoku with 54 or fewer clues: beat the 55-clue record (OEIS A198297, 15 <= a(4) <= 55)
ab-offlattice-protein-3d-best-energies	Packings and physics	harvest	laptop-hours	known-unknowns/packings-physics/ab-offlattice-protein-3d-best-energies.md	3D AB off-lattice protein model: beat the best published energy for a standard Fibonacci or PDB-derived benchmark sequence
fifth-powers-5-1-4-new-primitive	Number hunts	harvest	needs cluster	known-unknowns/number-hunts/fifth-powers-5-1-4-new-primitive.md	A fifth primitive solution to a^5 + b^5 + c^5 + d^5 = e^5 (or a third all-positive one)
ame-states-open-cells-huber-table	Physics	standard	laptop-days	known-unknowns/physics/ame-states-open-cells-huber-table.md	Absolutely maximally entangled states: settle an open AME(n,D) cell of the Huber-Wyderka table (e.g. AME(8,6), AME(8,4), AME(11,3))
akkadian-lacuna-restoration-heldout	Ancient texts and fragments	harvest	laptop-hours	known-unknowns/ancient-texts/akkadian-lacuna-restoration-heldout.md	Akkadian: restore masked/damaged signs in Oracc/eBL transliterations, beating the Lazar et al. 2021 held-out benchmark with frozen predictions
amicable-pair-smallest-ratio	Number hunts	harvest	laptop-hours	known-unknowns/number-hunts/amicable-pair-smallest-ratio.md	Amicable pairs: beat the smallest known ratio m/n
apn-new-ccz-class-dim9-10	Crypto math	harvest	laptop-hours	known-unknowns/crypto-math/apn-new-ccz-class-dim9-10.md	APN functions: a new CCZ-inequivalent APN function (or APN permutation) in dimension 9 or 10
arch-comp-ainncs-cartpole-full-initial-set	ML robustness	standard	laptop-hours	known-unknowns/ml-robustness/arch-comp-ainncs-cartpole-full-initial-set.md	ARCH-COMP AINNCS CartPole (Balancing): verify or falsify 1e-3 settling of the neural controller on the full initial set
go2-monarch-of-the-mountain-scopf	Optimization benchmarks	harvest	laptop-days	known-unknowns/optimization-benchmarks/go2-monarch-of-the-mountain-scopf.md	ARPA-E GO Competition Challenge 2 (SCOPF with switching): beat a Monarch of the Mountain best-known objective
cryoem-automated-model-building-completeness	Biology	standard	needs cluster	known-unknowns/biology/cryoem-automated-model-building-completeness.md	Automated cryo-EM model building: raise completeness above ModelAngelo's 77% on its 177-map held-out set
synchronizing-avoiding-threshold-2n-2	Graphs, games and automata	standard	laptop-hours to laptop-…	known-unknowns/graphs-games-automata/synchronizing-avoiding-threshold-2n-2.md	Avoiding words in synchronizing automata: an automaton with n >= 8 states and 1-avoiding threshold 2n-2 (largest known example has 7 states), or one above 2n-2
bb33-bb25-cryptid-adjacent	Number hunts	harvest	laptop-hours	known-unknowns/number-hunts/bb33-bb25-cryptid-adjacent.md	BB(3,3) non-Bigfoot holdouts and BB(2,5) non-Hydra holdouts
beale-1-and-3	Unbroken ciphers	standard	laptop-hours	known-unknowns/unbroken-ciphers/beale-1-and-3.md	Beale ciphers #1 (location) and #3 (names): book-cipher key-text search
ccd-binary-gupta-nanoalloys-38-55	Packings and physics	harvest	laptop-hours	known-unknowns/packings-physics/ccd-binary-gupta-nanoalloys-38-55.md	Binary Gupta nanoalloys (Ag-Au, Cu-Ag, Cu-Au 55-atom; Cu-Au 38-atom; Li-Na and Na-K 55-atom): lower the best homotop energy for some composition
mint-binary-nonlinear-oa-strength	Record tables	harvest	laptop-hours	known-unknowns/record-tables/mint-binary-nonlinear-oa-strength.md	Binary orthogonal arrays with 2^m runs beyond every linear OA: higher strength than MinT's best known (smallest: OA(256, 20, 2, 4))
birdset-soundscape-cmap	Ecology and bioacoustics	harvest	needs cluster	known-unknowns/ecology/birdset-soundscape-cmap.md	BirdSet soundscapes: beat the best published class-mean AP (mean 0.440 over seven test sites) for multi-label bird detection
bloch-constant-lower-bound	Erdős problems and proofs	standard	laptop-days	known-unknowns/erdos-and-proofs/bloch-constant-lower-bound.md	Bloch's constant B (C_57a): a certified lower bound above Wikstrom's sqrt(3)/4 + 0.0153 = 0.448312701 (claimed upper bound 0.471861652113, Zhang 2026)
burnt-pancake-graph-diameter-n18	Graphs, games and automata	standard	needs cluster for a ful…	known-unknowns/graphs-games-automata/burnt-pancake-graph-diameter-n18.md	Burnt pancake graph diameter g(18) (OEIS A078941): decide 29 or 30
butson-hadamard-bh-n-6-undecided-orders	Record tables	standard	laptop-days	known-unknowns/record-tables/butson-hadamard-bh-n-6-undecided-orders.md	Butson Hadamard matrices BH(n,6): settle one of the undecided even orders below 100 (46, 74, 86, 94)
hypercube-c4-free-erdos-86	Erdős problems and proofs	harvest	laptop-days	known-unknowns/erdos-and-proofs/hypercube-c4-free-erdos-86.md	C4-free subgraphs of the hypercube (Erdős #86): settle ex(Q7,C4) in [304,308], beat 682 for Q8, or certify a bound below Baber's 0.60318
cami2-metagenome-assembly-strain-f1	Genomes	standard	needs cluster	known-unknowns/genomics/cami2-metagenome-assembly-strain-f1.md	CAMI II metagenome assembly: beat MetaHipMer 2.2.0's strain F1 on the marine short-read co-assembly in the CAMI Benchmarking Portal
chess-ply-count-sequences-next-terms	Recreational math	harvest	needs cluster for perft	known-unknowns/recreational-math/chess-ply-count-sequences-next-terms.md	Chess from the opening position: the next term of the per-ply counts (distinct positions at ply 12, checkmates at ply 14, perft(16))
standard-map-golden-circle-breakup-rigorous-window	Physics	standard	laptop-days	known-unknowns/physics/standard-map-golden-circle-breakup-rigorous-window.md	Chirikov standard map: shrink the rigorous window [0.9716, 0.9718] around the breakup of the golden invariant circle
hypercube-square-chromatic-q9-q11	Graphs, games and automata	standard	laptop-days	known-unknowns/graphs-games-automata/hypercube-square-chromatic-q9-q11.md	Chromatic number of the square of the hypercube: is Q_9^2 13-colourable? (13 <= chi <= 14; n = 10, 11 also open)
voronoi-lattice-chromatic-dim5-k12-bw16	Graphs, games and automata	standard	laptop-days	known-unknowns/graphs-games-automata/voronoi-lattice-chromatic-dim5-k12-bw16.md	Chromatic numbers of lattices (Voronoi graphs): settle a 5-dimensional primitive lattice, the Coxeter-Todd lattice K12 or the Barnes-Wall lattice BW16
av1324-inversion-monotonicity-conjecture	Recreational math	standard	laptop-days	known-unknowns/recreational-math/av1324-inversion-monotonicity-conjecture.md	Claesson-Jelinek-Steingrimsson conjecture: 1324-avoiders with k inversions never decrease from length n to n+1 (counterexample, or the first full table at n = 18)
clay-cft-local-field-sorries	Formal proofs	harvest	laptop-hours	known-unknowns/formal-proofs/clay-cft-local-field-sorries.md	Clay Class Field Theory project: Herbrand quotient of local units and unramified cohomology vanishing
erdos-problems-computational-nt	Number hunts	harvest	laptop-hours	known-unknowns/number-hunts/erdos-problems-computational-nt.md	Computationally decidable open number-theory Erdős problems (erdosproblems.com)
coco-trs-never-answered-confluence	Formal proofs	standard	laptop-hours	known-unknowns/formal-proofs/coco-trs-never-answered-confluence.md	Confluence Competition: certified YES/NO for a first-order TRS in ARI-COPS that no CoCo tool has answered since 2019
guts-n-player-asynchronous-coalition	Graphs, games and automata	standard	laptop-hours to laptop-…	known-unknowns/graphs-games-automata/guts-n-player-asynchronous-coalition.md	Continuous Guts: is the asynchronous coalition value zero for every n >= 4?
conway-subprime-fibonacci-new-loop	Number hunts	standard	laptop-days	known-unknowns/number-hunts/conway-subprime-fibonacci-new-loop.md	Conway's subprime Fibonacci sequences: a seventh non-trivial cycle, or an exhaustive check of starting pairs beyond 10^6
topswops-22-cards	Recreational math	harvest	needs cluster for the e…	known-unknowns/recreational-math/topswops-22-cards.md	Conway's Topswops: the maximum number of steps for 22 cards (next term of OEIS A000375 after Chaffin's f(21) = 282), or longer 22- and 23-card decks
cryobench-heterogeneity-fsc-auc	Biology	standard	needs cluster	known-unknowns/biology/cryobench-heterogeneity-fsc-auc.md	CryoBench: beat the best published per-image FSC AUC for cryo-EM heterogeneity on a ground-truth dataset
cuneiform-sign-detection-maicubeda	Ancient texts and fragments	harvest	laptop-hours	known-unknowns/ancient-texts/cuneiform-sign-detection-maicubeda.md	Cuneiform sign detection on the open MaiCuBeDa 3D-rendering benchmark: beat a reproduced RepPoints baseline (AP@50/AP@75) on a fixed, period-filtered split
cunningham-chain-records	Number hunts	harvest	laptop-hours	known-unknowns/number-hunts/cunningham-chain-records.md	Cunningham chains: beat a largest-known record for some length, or find a chain of length 21
cb-ctt-itc2007-comp-open-instances	Optimization benchmarks	harvest	laptop-days	known-unknowns/optimization-benchmarks/cb-ctt-itc2007-comp-open-instances.md	Curriculum-based course timetabling (ITC-2007 track 3, UD2): beat the best known penalty on an open comp instance
cycle-versus-complete-ramsey-small	Record tables	harvest	laptop-hours for lower…	known-unknowns/record-tables/cycle-versus-complete-ramsey-small.md	Cycles versus complete graphs: close R(C4,K11) 40-43, R(C4,K12) 43-51 or R(C5,K9) 33-36
dagapeyeff-1939	Unbroken ciphers	standard	laptop-hours	known-unknowns/unbroken-ciphers/dagapeyeff-1939.md	D'Agapeyeff cipher (1939 textbook challenge)
wind-waves-dh-type2-missed-vs-cdaw	Earth and sky	harvest	laptop-hours	known-unknowns/earth-and-sky/wind-waves-dh-type2-missed-vs-cdaw.md	Decametric-hectometric type II radio burst in open Wind/WAVES (and STEREO/WAVES) data absent from the CDAW type II list
degree-diameter-bipartite-table	Record tables	harvest	laptop-hours	known-unknowns/record-tables/degree-diameter-bipartite-table.md	Degree-diameter problem for bipartite graphs: a larger bipartite (d,k)-graph than the Combinatorics Wiki table
linf-certified-training-accuracy-records	ML robustness	standard	laptop-days	known-unknowns/ml-robustness/linf-certified-training-accuracy-records.md	Deterministic Linf certified accuracy records (MNIST 0.1/0.3, CIFAR-10 2/255 and 8/255, TinyImageNet 1/255): certify more test images than the best published model
lrx-cayley-diameter-sn	Graphs, games and automata	standard	needs cluster	known-unknowns/graphs-games-automata/lrx-cayley-diameter-sn.md	Diameter of the Cayley graph of S_n with generators (1,2) and the two n-cycle rotations (LRX): prove n(n-1)/2, or compute a(16) exactly
dujella-dn-quintuple-smallest-n	Number hunts	standard	laptop-days	known-unknowns/number-hunts/dujella-dn-quintuple-smallest-n.md	Diophantine D(n)-quintuples: a quintuple with -255 < n < 256 (beat Dujella's n1 <= 256 or n2 >= -255)
dreval-exvivo-beataml2-pdx-transfer	Disease research	moonshot	laptop-days	known-unknowns/disease-research/dreval-exvivo-beataml2-pdx-transfer.md	DrEval ex vivo transfer: beat the naive baseline when a cell-line drug-response model meets AML patient samples and breast-cancer PDX
ccd-dzugutov-zetterling-polytetrahedral-clusters	Packings and physics	harvest	laptop-hours	known-unknowns/packings-physics/ccd-dzugutov-zetterling-polytetrahedral-clusters.md	Dzugutov, modified-Dzugutov and Z1/Z2 clusters: lower a putative global minimum in the Doye-Wales polytetrahedral tables
elliptic-curve-rank-small-conductor-records	Number hunts	harvest	laptop-days	known-unknowns/number-hunts/elliptic-curve-rank-small-conductor-records.md	Elliptic curves over Q of rank r = 5..11 with smaller conductor than the Elkies-Watkins records
erdos-1082i-distinct-distances-general-position	Erdős problems and proofs	harvest	laptop-hours	known-unknowns/erdos-and-proofs/erdos-1082i-distinct-distances-general-position.md	Erdos #1082(i): n points, no three collinear, with fewer than floor(n/2) distinct distances
erdos-1095-erdos-selfridge-function-g401	Erdős problems and proofs	harvest	needs cluster	known-unknowns/erdos-and-proofs/erdos-1095-erdos-selfridge-function-g401.md	Erdos #1095 (Ecklund-Erdos-Selfridge function g(k)): g(401) and beyond, or an independent replay of g(378..400)
erdos-307-barbeau-prime-reciprocals	Erdős problems and proofs	harvest	laptop-hours	known-unknowns/erdos-and-proofs/erdos-307-barbeau-prime-reciprocals.md	Erdos #307 (Barbeau): disjoint prime sets P, Q with (sum 1/p)(sum 1/q) = 1
erdos-506-circles-small-n	Erdős problems and proofs	harvest	laptop-hours	known-unknowns/erdos-and-proofs/erdos-506-circles-small-n.md	Erdos #506: minimum number of circles determined by n points, beating or closing the n <= 393 gap
erdos-617-balanced-coloring-r5	Erdős problems and proofs	harvest	laptop-hours	known-unknowns/erdos-and-proofs/erdos-617-balanced-coloring-r5.md	Erdos #617 (Erdos-Gyarfas): balanced 5-colouring of K_26
erdos-699-binomial-gcd	Erdős problems and proofs	harvest	laptop-hours	known-unknowns/erdos-and-proofs/erdos-699-binomial-gcd.md	Erdos #699: a prime p >= i dividing gcd(C(n,i), C(n,j)), for a full proof
erdos-835-large-steiner-systems	Erdős problems and proofs	harvest	pure thought + laptop-m…	known-unknowns/erdos-and-proofs/erdos-835-large-steiner-systems.md	Erdos #835: (k+1)-colouring of J(2k,k), equivalently large sets of Steiner systems S(k-1,k,2k)
sunflower-free-capacity-lower-bound	Erdős problems and proofs	harvest	laptop-hours	known-unknowns/erdos-and-proofs/sunflower-free-capacity-lower-bound.md	Erdos-Szemeredi 3-sunflower-free capacity: beat the 1997 lower bound 1.551 (optimization constant C_49)
erdos-217-crescent-configuration-n9	Erdős problems and proofs	standard	laptop-days	known-unknowns/erdos-and-proofs/erdos-217-crescent-configuration-n9.md	Erdős #217 (crescent configurations): 9 points in general position whose 8 distances occur 1, 2, ..., 8 times
erdos-272-ap-intersection-families	Erdős problems and proofs	standard	laptop-days	known-unknowns/erdos-and-proofs/erdos-272-ap-intersection-families.md	Erdős #272: more than C(N,2)+1+floor((N-1)/4) subsets of {1..N} with pairwise AP intersections, or the exact t(13)
erdos-396-389-binomial-product-witnesses	Number hunts	harvest	laptop-days to needs cl…	known-unknowns/number-hunts/erdos-396-389-binomial-product-witnesses.md	Erdős #396 and #389: the first n with (n)(n-1)...(n-17) dividing C(2n,n), or a first witness for #389 at n = 36
erdos-82-regular-induced-subgraph-ramsey	Erdős problems and proofs	harvest	laptop-days	known-unknowns/erdos-and-proofs/erdos-82-regular-induced-subgraph-ramsey.md	Erdős #82 small cases: a graph on 21 vertices with no regular induced subgraph of order >= 6, or on 30 vertices with none of order >= 7
unit-distance-small-n	Record tables	harvest	laptop-hours	known-unknowns/record-tables/unit-distance-small-n.md	Erdős unit distance problem for small n: more unit distances among n points than the best known (n = 22..100)
friedman-packing-records	Record tables	harvest	laptop-hours	known-unknowns/record-tables/friedman-packing-records.md	Erich Friedman Packing Center: beat a listed packing
iig-benchmark-exact-nash-values	Graphs, games and automata	harvest	laptop-days	known-unknowns/graphs-games-automata/iig-benchmark-exact-nash-values.md	Exact Nash values of the ICLR-2026 imperfect-information benchmarks: Phantom Tic-Tac-Toe, Abrupt Phantom Tic-Tac-Toe, Abrupt 3x3 Dark Hex, 2-dice 5-face Liar's Dice
exominerpp-tess-2min-cv-pr-auc	Planets and moons	standard	laptop-days	known-unknowns/planetary-science/exominerpp-tess-2min-cv-pr-auc.md	ExoMiner++ TESS 2-minute TCE vetting benchmark: beat the published 10-fold cross-validated PR-AUC (0.976) on the 57,162 labelled SPOC TCEs with the released folds
fasd13-few-shot-animal-sound-detection	Ecology and bioacoustics	standard	laptop-days	known-unknowns/ecology/fasd13-few-shot-animal-sound-detection.md	FASD13 few-shot animal sound detection: beat DRASDIC's 5-shot event F1 averaged over the twelve animal datasets
sloane-cohn-max-volume-polyhedra-s2	Packings and physics	harvest	laptop-hours	known-unknowns/packings-physics/sloane-cohn-max-volume-polyhedra-s2.md	Fejes Toth problem: N points on the unit sphere whose convex hull has larger volume than the best known (Hardin-Sloane-Smith and Deeter tables, N = 10..130 except 12)
order-preserving-gray-path-n11	Algorithms	moonshot	laptop-days to needs cl…	known-unknowns/algorithms/order-preserving-gray-path-n11.md	Felsner-Trotter order-preserving Gray paths: one for n = 11 (open for all n >= 11), or the exact count for n = 8 (OEIS A259839)
fermat-numbers-new-factor	Number hunts	harvest	laptop-days	known-unknowns/number-hunts/fermat-numbers-new-factor.md	Fermat numbers F_m = 2^(2^m)+1: a new prime factor not in Keller's table, above all for F12-F33
flip-aav-capsid-plmfit-spearman	Biology	standard	laptop-days	known-unknowns/biology/flip-aav-capsid-plmfit-spearman.md	FLIP AAV capsid fitness: beat the PLMFit scoreboard Spearman on the one-vs-rest (one_vs_many) split
flip-meltome-mixed-plmfit-spearman	Biology	standard	laptop-days	known-unknowns/biology/flip-meltome-mixed-plmfit-spearman.md	FLIP meltome mixed split: beat the PLMFit scoreboard Spearman for melting temperature from sequence
fractional-plane-explicit-finite-udg-above-4	Graphs, games and automata	standard	laptop-days	known-unknowns/graphs-games-automata/fractional-plane-explicit-finite-udg-above-4.md	Fractional chromatic number of the plane: an explicit finite unit-distance graph with fractional chromatic number above 4 (best explicit: about 3.9898)
gbm-counterpart-o4-gw-candidate	Sky archives	standard	laptop-days	known-unknowns/sky-archives/gbm-counterpart-o4-gw-candidate.md	Gamma-ray counterpart candidate in public Fermi-GBM data for an O4a/O4b gravitational-wave candidate, sub-threshold ones included
fermi-lat-pulsations-known-radio-pulsar	Sky archives	standard	laptop-hours	known-unknowns/sky-archives/fermi-lat-pulsations-known-radio-pulsar.md	Gamma-ray pulsations from a known radio pulsar not yet on the public list of LAT-detected pulsars
theobald-geometric-dissections-fewer-pieces	Recreational math	harvest	laptop-hours	known-unknowns/recreational-math/theobald-geometric-dissections-fewer-pieces.md	Gavin Theobald's Geometric Dissections: a dissection with fewer pieces than the catalogue's best
collatz-type-maps-new-cycles	Number hunts	harvest	laptop-hours to laptop-…	known-unknowns/number-hunts/collatz-type-maps-new-cycles.md	Generalized Collatz maps: a cycle missing from the known lists (Lagarias 3x+k for k < 20000, 3x-k, and the three known 5x+1 cycles)
generalized-repunit-first-prime-bases-to-1024	Number hunts	harvest	laptop-days per base fo…	known-unknowns/number-hunts/generalized-repunit-first-prime-bases-to-1024.md	Generalized repunits (b^p-1)/(b-1): a first (probable) prime for one of the 26 bases b <= 1024 with none known (smallest: b = 185)
generalized-wagstaff-first-prime-bases-to-1024	Number hunts	harvest	laptop-days per base	known-unknowns/number-hunts/generalized-wagstaff-first-prime-bases-to-1024.md	Generalized Wagstaff / negative-base repunits (b^p+1)/(b+1): a first (probable) prime for one of the 41 bases b <= 1024 with none known (smallest: b = 97)
giuga-numbers-new	Number hunts	standard	laptop-hours	known-unknowns/number-hunts/giuga-numbers-new.md	Giuga numbers: find one not yet known
ccd-glue-potential-al-pb-clusters	Packings and physics	harvest	laptop-hours	known-unknowns/packings-physics/ccd-glue-potential-al-pb-clusters.md	Glue-potential aluminium (N <= 190) and lead (N <= 160) clusters: lower a putative global minimum in Doye's polytetrahedral tables
graph-golf-order-degree-aspl	Graphs, games and automata	harvest	laptop-days	known-unknowns/graphs-games-automata/graph-golf-order-degree-aspl.md	Graph Golf (order/degree and host-switch problems): beat a 2021 best diameter and average shortest path length
hypercube-q6-hamiltonian-paths	Graphs, games and automata	standard	needs cluster	known-unknowns/graphs-games-automata/hypercube-q6-hamiltonian-paths.md	Gray codes: the number of Hamiltonian paths in the 6-cube (A091299(6), open since 2005)
iphi-greek-inscription-attribution-ithaca	Ancient texts and fragments	harvest	laptop-days	known-unknowns/ancient-texts/iphi-greek-inscription-attribution-ithaca.md	Greek inscriptions (I.PHI): beat Ithaca's region (70.8% top-1) and date (29.3 years) attribution on the PHI-digit-3 test split
iphi-greek-restoration-stoicheia-frozen3000	Ancient texts and fragments	standard	laptop-days	known-unknowns/ancient-texts/iphi-greek-restoration-stoicheia-frozen3000.md	Greek inscriptions: beat Stoicheia v2 (CER 15.5, top-1 74.5) on the frozen 3,000-gap file cut from Ithaca's PHI-digit-3 test split
dclp-unidentified-literary-papyri	Ancient texts and fragments	harvest	laptop-hours	known-unknowns/ancient-texts/dclp-unidentified-literary-papyri.md	Greek literary papyri: identify DCLP 'unidentified' fragments as witnesses of known works via open-corpus text matching
gross-code-syndrome-circuit-distance	Physics	standard	laptop-days	known-unknowns/physics/gross-code-syndrome-circuit-distance.md	Gross code syndrome extraction: settle the Strikis-Browne-Beverland conjecture that their depth-8 circuit has circuit distance 11, or reach 12 with an interleaved circuit
lattice-animal-growth-constant-certified-bounds	Physics	standard	laptop-days	known-unknowns/physics/lattice-animal-growth-constant-certified-bounds.md	Growth constants of lattice animals: a certified bound beating lambda_2 in [4.00253, 4.5252] for polyominoes or lambda_3 in [6.6799, 9.3835] for polycubes
gset-maxcut-nontoroidal-records	Optimization benchmarks	harvest	laptop-days	known-unknowns/optimization-benchmarks/gset-maxcut-nontoroidal-records.md	Gset Max-Cut: a larger cut than the best published for a non-toroidal Gset graph (G60 14190, G61 5799, G63 27047, G64 8753, G70 9595, ...)
hadamard-open-orders-below-10000	Record tables	harvest	laptop-days	known-unknowns/record-tables/hadamard-open-orders-below-10000.md	Hadamard conjecture frontier: a Hadamard matrix at one of the 85 orders up to 10000 with no known construction (smallest 2396)
hadwiger-nelson-smaller-5-chromatic-udg	Erdős problems and proofs	harvest	laptop-hours	known-unknowns/erdos-and-proofs/hadwiger-nelson-smaller-5-chromatic-udg.md	Hadwiger-Nelson finite witnesses (Erdos #508 context): a 5-chromatic unit-distance graph with fewer than 509 vertices
hales-jewett-small-lower-bounds	Record tables	harvest	laptop-hours	known-unknowns/record-tables/hales-jewett-small-lower-bounds.md	Hales-Jewett numbers: beat HJ(3,3) >= 22 or HJ(4,2) >= 14 with an explicit line-free colouring
hall-conjecture-good-examples	Number hunts	harvest	laptop-hours	known-unknowns/number-hunts/hall-conjecture-good-examples.md	Hall's conjecture: new good examples beyond 10^29 or beat Elkies' ratio 46.6
grid-hamiltonian-cycles-28x28	Graphs, games and automata	standard	needs cluster	known-unknowns/graphs-games-automata/grid-hamiltonian-cycles-28x28.md	Hamiltonian cycles on the 28 x 28 grid: the next term of OEIS A003763 (known to 26 x 26 since Pettersson 2014)
apollonian-gasket-dimension-certified-digits	Number hunts	standard	needs cluster	known-unknowns/number-hunts/apollonian-gasket-dimension-certified-digits.md	Hausdorff dimension of the Apollonian gasket: more than Vytnova-Wormell's 128 rigorous decimals
heilbronn-records	Record tables	harvest	laptop-hours	known-unknowns/record-tables/heilbronn-records.md	Heilbronn triangle problem: new best configurations (square, triangle, convex region)
vesuvius-9um-ink-never-seen-pherc0841	Herculaneum scrolls	standard	laptop-days	known-unknowns/herculaneum-scrolls/vesuvius-9um-ink-never-seen-pherc0841.md	Herculaneum 9 µm ink detection on a never-seen scroll: beat every public 9 µm model's AUC on the three human-labelled PHerc. 0841 segments (9.366 µm / 113 keV) with a model that n…
hg002-q100-gqc-automated-assembly-errors	Genomes	standard	needs cluster	known-unknowns/genomics/hg002-q100-gqc-automated-assembly-errors.md	HG002 vs the Q100 genome benchmark: an automated diploid assembly with fewer GQC errors than the best listed non-curated assembly (38,072)
dujella-torsion-rank-records-q	Number hunts	harvest	laptop-hours	known-unknowns/number-hunts/dujella-torsion-rank-records-q.md	High-rank elliptic curves over Q with prescribed torsion: beat a cell of Dujella's table
hilbert-numbers-degree-3-to-8-lower-bounds	Wildcard	harvest	laptop-days	known-unknowns/wildcard/hilbert-numbers-degree-3-to-8-lower-bounds.md	Hilbert numbers H(3)..H(8): a planar polynomial vector field with more limit cycles than 13, 28, 37, 53, 74 or 96
read2016-ratsprotokolle-line-htr-closed	Ancient texts and fragments	standard	laptop-days	known-unknowns/ancient-texts/read2016-ratsprotokolle-line-htr-closed.md	Historical handwriting (READ 2016 Ratsprotokolle, line level): beat HTR-ConvText's 3.6% CER and 15.7% WER on the 1,138 test lines without external data
hp-lattice-folding-benchmark-energies	Biology	harvest	laptop-hours	known-unknowns/biology/hp-lattice-folding-benchmark-energies.md	HP lattice protein folding: beat a best-known energy on a standard 2D/3D benchmark sequence
hwmcc25-unsolved-first-certified	Optimization benchmarks	harvest	laptop-days per benchma…	known-unknowns/optimization-benchmarks/hwmcc25-unsolved-first-certified.md	HWMCC'25: first certified answer for a hardware model-checking benchmark that no participant solved
pte-ideal-size-11-13	Number hunts	harvest	laptop-hours	known-unknowns/number-hunts/pte-ideal-size-11-13.md	Ideal Prouhet-Tarry-Escott solution of size 11 or 13
misere-quotient-period-5-element	Graphs, games and automata	standard	laptop-hours to laptop-…	known-unknowns/graphs-games-automata/misere-quotient-period-5-element.md	Impartial misere quotients: exhibit an element of period 5 (or 8, or any period other than 1, 2, 3, 4, 6)
flt-imperial-unclaimed-prop-sorries	Formal proofs	harvest	laptop-hours	known-unknowns/formal-proofs/flt-imperial-unclaimed-prop-sorries.md	Imperial FLT project: fill an unclaimed Prop-valued sorry (de Smit-Lenstra representability, compact exponent-p groups, quaternion base change)
erdos-moser-bound	Number hunts	harvest	laptop-hours	known-unknowns/number-hunts/erdos-moser-bound.md	Improve the Erdős-Moser equation lower bound (beyond the 2026 claim m > 8.213e1,800,000,044)
taxicab-7-upper-bound	Number hunts	harvest	laptop-hours	known-unknowns/number-hunts/taxicab-7-upper-bound.md	Improve the upper bound on Taxicab(7) (and higher taxicab bounds)
queens-graph-chromatic-27	Graphs, games and automata	standard	laptop-hours	known-unknowns/graphs-games-automata/queens-graph-chromatic-27.md	Is the 27 x 27 queens graph 27-colourable? (first open chromatic number of the queens graph)
ispd2024-global-routing-best-score	Engineering and chips	harvest	laptop-hours for benchm…	known-unknowns/engineering/ispd2024-global-routing-best-score.md	ISPD 2024 large-scale global routing benchmarks: a lower official evaluator cost than the best published router
ispd2026-buffering-sizing-dominance	Engineering and chips	standard	laptop-hours to laptop-…	known-unknowns/engineering/ispd2026-buffering-sizing-dominance.md	ISPD 2026 contest (post-placement buffering and sizing): a result that dominates the per-design winner on every non-runtime metric
ito-negaperiodic-golay-pair-length-94	Record tables	standard	laptop-days	known-unknowns/record-tables/ito-negaperiodic-golay-pair-length-94.md	Ito's conjecture at t = 47: a negaperiodic Golay pair of length 94 (equivalently quasi-Williamson matrices of order 47)
wilds-iwildcam-ood-macro-f1	Ecology and bioacoustics	standard	needs cluster	known-unknowns/ecology/wilds-iwildcam-ood-macro-f1.md	iWildCam2020-WILDS camera-trap species ID: beat the leaderboard's best out-of-distribution test macro F1 (52.0, AutoFT)
jsp-optimizizer-open-upper-bounds	Optimization benchmarks	harvest	laptop-hours	known-unknowns/optimization-benchmarks/jsp-optimizizer-open-upper-bounds.md	Job-shop scheduling: lower the makespan upper bound on an open Taillard / Demirkol / SWV / YN / ABZ instance (Optimizizer tables)
komlos-constant-lower-bound	Erdős problems and proofs	standard	laptop-hours	known-unknowns/erdos-and-proofs/komlos-constant-lower-bound.md	Komlos discrepancy constant C_24: a finite matrix with unit-norm columns whose discrepancy beats Kunisky's 1 + sqrt(2)
kourovka-16-46-conder-finite-quotient	Wildcard	standard	laptop-hours	known-unknowns/wildcard/kourovka-16-46-conder-finite-quotient.md	Kourovka 16.46 (Conder): does the index-8 subgroup K of an amalgam acting on the 3-valent tree have a non-trivial finite quotient?
led-latin-inscription-attribution-aeneas	Ancient texts and fragments	harvest	laptop-days	known-unknowns/ancient-texts/led-latin-inscription-attribution-aeneas.md	Latin inscriptions (LED): beat Aeneas on dating (13.4 years) and province attribution (72.3% top-1) on the id-digit-3 test split
latin-tableau-conjecture	Erdős problems and proofs	standard	laptop-days	known-unknowns/erdos-and-proofs/latin-tableau-conjecture.md	Latin Tableau Conjecture (Chow et al.): a Young diagram with no Latin tableau of type delta, or a certified extension of the 12 x 12 verification
lazy-beaver-missing-cells	Graphs, games and automata	standard	laptop-days to needs cl…	known-unknowns/graphs-games-automata/lazy-beaver-missing-cells.md	Lazy Beaver: compute a missing LB(n, m) value (LB(7,2), LB(5,3), LB(4,4), LB(3,5) or LB(2,7))
leancamcombi-bkr-reimer-inequality	Formal proofs	standard	laptop-hours	known-unknowns/formal-proofs/leancamcombi-bkr-reimer-inequality.md	LeanCamCombi: formal proof of the van den Berg-Kesten-Reimer inequality (card_certificator_le)
lebesgue-universal-cover-bounds	Record tables	standard	laptop-days	known-unknowns/record-tables/lebesgue-universal-cover-bounds.md	Lebesgue's universal covering problem (C13b): a certified lower bound above 0.8344 or a convex cover below 0.8440935944
legendre-pairs-open-odd-lengths	Record tables	standard	laptop-days	known-unknowns/record-tables/legendre-pairs-open-odd-lengths.md	Legendre pairs: settle an open odd length below 200 (115, 145, 159, 161, 169, 175, 177, 185, 187, 195)
levine-hat-two-player-value	Graphs, games and automata	standard	laptop-days	known-unknowns/graphs-games-automata/levine-hat-two-player-value.md	Levine's two-player hat puzzle: tighten the published 7/20 and 81/224 bounds, and certify finite-stack optima
linear-a-kuro-arithmetic	Undeciphered scripts	harvest	laptop-hours	known-unknowns/undeciphered-scripts/linear-a-kuro-arithmetic.md	Linear A: KU-RO totals and fraction-sign values reconciled by arithmetic
unit-demand-lottery-vs-item-pricing-gap	Graphs, games and automata	standard	laptop-hours	known-unknowns/graphs-games-automata/unit-demand-lottery-vs-item-pricing-gap.md	Lotteries vs item prices for a unit-demand buyer with independent values: an explicit menu earning more than (1 + ln2/5) ~ 1.1386 times any item pricing (gap [1.1386, 3])
lottery-numbers-l-n-6-6-2-beyond-70	Record tables	harvest	laptop-hours to laptop-…	known-unknowns/record-tables/lottery-numbers-l-n-6-6-2-beyond-70.md	Lottery numbers L(n,6,6,2) for n >= 71: fewest 6-number tickets that guarantee a 2-match prize (UK-lottery problem, past the published range)
labs-merit-factor-records	Record tables	harvest	laptop-hours	known-unknowns/record-tables/labs-merit-factor-records.md	Low-autocorrelation binary sequences: best-known merit factors for lengths 67-600
luna16-nodule-detection-cpm-10fold	Disease research	standard	laptop-days	known-unknowns/disease-research/luna16-nodule-detection-cpm-10fold.md	LUNA16 lung-nodule detection and false-positive reduction: beat the best CPM (0.951 detection, 0.968 false-positive reduction) under the official 10-fold protocol
m4-competition-beat-nbeats-owa	Machine learning	standard	laptop-days	known-unknowns/machine-learning/m4-competition-beat-nbeats-owa.md	M4 competition (100,000 series): an honestly out-of-sample point forecast with overall OWA below N-BEATS's 0.795
m5-accuracy-beat-winner-wrmsse	Machine learning	standard	laptop-hours to laptop-…	known-unknowns/machine-learning/m5-accuracy-beat-winner-wrmsse.md	M5 accuracy competition (Walmart unit sales): beat the winning private WRMSSE 0.52044 with a frozen, test-blind pipeline
m5-uncertainty-beat-winner-wspl	Machine learning	standard	laptop-hours to laptop-…	known-unknowns/machine-learning/m5-uncertainty-beat-winner-wspl.md	M5 uncertainty competition: beat the winning private WSPL 0.15420 for nine-quantile Walmart sales forecasts
madry-cifar10-challenge-whitebox-below-leader	ML robustness	harvest	laptop-hours	known-unknowns/ml-robustness/madry-cifar10-challenge-whitebox-below-leader.md	MadryLab CIFAR-10 challenge (white-box, Linf 8/255): push the secret model's accuracy below 43.95%
magic-state-distillation-fewest-qubits	Physics	standard	laptop-days to needs cl…	known-unknowns/physics/magic-state-distillation-fewest-qubits.md	Magic-state distillation footprint: a distance-4 T-to-T protocol on 8 or 9 qubits (known 8 <= N_T(4) <= 10), or distance 5 on at most 10 qubits
insight-marsquake-missed-vs-mqs-v14	Earth and sky	harvest	laptop-hours to laptop-…	known-unknowns/earth-and-sky/insight-marsquake-missed-vs-mqs-v14.md	Marsquake in open InSight SEIS waveforms absent from the Marsquake Service catalogue V14 and the MarsQuakeNet extension
latin-max-transversals-n10-20	Record tables	harvest	laptop-hours to laptop-…	known-unknowns/record-tables/latin-max-transversals-n10-20.md	Maximum number of transversals T(n): a Latin square of order 10 with more than Parker's 5504, or a new record for n = 11..20
parsimony-benchmark-best-scores	Biology	standard	laptop-hours	known-unknowns/biology/parsimony-benchmark-best-scores.md	Maximum parsimony: a tree with fewer steps than the best-known score on a classic benchmark alignment
partial-spreads-smallest-open-cases	Record tables	standard	laptop-days	known-unknowns/record-tables/partial-spreads-smallest-open-cases.md	Maximum partial spreads: settle 129 <= A_2(11,8;4) <= 132 or 244 <= A_3(8,6;3) <= 248
meroitic-semantic-induction	Undeciphered scripts	standard	laptop-hours	known-unknowns/undeciphered-scripts/meroitic-semantic-induction.md	Meroitic: meanings for unknown words from distribution, validated on held-out known words
mertens-ratio-oscillation-hurst-bounds	Number hunts	standard	needs cluster	known-unknowns/number-hunts/mertens-ratio-oscillation-hurst-bounds.md	Mertens function oscillations: a certified bound beating Hurst's liminf M(x)/sqrt(x) < -1.837625 or limsup > 1.826054
minlplib-finance-open-instances	Optimization benchmarks	standard	laptop-hours	known-unknowns/optimization-benchmarks/minlplib-finance-open-instances.md	MINLPLib finance and marketing instances still open: beat saa_2 (strategic asset allocation) or close pricing050 (product pricing) with a certificate
minlplib-open-primal-bound	Optimization benchmarks	harvest	laptop-hours	known-unknowns/optimization-benchmarks/minlplib-open-primal-bound.md	MINLPLib: better feasible point for an open mixed-integer nonlinear instance
misere-sprouts-21-spots	Graphs, games and automata	standard	laptop-days	known-unknowns/graphs-games-automata/misere-sprouts-21-spots.md	Misère Sprouts: settle the 21-spot game (first unknown since 2011)
modded-nanogpt-track3-fewest-steps	Machine learning	standard	needs cluster	known-unknowns/machine-learning/modded-nanogpt-track3-fewest-steps.md	Modded-NanoGPT track 3 (optimization): reach 3.28 FineWeb val loss with the fixed GPT-2-small setup in fewer than 2,690 steps (2,450 pending)
mols-lower-bounds-small-orders	Record tables	harvest	laptop-days	known-unknowns/record-tables/mols-lower-bounds-small-orders.md	MOLS table: more mutually orthogonal Latin squares of some order n < 500 than the current lower bound (e.g. 4 MOLS of order 22)
monostable-polyhedron-fewer-than-14-faces	Recreational math	standard	laptop-hours	known-unknowns/recreational-math/monostable-polyhedron-fewer-than-14-faces.md	Monostable polyhedron with fewer faces: a homogeneous convex polyhedron that rests stably on only one face, with fewer than Reshetov's 14 faces
monusac-2020-test-weighted-pq	Disease research	standard	laptop-hours	known-unknowns/disease-research/monusac-2020-test-weighted-pq.md	MoNuSAC 2020 nucleus segmentation and classification: beat TIA-Lab's challenge-best PQ 0.6119 on the public test set
monuseg-2018-test-aji	Disease research	standard	laptop-hours	known-unknowns/disease-research/monuseg-2018-test-aji.md	MoNuSeg 2018 multi-organ nucleus segmentation: beat the best published AJI (0.7063; challenge best 0.6907) on the public 14-image test set
mordell-curve-rank-records	Number hunts	harvest	laptop-days	known-unknowns/number-hunts/mordell-curve-rank-records.md	Mordell curves y^2 = x^3 + k: a smaller |k| of given rank 7..16 than the OEIS upper bounds, or rank >= 18
moser-worm-convex-cover-bounds	Record tables	standard	laptop-days	known-unknowns/record-tables/moser-worm-convex-cover-bounds.md	Moser's worm problem (convex covers, C13a): certify a lower bound above 0.239 or a rotation-only convex cover below 0.257883595
binary-action-games-max-nash-equilibria	Graphs, games and automata	standard	laptop-days	known-unknowns/graphs-games-automata/binary-action-games-max-nash-equilibria.md	Most Nash equilibria in a generic 4-player game with two actions each: find 39 or more (bounds 37 and 65), refuting Hertling-Vujić Conjecture 4.5
multi-controlled-z-t-count-below-4n-6	Physics	standard	laptop-hours	known-unknowns/physics/multi-controlled-z-t-count-below-4n-6.md	Multi-controlled Z with fewer T gates: an exact C^nZ (n >= 4 controls) with T-count below Gidney-Jones' 4n - 6
multimagie-smallest-multiplicative-addmult	Recreational math	harvest	laptop-hours	known-unknowns/recreational-math/multimagie-smallest-multiplicative-addmult.md	Multimagie.com: smaller best-known multiplicative or additive-multiplicative magic squares (orders 7-17)
gf2-polymult-8term-25-products	Algorithms	standard	laptop-days	known-unknowns/algorithms/gf2-polymult-8term-25-products.md	Multiply two 8-term binary polynomials with 25 products (NIST open problem), or a smaller GF(2^8) AES-field multiplier circuit
mtc3-double-transposition-reloaded	Unbroken ciphers	harvest	laptop-hours	known-unknowns/unbroken-ciphers/mtc3-double-transposition-reloaded.md	MysteryTwister 'Double Column Transposition Reloaded' Parts 1-3 (0 solvers since 2013)
mtc3-spirale-4	Unbroken ciphers	harvest	laptop-hours	known-unknowns/unbroken-ciphers/mtc3-spirale-4.md	MysteryTwister 'Spirale Part 4' (hand 'OTP' cipher, 0 solvers)
mtc3-spanish-strip-cipher-3	Unbroken ciphers	standard	laptop-hours	known-unknowns/unbroken-ciphers/mtc3-spanish-strip-cipher-3.md	MysteryTwister Spanish Strip Cipher Part 3 (Spanish Civil War telegram, 0 solvers)
ccmc-cme-arrival-scoreboard-mae-2023-2024	Earth and sky	standard	laptop-hours	known-unknowns/earth-and-sky/ccmc-cme-arrival-scoreboard-mae-2023-2024.md	NASA CCMC CME Scoreboard: CME arrival-time forecasts for 2023-2024 with a lower mean absolute error than every scoreboard method
abc-high-quality-triples	Number hunts	harvest	laptop-hours	known-unknowns/number-hunts/abc-high-quality-triples.md	New high-quality abc triples (q >= 1.4, c > 10^20) or beat Reyssat's 1.6299
giant-planet-satellite-archival-shift-and-stack	Planets and moons	standard	laptop-days	known-unknowns/planetary-science/giant-planet-satellite-archival-shift-and-stack.md	New irregular (or small inner) satellite of Jupiter, Saturn, Uranus or Neptune in public archival images, shown bound by an orbit fit
mw-satellite-candidate-not-in-lvdb	Sky archives	standard	laptop-days	known-unknowns/sky-archives/mw-satellite-candidate-not-in-lvdb.md	New Milky Way satellite (ultra-faint dwarf or faint halo star cluster) in public DECam or Legacy Surveys catalogues, absent from the Local Volume Database
parkes-archival-new-pulsar-candidate	Sky archives	standard	laptop-days	known-unknowns/sky-archives/parkes-archival-new-pulsar-candidate.md	New pulsar candidate in public Parkes (Murriyang) search-mode archival data, detected in two independent observations and absent from all pulsar lists
mahler-measure-new-small-polynomials	Number hunts	harvest	laptop-hours	known-unknowns/number-hunts/mahler-measure-new-small-polynomials.md	New small-Mahler-measure polynomials / Salem numbers beyond the proven-complete ranges
no-three-in-line-n75	Graphs, games and automata	harvest	laptop-hours	known-unknowns/graphs-games-automata/no-three-in-line-n75.md	No-three-in-line: 150 points on the 75x75 grid (smallest open n)
swpc-3day-kp-g1-slot-hss-2025	Earth and sky	standard	laptop-hours	known-unknowns/earth-and-sky/swpc-3day-kp-g1-slot-hss-2025.md	NOAA SWPC 3-day forecast 2025: beat SWPC's Heidke skill for G1+ (Kp >= 5-) 3-hour slots at 1-3 day lead
noise-backprop-free-pretraining-records	Machine learning	harvest	needs cluster	known-unknowns/machine-learning/noise-backprop-free-pretraining-records.md	Noise: pretraining a fixed 37.7M transformer without backpropagation, below 3.338 val loss on 30M FineWeb tokens
noita-eye-messages	Unbroken ciphers	moonshot	laptop-hours	known-unknowns/unbroken-ciphers/noita-eye-messages.md	Noita Eye Messages (designed game cipher, developer-confirmed real)
gnu-unknown-orders-below-20000	Wildcard	harvest	laptop-days	known-unknowns/wildcard/gnu-unknown-orders-below-20000.md	Number of groups of order n: settle an order up to 20,000 that is still unknown in Max Horn's table (smallest: 3072, 4096, 4608, 5120, 6144, 6400, 6912, 7168)
numerical-semigroups-count-genus-81-frobenius-133	Number hunts	standard	needs cluster	known-unknowns/number-hunts/numerical-semigroups-count-genus-81-frobenius-133.md	Numerical semigroups: the next exact count by genus (n_81, OEIS A007323) or by Frobenius number (N_133, OEIS A124506)
curtois-nrp-open-gaps-bcv-mer-instance24	Optimization benchmarks	standard	laptop-hours	known-unknowns/optimization-benchmarks/curtois-nrp-open-gaps-bcv-mer-instance24.md	Nurse rostering benchmark (Curtois / schedulingbenchmarks.org): close an open gap on BCV-3.46.1, MER or Instance24
ssh-mapping-natl60-2020a-osse	Earth and sky	harvest	laptop-hours	known-unknowns/earth-and-sky/ssh-mapping-natl60-2020a-osse.md	Ocean data challenge 2020a (SSH mapping OSSE, NATL60): beat a leaderboard resolution score
octahedron-ramsey-number	Graphs, games and automata	standard	laptop-days	known-unknowns/graphs-games-automata/octahedron-ramsey-number.md	Octahedron Ramsey number: is R(K_{2,2,2}, K_{2,2,2}) 30 or 31?
odd-boolean-nonlinearity-9-11-13	Record tables	standard	laptop-hours to laptop-…	known-unknowns/record-tables/odd-boolean-nonlinearity-9-11-13.md	Odd-variable Boolean nonlinearity: exceed 242, 996 or 4040
ogbg-molhiv-beat-leaderboard-roc-auc	Drug discovery	harvest	laptop-hours	known-unknowns/drug-discovery/ogbg-molhiv-beat-leaderboard-roc-auc.md	OGB ogbg-molhiv: beat the leaderboard's top mean test ROC-AUC under the official protocol
ogbl-collab-beat-leaderboard-hits50	Machine learning	harvest	laptop-hours	known-unknowns/machine-learning/ogbl-collab-beat-leaderboard-hits50.md	OGB ogbl-collab: beat the leaderboard's top test Hits@50 (0.7129) for future co-authorship prediction
orchard-planting-small-n-records	Record tables	harvest	laptop-days	known-unknowns/record-tables/orchard-planting-small-n-records.md	Orchard planting: more 3-point or 4-point lines among n points than the best known (3 per row for n >= 17, 4 per row for n >= 21)
oriented-chromatic-planar-girth-lower-bounds	Graphs, games and automata	harvest	laptop-days	known-unknowns/graphs-games-automata/oriented-chromatic-planar-girth-lower-bounds.md	Oriented chromatic number of planar graphs by girth: an explicit planar oriented graph beating a lower bound (18..80, 11..40, 7..16, 7..11, 6..7, 5..7, 5..6)
rectangle-piercing-packing-ratio-above-5-2	Graphs, games and automata	standard	laptop-days	known-unknowns/graphs-games-automata/rectangle-piercing-packing-ratio-above-5-2.md	Packing vs piercing for axis-parallel rectangles after Wegner's conjecture fell: a finite family with tau > (5/2) nu
packomania-csqv-sum-of-radii	Algorithms	harvest	laptop-hours	known-unknowns/algorithms/packomania-csqv-sum-of-radii.md	Packomania csqv: circles in the unit square with maximised sum of radii (AlphaEvolve problem), beat a table entry
pancake-number-p20	Graphs, games and automata	standard	needs cluster	known-unknowns/graphs-games-automata/pancake-number-p20.md	Pancake numbers: settle P(20), the diameter of the 20-pancake graph (OEIS A058986), now known to lie in {22, 23, 24}
vesuvius-scroll1-fiber-tracing-afv	Herculaneum scrolls	harvest	laptop-days at best	known-unknowns/herculaneum-scrolls/vesuvius-scroll1-fiber-tracing-afv.md	Papyrus fiber tracing on Scroll 1 (PHerc. Paris 4, 2.4 µm): beat the published automated fiber volume on precision against dense hand tracing with no loss of recall in the held-ou…
vesuvius-surface-topo-holdout	Herculaneum scrolls	harvest	laptop-hours	known-unknowns/herculaneum-scrolls/vesuvius-surface-topo-holdout.md	Papyrus surface detection: beat the released Kaggle-2026 1st-place nnU-Net (surface_m7_nnunet) on a frozen 88-volume holdout of the open 320^3 training mirror under a pinned open…
periodic-golay-pairs-undecided-lengths	Record tables	standard	laptop-days	known-unknowns/record-tables/periodic-golay-pairs-undecided-lengths.md	Periodic Golay pairs: settle an undecided length up to 300 (smallest 106)
pfsp-taillard-open-makespans	Optimization benchmarks	harvest	laptop-hours to laptop-…	known-unknowns/optimization-benchmarks/pfsp-taillard-open-makespans.md	Permutation flow shop (Taillard benchmarks): a makespan below the best known for one of the 12 open Taillard instances, with VRF instances as partial wins
pesplib-periodic-timetabling-records	Optimization benchmarks	harvest	laptop-hours	known-unknowns/optimization-benchmarks/pesplib-periodic-timetabling-records.md	PESPlib periodic timetabling: lower the best known weighted slack of a railway instance R1L1..R4L4
asteroid-tumbler-npa-model-not-in-damit	Planets and moons	standard	laptop-hours	known-unknowns/planetary-science/asteroid-tumbler-npa-model-not-in-damit.md	Physical model of a tumbling (non-principal-axis) asteroid from public lightcurves, beyond the tumbler models in DAMIT
polycubes-3d-next-term-n23	Graphs, games and automata	standard	needs cluster	known-unknowns/graphs-games-automata/polycubes-3d-next-term-n23.md	Polycubes: the number of 23-cell polycubes (next term of OEIS A001931 fixed and A000162 / A038119 free, open since Phillip Thompson's n = 22 in 2024)
pzktupel-largest-ktuplet-stale-patterns	Recreational math	harvest	laptop-hours	known-unknowns/recreational-math/pzktupel-largest-ktuplet-stale-patterns.md	Prime k-tuplets: a larger proven prime k-tuplet than the largest known for a stale (k, pattern) row (k = 11..17)
proteinbench-atlas-ensemble-distribution	Biology	standard	needs cluster	known-unknowns/biology/proteinbench-atlas-ensemble-distribution.md	ProteinBench (ATLAS): beat the best published conformational-ensemble distribution metrics for proteins
lychrel-new-base-proof	Number hunts	harvest	laptop-hours	known-unknowns/number-hunts/lychrel-new-base-proof.md	Prove Lychrel numbers exist in a new base (mechanical template-closure proof)
psplib-j120-rcpsp-upper-bounds	Optimization benchmarks	harvest	laptop-hours	known-unknowns/optimization-benchmarks/psplib-j120-rcpsp-upper-bounds.md	PSPLIB J120 (single-mode RCPSP): lower a best known heuristic makespan on an unproven instance
quark-gluon-pythia-tagging-auc-record	Particle physics	standard	laptop-days	known-unknowns/particle-physics/quark-gluon-pythia-tagging-auc-record.md	Pythia quark-gluon jet tagging (Komiske-Metodiev-Thaler dataset): beat PELICAN's AUC 0.9252 with particle-ID inputs
binary-coefficient-apn-dimension-11	Record tables	standard	laptop-days for a bound…	known-unknowns/record-tables/binary-coefficient-apn-dimension-11.md	Quadratic APN functions with coefficients in F2 in dimension 11: a seventh CCZ class
quasi-symmetric-2-designs-open-feasible	Record tables	harvest	laptop-days	known-unknowns/record-tables/quasi-symmetric-2-designs-open-feasible.md	Quasi-symmetric 2-designs: construct one for an open feasible parameter set with v <= 78 (smallest 2-(33,15,35), x=6, y=9)
quaternary-hermitian-self-dual-largest-min-weight	Record tables	standard	laptop-days for quasi-t…	known-unknowns/record-tables/quaternary-hermitian-self-dual-largest-min-weight.md	Quaternary Hermitian self-dual codes: an extremal [32,16,12] code, or a better minimum weight at length 42, 48, 54 or 60
queens-domination-26	Graphs, games and automata	standard	laptop-hours	known-unknowns/graphs-games-automata/queens-domination-26.md	Queen domination of the 26 x 26 board: 13 or 14 queens? (first open value of OEIS A075458)
qfo-swisstree-orthology-dominance	Genomes	standard	laptop-days	known-unknowns/genomics/qfo-swisstree-orthology-dominance.md	Quest for Orthologs 2022 SwissTree benchmark: ortholog predictions that beat every public method on recall and precision at once
quoridor-4x7-7-walls-exact	Graphs, games and automata	standard	laptop-hours	known-unknowns/graphs-games-automata/quoridor-4x7-7-walls-exact.md	Quoridor 4x7, 7 walls per player: exact initial outcome
schur-number-lower-bounds	Graphs, games and automata	harvest	laptop-hours	known-unknowns/graphs-games-automata/schur-number-lower-bounds.md	Raise the lower bound on Schur numbers S(6) / S(7) or weak Schur WS(6)
random-assignment-dec-ef-conjecture	Graphs, games and automata	standard	laptop-hours to laptop-…	known-unknowns/graphs-games-automata/random-assignment-dec-ef-conjecture.md	Random assignments: a finite SD-EF assignment with no Dec-EF decomposition (counterexample to Li-He-Li Conjecture 1)
dream-random-promoter-yeast-expression	Biology	standard	laptop-days	known-unknowns/biology/dream-random-promoter-yeast-expression.md	Random Promoter DREAM Challenge: beat the best published Pearson/Spearman score for predicting yeast expression from promoter sequence
randomized-list-update-partial-cost-bounds	Algorithms	standard	laptop-days	known-unknowns/algorithms/randomized-list-update-partial-cost-bounds.md	Randomized list update (partial cost model): a lower bound above Ambuhl's 1.50115, or a 5-item algorithm certified below COMB's 1.6
rectangular-sliding-puzzle-gods-numbers	Graphs, games and automata	harvest	needs cluster for an ex…	known-unknowns/graphs-games-automata/rectangular-sliding-puzzle-gods-numbers.md	Rectangular sliding-tile puzzles: the first unknown God's numbers of the m x n table (OEIS A151944): 3x6, 2x9, 4x5
boolean-degree-relevant-variables-c44	Erdős problems and proofs	harvest	laptop-hours	known-unknowns/erdos-and-proofs/boolean-degree-relevant-variables-c44.md	Relevant variables of degree-d Boolean functions (C_44): beat the 3/2 lower bound with an explicit function
restricted-additive-2-bases-k48	Record tables	harvest	laptop-days for preambl…	known-unknowns/record-tables/restricted-additive-2-bases-k48.md	Restricted additive 2-bases (restricted postage stamp, A006638): beat the Challis-Robinson symmetric-basis ranges for 48 <= k <= 82, or settle a(48)
robbins-problem-minimal-expected-rank-bounds	Wildcard	standard	laptop-days	known-unknowns/wildcard/robbins-problem-minimal-expected-rank-bounds.md	Robbins' problem (full-information expected rank): a certified bound beating 1.908 <= V <= 2.32614
robustbench-cifar10-l2-beat-autoattack	ML robustness	standard	laptop-hours	known-unknowns/ml-robustness/robustbench-cifar10-l2-beat-autoattack.md	RobustBench CIFAR-10 L2 (eps 0.5): lower a listed model's robust accuracy below the leaderboard value with a stronger L2 attack
robustbench-cifar10-linf-beat-autoattack	ML robustness	harvest	laptop-hours	known-unknowns/ml-robustness/robustbench-cifar10-linf-beat-autoattack.md	RobustBench CIFAR-10 Linf (eps 8/255): a stronger attack that lowers a listed model's robust accuracy below the leaderboard value
robustbench-imagenet-linf-beat-autoattack	ML robustness	harvest	laptop-days	known-unknowns/ml-robustness/robustbench-imagenet-linf-beat-autoattack.md	RobustBench ImageNet Linf (eps 4/255): lower a listed model's robust accuracy below the best published value with a stronger attack
rupert-open-classical-solids	Recreational math	standard	laptop-days	known-unknowns/recreational-math/rupert-open-classical-solids.md	Rupert's problem for the nine undecided classical solids: snub cube, snub dodecahedron, deltoidal and pentagonal hexecontahedra, Johnson solids J72-J75 and J77
r3-212-salem-spencer-unit-gap	Number hunts	standard	needs cluster for a com…	known-unknowns/number-hunts/r3-212-salem-spencer-unit-gap.md	Salem-Spencer sets: settle r_3(212) in {43, 44}, or beat a Wróblewski nonaveraging record a(n)
sartori-buriol-pdptw-bks	Optimization benchmarks	harvest	laptop-hours	known-unknowns/optimization-benchmarks/sartori-buriol-pdptw-bks.md	Sartori-Buriol real-road PDPTW instances (100-5000 locations): hierarchically beat a best known solution in the live GitHub table
sat-competition-2026-unknown-first-solve	Optimization benchmarks	harvest	laptop-days per instance	known-unknowns/optimization-benchmarks/sat-competition-2026-unknown-first-solve.md	SAT Competition 2026: first certified solve of a Main-track instance whose result is unknown
sctab-cellxgene-donor-holdout-macro-f1	Biology	standard	needs cluster or a GPU…	known-unknowns/biology/sctab-cellxgene-donor-holdout-macro-f1.md	scTab cross-tissue cell-type annotation: beat macro F1 0.8441 on the CELLxGENE donor-held-out test split (164 cell types)
saw-connective-constant-rigorous-bounds-2d	Physics	standard	laptop-days	known-unknowns/physics/saw-connective-constant-rigorous-bounds-2d.md	Self-avoiding walks: a certified bound on the square-lattice connective constant beating Couronne's upper bound 2.662342426 (2022) or Jensen's lower bound 2.625622 (2004)
semigroups-order-10-up-to-isomorphism	Wildcard	harvest	needs cluster for the f…	known-unknowns/wildcard/semigroups-order-10-up-to-isomorphism.md	Semigroups of order 10 up to isomorphism (OEIS A027851(10)), equivalently the self-converse semigroups of order 10, or the labeled count A023814(10)
hadamard-ingredient-sequences-smallest-open	Record tables	harvest	laptop-days to needs cl…	known-unknowns/record-tables/hadamard-ingredient-sequences-smallest-open.md	Sequences behind Hadamard constructions: settle a smallest open case in Table 3 of arXiv:2610.27175 (T-sequences, base sequences, Williamson-type matrices, Golay pairs)
shannon-capacity-odd-cycles	Record tables	harvest	laptop-hours	known-unknowns/record-tables/shannon-capacity-odd-cycles.md	Shannon capacity of odd cycles: larger independent sets in strong powers
superpermutations-n7-n8	Record tables	harvest	laptop-hours	known-unknowns/record-tables/superpermutations-n7-n8.md	Shorter superpermutations for n=7 (below 5905) or n=8 (below 46188)
lucas-chain-cl51	Number hunts	standard	laptop-days to a week	known-unknowns/number-hunts/lucas-chain-cl51.md	Shortest Lucas (differential addition) chains: compute C_L(51), the smallest n whose shortest Lucas chain has length 51 (OEIS A104892)
triorthogonal-codes-shortest-k1	Physics	standard	laptop-days	known-unknowns/physics/triorthogonal-codes-shortest-k1.md	Shortest triorthogonal (transversal-T) codes [[n,1,d]] at d >= 7: beat the Jain-Albert table, e.g. distance 7 with fewer than 95 qubits
all-permutations-supersequence-karp	Recreational math	standard	laptop-minutes to check…	known-unknowns/recreational-math/all-permutations-supersequence-karp.md	Shortest word containing every permutation of 1..n as a subsequence (Karp's problem, OEIS A062714): settle n = 10, or circular n = 7
sic-povm-new-dimension-numerical	Physics	standard	laptop-days	known-unknowns/physics/sic-povm-new-dimension-numerical.md	SIC-POVMs: the first publicly posted numerical Weyl-Heisenberg SIC fiducial in a dimension d >= 194 (outside known families)
silesia-per-file-specialized-record	Compression and code golf	harvest	laptop-hours	known-unknowns/compression-and-golf/silesia-per-file-specialized-record.md	Silesia corpus: beat the best per-file compressed size with a specialized open-source model
cubic-lattices-percolation-thresholds-digits	Physics	standard	needs cluster	known-unknowns/physics/cubic-lattices-percolation-thresholds-digits.md	Simple cubic, bcc, fcc and diamond percolation thresholds: beat the Xu-Wang-Lv-Deng (2014) precision, e.g. sc site 0.31160768(15), sc bond 0.24881185(10)
fewest-vertex-non-rupert-polyhedron	Recreational math	standard	laptop-days	known-unknowns/recreational-math/fewest-vertex-non-rupert-polyhedron.md	Simplest non-Rupert polyhedron: certify a convex polyhedron with fewer than 60 vertices that is not Rupert (Zeng's 8-vertex stellated tetrahedron P_11/20 is the leading candidate)
folding-ddg-s461-megascale-records	Biology	standard	laptop-hours for S461 i…	known-unknowns/biology/folding-ddg-s461-megascale-records.md	Single-point folding stability ddG: beat the published Pearson on the leak-controlled S461 blind set (and the Megascale split record)
z3-site-percolation-rigorous-lower-bound	Physics	standard	laptop-hours to laptop-…	known-unknowns/physics/z3-site-percolation-rigorous-lower-bound.md	Site percolation on the cubic lattice Z^3: a certified lower bound on p_c above Georgakopoulos-Panagiotis's 0.2522 (2023)
z3-site-percolation-rigorous-upper-bound	Physics	standard	laptop-hours	known-unknowns/physics/z3-site-percolation-rigorous-upper-bound.md	Site percolation on the cubic lattice Z^3: an explicit certified upper bound on p_c below Campanino-Russo's 1/2 (1985)
skempi2-binding-ddg-external-validation	Biology	standard	laptop-hours to laptop-…	known-unknowns/biology/skempi2-binding-ddg-external-validation.md	SKEMPI 2.0 binding ddG: beat the published external-validation Pearson on the fixed S1131 and M1707 test sets
skew-hadamard-unknown-orders	Record tables	harvest	laptop-days	known-unknowns/record-tables/skew-hadamard-unknown-orders.md	Skew-Hadamard matrices: an order where none is known (smallest 356 = 4*89)
small-steiner-3-designs-open	Record tables	standard	laptop-days	known-unknowns/record-tables/small-steiner-3-designs-open.md	Small Steiner 3-designs: construct S(3,5,41), S(3,6,46) or S(3,5,50), the open cases with v <= 50
small-ramsey-lower-bounds	Record tables	harvest	laptop-hours	known-unknowns/record-tables/small-ramsey-lower-bounds.md	Small two-color Ramsey numbers: new lower bounds via explicit graphs
smallest-cubic-crossing-number-graphs	Graphs, games and automata	harvest	laptop-days	known-unknowns/graphs-games-automata/smallest-cubic-crossing-number-graphs.md	Smallest cubic graphs with crossing number 12-15: beat an upper bound in OEIS A110507 (a(12) <= 30, a(13) <= 30, a(14) <= 36, a(15) <= 40)
snark-girth-7-smallest	Graphs, games and automata	standard	laptop-days for structu…	known-unknowns/graphs-games-automata/snark-girth-7-smallest.md	Smallest snark of girth 7: find one below 298 vertices (none exist up to 42), or a cyclically 7-edge-connected snark
qrac-qutrit-three-trits-smallest-open	Physics	standard	laptop-hours	known-unknowns/physics/qrac-qutrit-three-trits-smallest-open.md	Smallest unsolved quantum random access code: three trits into one qutrit (n = d = D = 3), best 0.69715 vs bounds 0.69853 (projective only) and about 0.699 (general POVMs, floatin…
smtlib-quantified-uf-uflia-unknown-refutation	Formal proofs	harvest	laptop-hours per benchm…	known-unknowns/formal-proofs/smtlib-quantified-uf-uflia-unknown-refutation.md	SMT-LIB quantified UF and UFLIA: a checked refutation or model for an unknown-status benchmark never decided at SMT-COMP
social-golfer-design-table-gaps	Optimization benchmarks	harvest	laptop-hours	known-unknowns/optimization-benchmarks/social-golfer-design-table-gaps.md	Social Golfer Problem (CSPLib 010): more rounds than the 2026 Miller-Valkov-Abel table for a (v,k) cell with at most 10 groups per round
tamam-shud-initialism	Unbroken ciphers	standard	laptop-hours	known-unknowns/unbroken-ciphers/tamam-shud-initialism.md	Somerton Man (Tamam Shud) code: exact initialism source search
sparse-ruler-excess-zero-beyond-213	Record tables	harvest	laptop-hours for constr…	known-unknowns/record-tables/sparse-ruler-excess-zero-beyond-213.md	Sparse rulers (minimal difference bases): fewer marks than Pegg's best-known table at some length n >= 245
gsp-pure-nash-poa-conjecture	Graphs, games and automata	standard	laptop-days	known-unknowns/graphs-games-automata/gsp-pure-nash-poa-conjecture.md	Sponsored-search GSP auction: a full-information pure Nash equilibrium (no overbidding) with welfare ratio above 1.259134, refuting the 2010 Lucier-Paes Leme conjecture (proven up…
square-site-percolation-threshold-13th-digit	Physics	standard	needs cluster	known-unknowns/physics/square-site-percolation-threshold-13th-digit.md	Square-lattice site percolation threshold: settle the 5-sigma clash between Yang-Zhou's 0.5927460507896(1) and Jacobsen's 0.59274605079016(1) (2024)
magic-state-stabilizer-rank-exponents	Physics	standard	laptop-days	known-unknowns/physics/magic-state-stabilizer-rank-exponents.md	Stabilizer rank of magic states: an exact decomposition of |T>^{(x)m} or |F>^{(x)m} into fewer stabilizer states than the best published exponent allows
superbridge-index-jeon-jin-candidates	Wildcard	standard	laptop-hours	known-unknowns/wildcard/superbridge-index-jeon-jin-candidates.md	Superbridge index: a polygon realising superbridge index 3 for one of Jeon-Jin's nine candidates (5_2, 6_1, ..., 8_9), or 4 for a 9-10 crossing knot listed [4,5]
superpatterns-seven-exact-length	Recreational math	standard	laptop-hours for upper-…	known-unknowns/recreational-math/superpatterns-seven-exact-length.md	Superpatterns: the shortest permutation containing all 5040 patterns of length 7 (OEIS A342474(7)), or the next row of A373778
swot-karin-noise-filtering-2022a	Earth and sky	harvest	laptop-hours	known-unknowns/earth-and-sky/swot-karin-noise-filtering-2022a.md	SWOT KaRIn noise-filtering data challenge 2022a: beat the leaderboard's best vorticity or current RMSE on cycle 13
symmetric-rendezvous-records	Graphs, games and automata	harvest	laptop-days	known-unknowns/graphs-games-automata/symmetric-rendezvous-records.md	Symmetric rendezvous search: a line strategy below Han et al.'s 4.2574 (unchanged since 2008) or a four-location strategy beating FSD
termcomp-tpdb-never-solved-certified	Formal proofs	harvest	laptop-hours to laptop-…	known-unknowns/formal-proofs/termcomp-tpdb-never-solved-certified.md	Termination Competition: a CeTA-certified termination or nontermination proof for a TPDB rewriting benchmark never solved at termCOMP 2023-2026
ternary-self-dual-largest-min-weight-12m	Record tables	standard	laptop-days for structu…	known-unknowns/record-tables/ternary-self-dual-largest-min-weight-12m.md	Ternary self-dual codes: raise the largest known minimum weight at length 84, 108 or 120
cryptocellar-truppenschluessel-1941	Unbroken ciphers	standard	laptop-hours	known-unknowns/unbroken-ciphers/cryptocellar-truppenschluessel-1941.md	The last 7 unbroken German Army Truppenschlüssel (TS) hand-cipher messages, 1941 (CryptoCellar)
r-sols-order-14-r-193	Record tables	standard	laptop-days	known-unknowns/record-tables/r-sols-order-14-r-193.md	The last open case of the r-self-orthogonal Latin square spectrum: a 193-SOLS of order 14
adfgvx-1918-nine-open	Unbroken ciphers	harvest	laptop-hours	known-unknowns/unbroken-ciphers/adfgvx-1918-nine-open.md	The still-open 1918 ADFGVX radiograms (Childs collection, Lasry/Schmeh 2017 challenge)
three-agent-additive-chores-efx	Graphs, games and automata	standard	laptop-hours to laptop-…	known-unknowns/graphs-games-automata/three-agent-additive-chores-efx.md	Three agents dividing additive chores: does a complete EFX allocation always exist?
all-in-three-player-ruin-angel-holmes-conjecture	Graphs, games and automata	standard	laptop-hours for a poin…	known-unknowns/graphs-games-automata/all-in-three-player-ruin-angel-holmes-conjecture.md	Three-player all-in betting game (Angel-Holmes): is being short-stacked always worse than tying your opponent? Prove or refute Conjecture 9
three-player-kuhn-equilibrium-completeness	Graphs, games and automata	standard	laptop-hours	known-unknowns/graphs-games-automata/three-player-kuhn-equilibrium-completeness.md	Three-player Kuhn poker: does the Szafron-Gibson-Sturtevant family contain every Nash equilibrium (on the path of play)?
three-player-von-neumann-poker-equilibrium	Graphs, games and automata	standard	laptop-minutes to lapto…	known-unknowns/graphs-games-automata/three-player-von-neumann-poker-equilibrium.md	Three-player von Neumann poker (Krityakierne-Thanatipanonda-Zeilberger 2024): is the conjectured threshold equilibrium a Nash equilibrium at bet size 2?
slide-24-puzzle-lower-bound	Graphs, games and automata	harvest	laptop-hours	known-unknowns/graphs-games-automata/slide-24-puzzle-lower-bound.md	Tighten God's number bounds for the 24-puzzle (5x5 sliding tiles, STM)
revenge-gods-number-bounds	Graphs, games and automata	harvest	laptop-hours	known-unknowns/graphs-games-automata/revenge-gods-number-bounds.md	Tighten God's number bounds for the 4x4x4 cube (OBTM)
tsb-ad-m-beat-leaderboard-vus-pr	Machine learning	harvest	laptop-hours	known-unknowns/machine-learning/tsb-ad-m-beat-leaderboard-vus-pr.md	TSB-AD multivariate anomaly detection: beat the leaderboard's best average VUS-PR on the evaluation set
varbench-variational-energy-records	Physics	standard	laptop-days	known-unknowns/physics/varbench-variational-energy-records.md	VarBench: a lower variational ground-state energy than every row of a VarBench table (e.g. J1-J2 10x10 at J2 = 0.8-1.0, pyrochlore, triangular, kagome)
tsp-vlsi-open-tours	Optimization benchmarks	harvest	laptop-hours to laptop-…	known-unknowns/optimization-benchmarks/tsp-vlsi-open-tours.md	VLSI TSP collection (Bonn / Waterloo): a shorter tour for one of the 30 unsolved instances (14,233 to 744,710 cities)
vnncomp-verifier-holds-soundness-counterexample	ML robustness	harvest	laptop-hours	known-unknowns/ml-robustness/vnncomp-verifier-holds-soundness-counterexample.md	VNN-COMP verifier soundness: a validated counterexample for an instance that a participating tool certified as 'holds'
voynich-generator-heldout-fingerprints	Undeciphered scripts	harvest	laptop-hours	known-unknowns/undeciphered-scripts/voynich-generator-heldout-fingerprints.md	Voynich: a manually executable generator that matches held-out structural fingerprints, or a decisive falsification of the Naibbe cipher
walshaw-graph-partitioning-archive	Optimization benchmarks	harvest	laptop-hours	known-unknowns/optimization-benchmarks/walshaw-graph-partitioning-archive.md	Walshaw Graph Partitioning Archive: beat a best known edge cut (k = 2..64, 0/1/3/5% imbalance)
s2s-ai-challenge-2020-rpss	Earth and sky	standard	laptop-days	known-unknowns/earth-and-sky/s2s-ai-challenge-2020-rpss.md	WMO S2S AI Challenge: beat the best RPSS for week 3-4 and 5-6 temperature and precipitation tercile forecasts in 2020
censorship-manual-steganograms	Unbroken ciphers	standard	laptop-hours	known-unknowns/unbroken-ciphers/censorship-manual-steganograms.md	WWII British censorship manual steganograms: locate the Morse code in the fashion drawing and recover the German text in the Amsterdam map
zarankiewicz-k33-k44-square-next-values	Record tables	harvest	laptop-days	known-unknowns/record-tables/zarankiewicz-k33-k44-square-next-values.md	Zarankiewicz numbers for K_{3,3} and K_{4,4}: the exact values z(17;3,3) and z(14;4,4) (next terms of OEIS A001198 and A006616)
magic-square-squares-7	Number hunts	standard	laptop-hours	known-unknowns/number-hunts/magic-square-squares-7.md	3x3 magic square with >= 7 square entries (second example) or nine squares
fourth-powers-three-ways-taxicab-4-2-3	Number hunts	moonshot	needs cluster	known-unknowns/number-hunts/fourth-powers-three-ways-taxicab-4-2-3.md	A number that is a sum of two fourth powers in three different ways (Taxicab(4,2,3))
abelian-difference-sets-open-ljcr	Record tables	harvest	laptop-hours to laptop-…	known-unknowns/record-tables/abelian-difference-sets-open-ljcr.md	Abelian difference sets: settle an 'Open' group entry with v <= 1000 in Gordon's La Jolla Difference Set Repository
alphaevolve-analytic-constants	Record tables	standard	laptop-hours	known-unknowns/record-tables/alphaevolve-analytic-constants.md	AlphaEvolve-family analytic constants: autocorrelation inequalities and Erdos minimum overlap
aac-second-counterexample	Number hunts	moonshot	needs cluster	known-unknowns/number-hunts/aac-second-counterexample.md	Ankeny-Artin-Chowla after Reinhart's counterexample: a second prime p = 1 mod 4 with p | y, or an independent check below 3.4e14
antihydra-collatz-cryptid	Number hunts	moonshot	pure thought	known-unknowns/number-hunts/antihydra-collatz-cryptid.md	Antihydra (BB(6) Cryptid): prove non-halting (Collatz-like / Mahler 3/2 problem)
chinese-gold-bars	Unbroken ciphers	standard	laptop-minutes	known-unknowns/unbroken-ciphers/chinese-gold-bars.md	Chinese gold bar cryptograms (Shanghai, 1933)
liber-primus-lp2	Unbroken ciphers	moonshot	laptop-hours	known-unknowns/unbroken-ciphers/liber-primus-lp2.md	Cicada 3301 Liber Primus: unsolved runic pages
quadratic-field-3-rank-record	Number hunts	standard	laptop-days	known-unknowns/number-hunts/quadratic-field-3-rank-record.md	Class groups of quadratic fields with record 3-rank: an imaginary quadratic field of 3-rank 9 (record 8, Elkies), or a real one of 3-rank 8
conway-99-graph	Graphs, games and automata	moonshot	laptop-hours	known-unknowns/graphs-games-automata/conway-99-graph.md	Conway's 99-graph, srg(99,14,1,2)
cosmetic-crossing-conjecture-counterexample	Wildcard	moonshot	laptop-days	known-unknowns/wildcard/cosmetic-crossing-conjecture-counterexample.md	Cosmetic crossing conjecture: a certified non-nugatory crossing change that preserves the knot type (KnotInfo lists 1,216 knots up to 13 crossings as open)
ultimate-enigma-challenge	Unbroken ciphers	moonshot	laptop-hours	known-unknowns/unbroken-ciphers/ultimate-enigma-challenge.md	CryptoCellar 'Ultimate Enigma Challenge' (5 Sept 1941 messages, possibly non-standard machine)
cubic-aacm-hirakawa-shimizu	Number hunts	moonshot	needs cluster for a cou…	known-unknowns/number-hunts/cubic-aacm-hirakawa-shimizu.md	Cubic Ankeny-Artin-Chowla-Mordell conjecture (Hirakawa-Shimizu): a prime p with p | beta for the fundamental unit of Q(p^(1/3)) or Q((2p)^(1/3)), or a certified verification for a…
cunningham-wanted-composites	Number hunts	harvest	needs cluster for NFS o…	known-unknowns/number-hunts/cunningham-wanted-composites.md	Cunningham project: a new factor of a composite cofactor of b^n +- 1 (b = 2..12), above all from the wanted lists
cypro-minoan-signary-crossscript	Undeciphered scripts	standard	laptop-hours	known-unknowns/undeciphered-scripts/cypro-minoan-signary-crossscript.md	Cypro-Minoan: sign-inventory merges and Cypriot-syllabary value transfer tested on held-out inscriptions
dorabella-1897	Unbroken ciphers	standard	laptop-hours	known-unknowns/unbroken-ciphers/dorabella-1897.md	Dorabella cipher (Elgar, 1897)
sixth-powers-equal-sums	Number hunts	standard	laptop-hours	known-unknowns/number-hunts/sixth-powers-equal-sums.md	Equal sums of sixth powers: 6.1.5 / 6.1.6 (Euler conjecture k=6) and 6.2.2
erdos-287-egyptian-gaps	Erdős problems and proofs	standard	pure thought	known-unknowns/erdos-and-proofs/erdos-287-egyptian-gaps.md	Erdos #287: unit-fraction representations of 1 must have a gap >= 3, for a full proof
erdos-993-tree-independence-unimodality	Erdős problems and proofs	standard	laptop-hours	known-unknowns/erdos-and-proofs/erdos-993-tree-independence-unimodality.md	Erdos #993: a tree (or forest) with non-unimodal independent-set sequence
fermat-catalan-new-solution-with-square	Number hunts	moonshot	needs cluster	known-unknowns/number-hunts/fermat-catalan-new-solution-with-square.md	Fermat-Catalan: an eleventh solution of a^m + b^n = c^k with 1/m + 1/n + 1/k < 1 (one exponent equal to 2)
first-continuous-gw-signal-confirmed-candidate	Sky archives	moonshot	needs cluster for broad…	known-unknowns/sky-archives/first-continuous-gw-signal-confirmed-candidate.md	First continuous gravitational-wave signal: a candidate in public LIGO data confirmed in an independent observing run
costas-order-32	Graphs, games and automata	moonshot	laptop-hours	known-unknowns/graphs-games-automata/costas-order-32.md	First Costas array of order 32 or 33
gwosc-o4-subsolar-mass-binary-candidate	Sky archives	moonshot	needs cluster for a ful…	known-unknowns/sky-archives/gwosc-o4-subsolar-mass-binary-candidate.md	First significant sub-solar-mass compact-binary candidate in public LIGO-Virgo strain (O1-O4b)
four-agent-additive-goods-efx-obstruction	Graphs, games and automata	moonshot	laptop-hours to laptop-…	known-unknowns/graphs-games-automata/four-agent-additive-goods-efx-obstruction.md	Four additive agents: an exact finite counterexample to complete EFX existence
willow-surface-code-d7-decoding	Physics	standard	laptop-days	known-unknowns/physics/willow-surface-code-d7-decoding.md	Google Willow surface-code memory (public data): decode the distance-7 experiment to a logical error per cycle below the neural decoder's 1.43e-3
goormaghtigh-new-solution	Number hunts	moonshot	needs cluster	known-unknowns/number-hunts/goormaghtigh-new-solution.md	Goormaghtigh conjecture: a third number that is a repunit ( > = 3 digits) in two bases
grundys-game-periodicity	Graphs, games and automata	moonshot	needs cluster for a new…	known-unknowns/graphs-games-automata/grundys-game-periodicity.md	Grundy's game: certify an eventual period (or that of 0.6111...), beyond Flammenkamp's 2^39 computation
hadwiger-nelson-six-or-seven	Erdős problems and proofs	moonshot	laptop-hours for bounde…	known-unknowns/erdos-and-proofs/hadwiger-nelson-six-or-seven.md	Hadwiger–Nelson: does the plane require six colours or seven?
debosnys-1883	Unbroken ciphers	standard	laptop-hours	known-unknowns/unbroken-ciphers/debosnys-1883.md	Henry Debosnys cryptograms (1882-83)
vesuvius-first-letters-unread	Herculaneum scrolls	standard	needs cluster	known-unknowns/herculaneum-scrolls/vesuvius-first-letters-unread.md	Herculaneum papyri: first legible letters in one of the 21 still-unread Vesuvius Challenge First Letters scrolls (official credit only)
hofstadter-q-sequence-death	Number hunts	moonshot	needs cluster	known-unknowns/number-hunts/hofstadter-q-sequence-death.md	Hofstadter's Q-sequence: does it die? Find an n where Q(n) is undefined, or push the existence frontier past 3*10^10
isthmian-family-bayes	Undeciphered scripts	standard	laptop-hours	known-unknowns/undeciphered-scripts/isthmian-family-bayes.md	Isthmian (Epi-Olmec): reproducible language-family test and a check of the Justeson-Kaufman grid on texts it was not built from
jetclass-ten-class-accuracy-auc	Particle physics	moonshot	needs cluster	known-unknowns/particle-physics/jetclass-ten-class-accuracy-auc.md	JetClass 10-class jet tagging: beat L-GATr's 0.866 accuracy and 0.9885 macro AUC on the 20M-jet test set
khitan-small-unread-graphemes	Undeciphered scripts	standard	laptop-hours	known-unknowns/undeciphered-scripts/khitan-small-unread-graphemes.md	Khitan small script: phonetic values for unread graphemes from Chinese loanwords and titles
kissing-number-low-dim	Record tables	moonshot	laptop-hours	known-unknowns/record-tables/kissing-number-low-dim.md	Kissing number lower bounds in dimensions 9-23
kryptos-k4-method	Unbroken ciphers	moonshot	laptop-hours	known-unknowns/unbroken-ciphers/kryptos-k4-method.md	Kryptos K4: recover the encryption METHOD (plaintext known only to Sanborn and archive owners)
fifth-powers-lps-5-2-2-or-5-1-3	Number hunts	moonshot	needs cluster	known-unknowns/number-hunts/fifth-powers-lps-5-2-2-or-5-1-3.md	Lander-Parkin-Selfridge at k = 5: a solution of a^5 + b^5 = c^5 + d^5 (5.2.2) or a^5 + b^5 + c^5 = d^5 (5.1.3)
langton-ant-highway	Graphs, games and automata	moonshot	laptop-hours	known-unknowns/graphs-games-automata/langton-ant-highway.md	Langton's ant highway conjecture
cap-set-dim7-dim8	Record tables	moonshot	laptop-hours	known-unknowns/record-tables/cap-set-dim7-dim8.md	Larger cap sets in F_3^7 (beat 236) or F_3^8 (beat 512)
largest-small-even-polygons-area	Packings and physics	standard	laptop-hours	known-unknowns/packings-physics/largest-small-even-polygons-area.md	Largest small polygons: a convex n-gon of diameter 1 with larger area than Bingane-Mossinghoff's P_n* for some even n = 14..120
lehmer-totient	Number hunts	moonshot	pure thought	known-unknowns/number-hunts/lehmer-totient.md	Lehmer's totient problem: composite n with phi(n) | n - 1
lerch-primes-sixth	Number hunts	standard	laptop-days	known-unknowns/number-hunts/lerch-primes-sixth.md	Lerch primes: a sixth one beyond 2*10^8 (OEIS A197632)
linear-elamite-residual-signs	Undeciphered scripts	standard	laptop-hours	known-unknowns/undeciphered-scripts/linear-elamite-residual-signs.md	Linear Elamite: values for the 4 undeciphered signs, and a predictive test of the 2022 grid
antichess-open-first-moves	Graphs, games and automata	standard	needs cluster	known-unknowns/graphs-games-automata/antichess-open-first-moves.md	Losing chess (antichess): solve one of White's six first moves still marked Unknown (1.a4, 1.b3, 1.c4, 1.g3, 1.g4, 1.Nh3)
matbench-large-mp-tasks	Chemistry and materials	standard	needs cluster	known-unknowns/chemistry-materials/matbench-large-mp-tasks.md	Matbench v0.1 large tasks (mp_e_form, mp_gap, mp_is_metal): beat the best published Matbench-protocol score (JMP-L's 0.0101 eV/atom and 0.091 eV, CGCNN's 0.9520 balanced accuracy)
modded-nanogpt-track1-wallclock-record	Machine learning	moonshot	needs cluster	known-unknowns/machine-learning/modded-nanogpt-track1-wallclock-record.md	Modded-NanoGPT speedrun: train to 3.28 FineWeb val loss on 8xH100 faster than the 39.9 s README record (and the pending claims)
fmm-4x4x4-rank47-3x3x3-rank22	Algorithms	moonshot	laptop-hours	known-unknowns/algorithms/fmm-4x4x4-rank47-3x3x3-rank22.md	MOONSHOT - 4x4 matrices with 47 multiplications in characteristic 0, or 3x3 matrices with 22
szilassi-12-face-neighborly-polyhedron	Wildcard	moonshot	needs cluster for full…	known-unknowns/wildcard/szilassi-12-face-neighborly-polyhedron.md	MOONSHOT - A 12-face Szilassi-type polyhedron: an embedded genus-6 polyhedron whose 12 faces pairwise share an edge
dujella-dn-quadruple-exceptional-n	Number hunts	moonshot	needs cluster	known-unknowns/number-hunts/dujella-dn-quadruple-exceptional-n.md	MOONSHOT - a D(n)-quadruple for n in {-3, 3, 5, 8, 12, 20} (disprove Dujella's conjecture)
wilson-prime-beyond-2e13	Number hunts	moonshot	needs cluster	known-unknowns/number-hunts/wilson-prime-beyond-2e13.md	MOONSHOT - a fourth Wilson prime (p^2 | (p-1)! + 1) beyond 2*10^13
pg2-128-new-hyperoval	Record tables	moonshot	laptop-days for search	known-unknowns/record-tables/pg2-128-new-hyperoval.md	MOONSHOT - A hyperoval in PG(2,128) not equivalent to any known hyperoval
vandiver-euler-prime-beyond-1e11	Number hunts	moonshot	needs cluster	known-unknowns/number-hunts/vandiver-euler-prime-beyond-1e11.md	MOONSHOT - a ninth Vandiver (Euler) prime, p | E_(p-3), beyond 10^11 (OEIS A198245)
rational-diophantine-septuple	Number hunts	moonshot	laptop-hours	known-unknowns/number-hunts/rational-diophantine-septuple.md	MOONSHOT - a rational Diophantine septuple
unitary-perfect-sixth-erdos-1052	Number hunts	moonshot	laptop-days	known-unknowns/number-hunts/unitary-perfect-sixth-erdos-1052.md	MOONSHOT - a sixth unitary perfect number (Erdős #1052, OEIS A002827)
wieferich-base-2-beyond-2-64	Number hunts	moonshot	needs cluster	known-unknowns/number-hunts/wieferich-base-2-beyond-2-64.md	MOONSHOT - a third Wieferich prime (p^2 | 2^(p-1) - 1) beyond 2^64
wolstenholme-prime-beyond-1e11	Number hunts	moonshot	needs cluster	known-unknowns/number-hunts/wolstenholme-prime-beyond-1e11.md	MOONSHOT - a third Wolstenholme prime (p | B_(p-3) numerator, i.e. C(2p-1,p-1) == 1 mod p^4) beyond 10^11
wall-sun-sun-prime-beyond-2-64	Number hunts	moonshot	needs cluster	known-unknowns/number-hunts/wall-sun-sun-prime-beyond-2-64.md	MOONSHOT - a Wall-Sun-Sun (Fibonacci-Wieferich) prime: p^2 | F_(p - (p/5)), beyond 2^64
four-nonnegative-cubes-dhl-counterexample	Number hunts	moonshot	needs cluster	known-unknowns/number-hunts/four-nonnegative-cubes-dhl-counterexample.md	MOONSHOT - an integer above 7373170279850 that is not a sum of four nonnegative cubes (Deshouillers-Hennecart-Landreau)
burnside-b25-finite-presentation	Wildcard	moonshot	needs cluster	known-unknowns/wildcard/burnside-b25-finite-presentation.md	MOONSHOT - Burnside group B(2,5): finite or infinite? (with Kourovka 11.48, Kostrikin's fifth-power question)
chromatic-number-r3-7-chromatic-udg	Erdős problems and proofs	moonshot	needs cluster	known-unknowns/erdos-and-proofs/chromatic-number-r3-7-chromatic-udg.md	MOONSHOT - Chromatic number of 3-space: a finite unit-distance graph in R^3 that is not 6-colourable (lower bound 6, upper bound 15)
chvatal-conjecture-ground-set-8	Erdős problems and proofs	moonshot	needs cluster	known-unknowns/erdos-and-proofs/chvatal-conjecture-ground-set-8.md	MOONSHOT - Chvátal's conjecture (Erdős #701): a downset whose largest intersecting subfamily beats every star, or a certified verification for ground sets of 8 elements
classical-ramsey-upper-bounds-certified	Record tables	moonshot	needs cluster	known-unknowns/record-tables/classical-ramsey-upper-bounds-certified.md	MOONSHOT - Classical Ramsey upper bounds with machine-checkable certificates: R(3,3,3,3) <= 60, R(3,10) <= 40, R(4,6) <= 39, R(5,5) <= 45, R(3,3,5) <= 56, R(3,4,4) <= 76
congruent-ellipsoids-densest-packing	Packings and physics	moonshot	laptop-days	known-unknowns/packings-physics/congruent-ellipsoids-densest-packing.md	MOONSHOT - Congruent ellipsoids: a periodic packing denser than the Donev-Stillinger-Chaikin-Torquato SM2 crystal (0.770732, aspect ratios >= sqrt3)
davenport-rank-3-above-dstar	Number hunts	moonshot	laptop-days	known-unknowns/number-hunts/davenport-rank-3-above-dstar.md	MOONSHOT - Davenport constant in rank 3: a group C_n1 + C_n2 + C_n3 with D(G) > D*(G)
cohn-sphere-packing-density-table	Record tables	moonshot	laptop-hours	known-unknowns/record-tables/cohn-sphere-packing-density-table.md	MOONSHOT - denser sphere packing than Cohn's table in some dimension 10..48
cube-domino-tilings-a028446-8x8x8	Graphs, games and automata	moonshot	needs cluster	known-unknowns/graphs-games-automata/cube-domino-tilings-a028446-8x8x8.md	MOONSHOT - Domino tilings of the 8 x 8 x 8 cube: the exact count A028446(4) (6 x 6 x 6 solved in March 2026)
durer-convex-edge-unfolding-counterexample	Wildcard	moonshot	laptop-days for candida…	known-unknowns/wildcard/durer-convex-edge-unfolding-counterexample.md	MOONSHOT - Dürer's problem: a convex polyhedron with no edge unfolding to a net
earth-moon-biplanar-10-chromatic	Erdős problems and proofs	moonshot	laptop-hours	known-unknowns/erdos-and-proofs/earth-moon-biplanar-10-chromatic.md	MOONSHOT - Earth-Moon problem: a biplanar (thickness-2) graph with chromatic number 10
etp-finite-magma-677-255	Formal proofs	moonshot	laptop-hours	known-unknowns/formal-proofs/etp-finite-magma-677-255.md	MOONSHOT - Equational Theories Project: settle the last 2 finite-magma implications (Eq677 ⇒ Eq255, Eq2910 ⇒ Eq47)
erdos-107-happy-ending-n7	Erdős problems and proofs	moonshot	needs cluster	known-unknowns/erdos-and-proofs/erdos-107-happy-ending-n7.md	MOONSHOT - Erdos #107 (Happy Ending): 33 points with no convex heptagon
erdos-7-odd-covering-system	Erdős problems and proofs	moonshot	needs cluster	known-unknowns/erdos-and-proofs/erdos-7-odd-covering-system.md	MOONSHOT - Erdos #7 / Selfridge: a covering system with distinct odd moduli
erdos-723-projective-plane-order-12	Erdős problems and proofs	moonshot	needs cluster	known-unknowns/erdos-and-proofs/erdos-723-projective-plane-order-12.md	MOONSHOT - Erdos #723: a projective plane of order 12 (fallback: 6 MOLS of order 12)
egz-odd-exponent-rank3-9n-8	Number hunts	moonshot	laptop-days	known-unknowns/number-hunts/egz-odd-exponent-rank3-9n-8.md	MOONSHOT - Erdős–Ginzburg–Ziv constant for odd n: refute s(C_n^3) = 9n-8 (smallest open n = 7) or beat 20n-19 in rank 4
eternity-ii-480-edge-board	Recreational math	moonshot	needs cluster	known-unknowns/recreational-math/eternity-ii-480-edge-board.md	MOONSHOT - Eternity II: the full 480-edge solution, or a board beating the 470/480 record (or the 465 five-clue record)
euclid-mullin-a52	Number hunts	moonshot	needs cluster	known-unknowns/number-hunts/euclid-mullin-a52.md	MOONSHOT - Euclid-Mullin sequence: the 52nd term (least prime factor of a 335-digit number)
mub-dimension-six-four-bases	Physics	moonshot	laptop-days	known-unknowns/physics/mub-dimension-six-four-bases.md	MOONSHOT - Four mutually unbiased bases in C^6 (only three known), or a checkable proof that none exist
gerstenhaber-commuting-triples	Erdős problems and proofs	moonshot	laptop-hours	known-unknowns/erdos-and-proofs/gerstenhaber-commuting-triples.md	MOONSHOT - Gerstenhaber problem: three commuting d x d matrices generating an algebra of dimension > d (or reducibility of C(3,d) for some 11 <= d <= 28)
goldbach-verification-beyond-4e18	Number hunts	moonshot	needs cluster	known-unknowns/number-hunts/goldbach-verification-beyond-4e18.md	MOONSHOT - Goldbach verification beyond 4 x 10^18 (Oliveira e Silva, Herzog and Pardi, 2012/2014)
graceful-tree-conjecture-beyond-35	Graphs, games and automata	moonshot	needs cluster	known-unknowns/graphs-games-automata/graceful-tree-conjecture-beyond-35.md	MOONSHOT - Graceful tree (Ringel-Kotzig) conjecture: a tree with no graceful labeling, a formal proof, or the first verification past Fang's 35 vertices
helium-ground-state-energy-digits	Physics	moonshot	laptop-days	known-unknowns/physics/helium-ground-state-energy-digits.md	MOONSHOT - Helium atom nonrelativistic ground-state energy: more correct digits than Schwartz's 2006 record
hilbert-16-quadratic-fifth-limit-cycle	Wildcard	moonshot	laptop-hours per candid…	known-unknowns/wildcard/hilbert-16-quadratic-fifth-limit-cycle.md	MOONSHOT - Hilbert's 16th problem for quadratic systems: a quadratic vector field with five limit cycles (H(2) >= 4 since Shi 1980)
home-prime-hp49	Number hunts	moonshot	needs cluster	known-unknowns/number-hunts/home-prime-hp49.md	MOONSHOT - home prime HP(49) = HP(77): factor the c251 at step 119 and continue to a prime
henon-classical-parameters-sink	Physics	moonshot	needs cluster	known-unknowns/physics/henon-classical-parameters-sink.md	MOONSHOT - Is the Henon attractor a sink? A certified attracting periodic orbit at exactly (a, b) = (1.4, 0.3), or a sink closer than Galias-Tucker's
kurepa-left-factorial-beyond-2-40	Number hunts	moonshot	needs cluster	known-unknowns/number-hunts/kurepa-left-factorial-beyond-2-40.md	MOONSHOT - Kurepa's left factorial conjecture: an odd prime p dividing !p = 0!+1!+...+(p-1)!, beyond 2^40
hamming-cube-l1-poincare-c11a-lower-bound	Erdős problems and proofs	moonshot	laptop-hours per candid…	known-unknowns/erdos-and-proofs/hamming-cube-l1-poincare-c11a-lower-bound.md	MOONSHOT - L1 Poincare constant of the Hamming cube (C_11a): a function on {-1,1}^n with ratio above sqrt(pi/2)
marcus-de-oliveira-determinantal-conjecture	Erdős problems and proofs	moonshot	laptop-hours	known-unknowns/erdos-and-proofs/marcus-de-oliveira-determinantal-conjecture.md	MOONSHOT - Marcus-de Oliveira determinantal conjecture: normal A, B with det(A + B) outside the convex hull of the n! eigenvalue products
matbench-discovery-cps-f1-kappa	Physics	moonshot	needs cluster	known-unknowns/physics/matbench-discovery-cps-f1-kappa.md	MOONSHOT - Matbench Discovery: beat the live best Combined Performance Score (0.912) with an openly released interatomic potential (the F1 0.931 and κ_SRME 0.0648 records are part…
neumann-lara-planar-2-dicolouring	Graphs, games and automata	moonshot	laptop-days for extendi…	known-unknowns/graphs-games-automata/neumann-lara-planar-2-dicolouring.md	MOONSHOT - Neumann-Lara conjecture: a planar oriented graph that cannot be split into two acyclic sets, or verification beyond 26 vertices
hypercube-q8-perfect-matchings	Graphs, games and automata	moonshot	needs cluster	known-unknowns/graphs-games-automata/hypercube-q8-perfect-matchings.md	MOONSHOT - Perfect matchings of the 8-cube: the exact count A005271(8)
planet-nine-distant-tno-archival-moonshot	Sky archives	moonshot	laptop-hours to laptop-…	known-unknowns/sky-archives/planet-nine-distant-tno-archival-moonshot.md	MOONSHOT - Planet Nine or a new extreme distant TNO candidate in public archival survey images
posets-topologies-17-unlabeled-20-labeled	Wildcard	moonshot	needs cluster	known-unknowns/wildcard/posets-topologies-17-unlabeled-20-labeled.md	MOONSHOT - Posets and topologies: unlabeled counts on 17 points (A000112, A001930) or labeled counts on 20 points (A001035, A000798)
post-tag-00-1101-problem	Graphs, games and automata	moonshot	needs cluster for exhau…	known-unknowns/graphs-games-automata/post-tag-00-1101-problem.md	MOONSHOT - Post's 1921 tag problem (00, 1101; delete 3): a word that never halts or cycles, or a proof that none exists
regular-heptagon-densest-packing	Packings and physics	moonshot	laptop-hours	known-unknowns/packings-physics/regular-heptagon-densest-packing.md	MOONSHOT - Regular heptagons in the plane: a packing of congruent regular heptagons denser than the Kuperberg double lattice (0.8926906861...)
regular-tetrahedra-densest-packing	Packings and physics	moonshot	laptop-days	known-unknowns/packings-physics/regular-tetrahedra-densest-packing.md	MOONSHOT - Regular tetrahedra: a packing of congruent regular tetrahedra denser than the Chen-Engel-Glotzer dimer double lattice 4000/4671 = 0.856347...
riemann-hypothesis-verification-height	Number hunts	moonshot	needs cluster for a new…	known-unknowns/number-hunts/riemann-hypothesis-verification-height.md	MOONSHOT - Riemann hypothesis verified beyond Platt-Trudgian's height 3.0001753328 x 10^12, or a rigorous window above it
rubiks-cube-qtm-distance-25-26	Graphs, games and automata	moonshot	laptop-hours	known-unknowns/graphs-games-automata/rubiks-cube-qtm-distance-25-26.md	MOONSHOT - Rubik's Cube in the quarter-turn metric: a new position at distance 26, or a third distance-25 position
kochen-specker-minimum-r3	Physics	moonshot	laptop-days	known-unknowns/physics/kochen-specker-minimum-r3.md	MOONSHOT - Smallest Kochen-Specker vector system in R^3: find one with at most 30 vectors (known range 24..31)
srg-open-parameter-existence	Record tables	moonshot	laptop-hours	known-unknowns/record-tables/srg-open-parameter-existence.md	MOONSHOT - Strongly regular graphs: construct an srg for an open parameter set in Brouwer's table
n-queens-q28	Graphs, games and automata	moonshot	needs cluster	known-unknowns/graphs-games-automata/n-queens-q28.md	MOONSHOT - The 28-queens count Q(28) (OEIS A000170(28), open since the Q27 project in 2016)
groups-of-order-2048-count	Wildcard	moonshot	needs cluster	known-unknowns/wildcard/groups-of-order-2048-count.md	MOONSHOT - The exact number of groups of order 2048
lehmer-five-aliquot	Number hunts	moonshot	needs cluster	known-unknowns/number-hunts/lehmer-five-aliquot.md	MOONSHOT - the Lehmer five: decide the fate of the aliquot sequence of 276, 552, 564, 660 or 966
dedekind-number-d10	Number hunts	moonshot	needs cluster	known-unknowns/number-hunts/dedekind-number-d10.md	MOONSHOT - The tenth Dedekind number D(10) (OEIS A000372(10)) or inequivalent monotone Boolean functions of 10 variables (A003182(10))
three-mols-order-10	Record tables	moonshot	needs cluster	known-unknowns/record-tables/three-mols-order-10.md	MOONSHOT - Three mutually orthogonal Latin squares of order 10 (is N(10) >= 3?)
torquato-jiao-centrosymmetric-polyhedra	Packings and physics	moonshot	laptop-days	known-unknowns/packings-physics/torquato-jiao-centrosymmetric-polyhedra.md	MOONSHOT - Torquato-Jiao conjecture: a non-lattice packing of a centrally symmetric Platonic or Archimedean solid denser than its optimal lattice packing
hanoi-five-peg-frame-stewart	Recreational math	moonshot	needs cluster	known-unknowns/recreational-math/hanoi-five-peg-frame-stewart.md	MOONSHOT - Tower of Hanoi with five or more pegs: a move sequence shorter than Frame-Stewart, or an extension of the exhaustive verification beyond Hinz-Petr's frontier
world-tsp-shorter-tour	Optimization benchmarks	moonshot	laptop-days to weeks	known-unknowns/optimization-benchmarks/world-tsp-shorter-tour.md	MOONSHOT - World TSP (1,904,711 cities): a tour shorter than Nagata's 7,515,755,912
ecpp-famous-unproven-prps	Number hunts	moonshot	needs cluster	known-unknowns/number-hunts/ecpp-famous-unproven-prps.md	MOONSHOT: an ECPP proof of a famous probable prime: Wagstaff (2^267017+1)/3, Lucas L(344293) or Fibonacci F(397379)
indus-decipherment	Undeciphered scripts	moonshot	laptop-days / pure thou…	known-unknowns/undeciphered-scripts/indus-decipherment.md	MOONSHOT: Indus script, sign values or meanings that predict held-out seals
linear-a-language-identification	Undeciphered scripts	moonshot	laptop-days / pure thou…	known-unknowns/undeciphered-scripts/linear-a-language-identification.md	MOONSHOT: Linear A, identifying the Minoan language with predictive translations
voynich-plaintext	Undeciphered scripts	moonshot	laptop-days	known-unknowns/undeciphered-scripts/voynich-plaintext.md	MOONSHOT: Voynich manuscript, a key that decrypts held-out folios into meaningful text
sudoku-minimal-puzzle-41-clues	Recreational math	moonshot	laptop-days	known-unknowns/recreational-math/sudoku-minimal-puzzle-41-clues.md	Most clues in a minimal 9 x 9 Sudoku: a minimal puzzle with 41 clues (only two 40-clue minimal puzzles are known)
moustier-altar-inscriptions	Unbroken ciphers	standard	laptop-hours	known-unknowns/unbroken-ciphers/moustier-altar-inscriptions.md	Moustier altar inscriptions (two 19th-century coded inscriptions, St Martin's Church, Belgium)
cyclotomic-norm-euclidean-open-cases	Number hunts	moonshot	needs cluster	known-unknowns/number-hunts/cyclotomic-norm-euclidean-open-cases.md	Norm-Euclidean cyclotomic rings Z[zeta_m]: decide one of the open class-number-one cases (m = 17, 19, 25, 27, 28, 33, 35, 36, 40, 44, 45, 48, 60, 84)
octal-games-unsettled-periodicity	Graphs, games and automata	moonshot	laptop-days per game	known-unknowns/graphs-games-automata/octal-games-unsettled-periodicity.md	Octal games: certify the period of one unsettled octal game with at most three code digits in Flammenkamp's table
oracle-bone-undeciphered-chars	Undeciphered scripts	standard	laptop-hours	known-unknowns/undeciphered-scripts/oracle-bone-undeciphered-chars.md	Oracle bone script: identifications of undeciphered characters validated by held-out prediction
perfect-cuboid	Number hunts	moonshot	pure thought	known-unknowns/number-hunts/perfect-cuboid.md	Perfect cuboid (perfect Euler brick)
perfect-triangle	Number hunts	standard	laptop-hours	known-unknowns/number-hunts/perfect-triangle.md	Perfect triangle: integer sides, rational medians, integer area
rational-distance-unit-square	Number hunts	standard	laptop-hours	known-unknowns/number-hunts/rational-distance-unit-square.md	Rational distance problem for the unit square (four-distance problem)
alternating-prm-plus-ergodic-convergence	Algorithms	standard	pure thought plus a for…	known-unknowns/algorithms/alternating-prm-plus-ergodic-convergence.md	Regret matching+ inside CFR+/PCFR+: does alternating predictive RM+ converge ergodically? Prove RM+ non-convergence on the 3x3 counterexample game
reinhart-unusual-orders-d-divides-y	Number hunts	standard	needs cluster	known-unknowns/number-hunts/reinhart-unusual-orders-d-divides-y.md	Reinhart's open problem: squarefree d = pq or 2pq with h(d) = 2 and d | y (orders with unusual sets of distances)
ccd-water-clusters-tip4p-tip5p	Packings and physics	standard	laptop-hours	known-unknowns/packings-physics/ccd-water-clusters-tip4p-tip5p.md	Rigid-water clusters (TIP4P, TIP5P): lower a putative global minimum for (H2O)_N, N <= 21 on the CCD, or beyond against published values
self-dual-quantum-codes-13-qubits-count	Physics	standard	needs cluster	known-unknowns/physics/self-dual-quantum-codes-13-qubits-count.md	Self-dual quantum codes on 13 qubits: count the LC orbits of connected 13-vertex graphs (next term of OEIS A090899, known to n = 12)
z-channel-single-error-codes	Record tables	standard	laptop-hours to laptop-…	known-unknowns/record-tables/z-channel-single-error-codes.md	Single-error-correcting codes for the Z-channel: beat 112, 198 or 379 (Sloane's 1zc challenge graphs), or certify a tighter upper bound
extremal-doubly-even-self-dual-72	Record tables	moonshot	needs cluster for any s…	known-unknowns/record-tables/extremal-doubly-even-self-dual-72.md	Sloane's 1973 question: an extremal doubly-even self-dual binary [72,36,16] code
sums-of-three-cubes-114	Number hunts	moonshot	needs cluster	known-unknowns/number-hunts/sums-of-three-cubes-114.md	Sums of three cubes: k = 114, 390, 627, 633, 732, 921, 975, and a fourth representation of 3
kerdock-set-ternary-m6	Record tables	moonshot	needs cluster for search	known-unknowns/record-tables/kerdock-set-ternary-m6.md	Ternary Kerdock set of 6x6 matrices: 243 skew-symmetric matrices over GF(3) with all pairwise differences nonsingular
moore-graph-57	Graphs, games and automata	moonshot	pure thought	known-unknowns/graphs-games-automata/moore-graph-57.md	The missing Moore graph (degree 57, diameter 2)
gamblers-ruin-scaling-conjecture	Graphs, games and automata	standard	laptop-hours	known-unknowns/graphs-games-automata/gamblers-ruin-scaling-conjecture.md	Three-player gambler's ruin (the final-table ICM problem): a counterexample to the Diaconis-Ethier 0.0004 scaling conjecture
turan-tetrahedron-k4-3-density-upper-bound	Erdős problems and proofs	moonshot	needs cluster	known-unknowns/erdos-and-proofs/turan-tetrahedron-k4-3-density-upper-bound.md	Turán's tetrahedron problem (Erdős #500): a certified upper bound on pi(K4^(3)) below 0.55733, or a K4^(3)-free construction above 5/9
modular-hadamard-128-open-orders	Record tables	standard	laptop-days to needs cl…	known-unknowns/record-tables/modular-hadamard-128-open-orders.md	128-modular Hadamard matrix at an order with no known Hadamard matrix (smallest 2396), or a first explicit 64-modular one there
av1324-exact-counts-beyond-n50	Recreational math	moonshot	needs cluster	known-unknowns/recreational-math/av1324-exact-counts-beyond-n50.md	1324-avoiding permutations: the exact count |Av_51(1324)| (first term beyond Conway-Guttmann-Zinn-Justin's n = 50)
roman-microlensing-data-challenge-2018-planet-recovery	Planets and moons	standard	laptop-days	known-unknowns/planetary-science/roman-microlensing-data-challenge-2018-planet-recovery.md	2018 WFIRST/Roman Microlensing Data Challenge: one automated pipeline that recovers more planetary (s, q) solutions than all four entries
esicup-nesting-sparrow-strip-length-records	Optimization benchmarks	harvest	laptop-hours	known-unknowns/optimization-benchmarks/esicup-nesting-sparrow-strip-length-records.md	2D irregular strip packing (nesting, ESICUP and Gardeyn instances): a shorter strip than a record in sparrow's live records folder
five-gdd-type-gu-possible-exceptions	Record tables	harvest	laptop-hours to laptop-…	known-unknowns/record-tables/five-gdd-type-gu-possible-exceptions.md	5-GDDs of type g^u: settle a possible exception in Forbes' 2023 theorem (smallest 2^15, then 10^7)
asteroid-yorp-detection-beyond-twelve	Planets and moons	standard	laptop-hours	known-unknowns/planetary-science/asteroid-yorp-detection-beyond-twelve.md	A new YORP detection: significant change in an asteroid's rotation rate measured from decades of public lightcurves
type-2-cubic-graph-girth-5	Graphs, games and automata	standard	laptop-days for constru…	known-unknowns/graphs-games-automata/type-2-cubic-graph-girth-5.md	A Type 2 cubic graph of girth at least 5 (total chromatic number 5), open since Cavicchioli et al. 2003
alternating-sign-hypermatrices-a144017-n7	Recreational math	standard	laptop-days	known-unknowns/recreational-math/alternating-sign-hypermatrices-a144017-n7.md	Alternating sign hypermatrices: the number of 7 x 7 x 7 ASHMs, A144017(7) (a(6) found in Feb 2026)
andrews-curtis-ak3-trivialisation	Wildcard	moonshot	laptop-days	known-unknowns/wildcard/andrews-curtis-ak3-trivialisation.md	Andrews-Curtis: an AC-trivialisation of AK(3), or of one of the last two open length-14 Miller-Schupp classes
anuraset-multilabel-macro-f1	Ecology and bioacoustics	standard	laptop-hours	known-unknowns/ecology/anuraset-multilabel-macro-f1.md	AnuraSet neotropical frog calls: beat the best published test macro F1 (60.8, Mixture of Mixups) for 42-species multi-label classification
hjelmslev-plane-arcs-chain-rings-16-25	Record tables	harvest	laptop-hours	known-unknowns/record-tables/hjelmslev-plane-arcs-chain-rings-16-25.md	Arcs in projective Hjelmslev planes over chain rings of order 16 and 25: raise a lower bound in the Honold-Kiermaier-Landjev tables
pure-quartic-norm-euclidean-61-116	Number hunts	standard	laptop-hours to laptop-…	known-unknowns/number-hunts/pure-quartic-norm-euclidean-61-116.md	Are the pure quartic fields Q(13^(1/4)), Q(61^(1/4)) and Q(116^(1/4)) norm-Euclidean? (last open cases of Lemmermeyer's classification)
go1-final-event-scopf-best-scores	Optimization benchmarks	harvest	laptop-hours	known-unknowns/optimization-benchmarks/go1-final-event-scopf-best-scores.md	ARPA-E GO Competition Challenge 1 (continuous SCOPF): beat the best Final Event score on a public synthetic scenario
decipherment-cognate-matching-tamburini-benchmarks	Ancient texts and fragments	harvest	laptop-hours	known-unknowns/ancient-texts/decipherment-cognate-matching-tamburini-benchmarks.md	Automatic decipherment on known scripts: beat CSA_OptMatcher's mean cognate-matching accuracy on the seven Tamburini 2025 benchmarks (Ugaritic, Linear B, Cypriot, Phoenician, Luvi…
random-edit-distance-constant-c91-bounds	Erdős problems and proofs	standard	laptop-hours to laptop-…	known-unknowns/erdos-and-proofs/random-edit-distance-constant-c91-bounds.md	Average edit distance of two random binary strings (C_91): a certified bound beating 0.216276 <= alpha_2 <= 0.315514
bci-iv-ds4-ecog-finger-flexion-strict	Neuroscience	standard	laptop-hours	known-unknowns/neuroscience/bci-iv-ds4-ecog-finger-flexion-strict.md	BCI Competition IV dataset 4 (ECoG finger flexion): beat the best published mean correlation (0.69, DTCNet 2025) on the official test labels under a strict no-test-tuning protocol
ccd-binary-lennard-jones-clusters	Packings and physics	harvest	laptop-hours	known-unknowns/packings-physics/ccd-binary-lennard-jones-clusters.md	Binary Lennard-Jones clusters: lower a putative global minimum in the Doye-Meyer table (N <= 100, size ratios 1.05-1.30) or its published improvements
biomassters-finnish-agb-test-rmse	Earth and sky	standard	needs cluster	known-unknowns/earth-and-sky/biomassters-finnish-agb-test-rmse.md	BioMassters (Finnish forest biomass from Sentinel-1/2 time series): beat the best published whole-test average RMSE (27.43, TESSERA) on the released test labels
blanking-beeping-beaver-small-domains	Graphs, games and automata	harvest	laptop-hours	known-unknowns/graphs-games-automata/blanking-beeping-beaver-small-domains.md	Blanking and Beeping Busy Beavers: beat a small-domain champion (BLB(2,4), BLB(2,5), BBB(2,4)) or settle BLB(4)
glm-bolide-not-in-nasa-catalog	Earth and sky	harvest	laptop-hours	known-unknowns/earth-and-sky/glm-bolide-not-in-nasa-catalog.md	Bolide in public GOES GLM lightning-mapper data absent from the NASA GLM bolide catalog
borsuk-finite-counterexample-below-63	Erdős problems and proofs	standard	laptop-hours	known-unknowns/erdos-and-proofs/borsuk-finite-counterexample-below-63.md	Borsuk's conjecture: a finite counterexample in dimension 62 or less (finite record 63, Grinsztajn 2026)
brier-number-smaller-than-clavier	Number hunts	standard	laptop-hours	known-unknowns/number-hunts/brier-number-smaller-than-clavier.md	Brier numbers (both Sierpiński and Riesel): one smaller than Clavier's 3316923598096294713661, or a missing small one
brun-constant-unconditional-upper-bound	Number hunts	standard	pure thought	known-unknowns/number-hunts/brun-constant-unconditional-upper-bound.md	Brun's constant (C_81): an unconditional upper bound below Platt-Trudgian's 2.288513
bush-type-hadamard-odd-n-196	Record tables	standard	laptop-days	known-unknowns/record-tables/bush-type-hadamard-odd-n-196.md	Bush-type Hadamard matrices of order 4n^2 with n odd: the first open case n = 7 (order 196)
post-tag-busy-beaver-bbpt	Graphs, games and automata	harvest	laptop-minutes to lapto…	known-unknowns/graphs-games-automata/post-tag-busy-beaver-bbpt.md	Busy Beaver for 2-tag systems: settle BB_PT(8) (7 holdouts) or beat a size 8-11 champion
cyclic-tag-busy-beaver-bbct	Graphs, games and automata	harvest	laptop-minutes to lapto…	known-unknowns/graphs-games-automata/cyclic-tag-busy-beaver-bbct.md	Busy Beaver for cyclic tag systems: settle BBCT(8) or beat a size 8-14 champion
fractran-busy-beaver-bbf	Graphs, games and automata	harvest	laptop-hours for enumer…	known-unknowns/graphs-games-automata/fractran-busy-beaver-bbf.md	Busy Beaver for FRACTRAN: beat a BBf(22..24) champion, decide BBf(23)'s or BBf(24)'s holdouts, or settle a Fenrir cryptid
butson-hadamard-small-catalogue-unknown-cells	Record tables	harvest	laptop-days	known-unknowns/record-tables/butson-hadamard-small-catalogue-unknown-cells.md	Butson Hadamard catalogue n <= 21, q <= 17: settle an unknown cell (BH(15,12), BH(16,15), BH(17,12), BH(17,15), BH(19,15))
caffe-calving-front-mean-distance-error	Earth and sky	standard	laptop-days on a GPU wo…	known-unknowns/earth-and-sky/caffe-calving-front-mean-distance-error.md	CaFFe glacier calving fronts in SAR: beat the best published mean distance error on the out-of-sample Mapple and Columbia test set
caid3-disorder-binding-average-precision	Disease research	harvest	laptop-hours	known-unknowns/disease-research/caid3-disorder-binding-average-precision.md	CAID3 (Critical Assessment of Intrinsic Disorder): beat the published best average precision on the frozen CAID3 reference
calms21-mouse-social-behavior-f1	Neuroscience	harvest	laptop-hours	known-unknowns/neuroscience/calms21-mouse-social-behavior-f1.md	CalMS21 mouse social behaviour classification: beat the best test F1 on Task 1 (0.878), Task 2 (0.809) or Task 3 (0.363)
camelyon16-test-froc-and-slide-auc	Disease research	standard	needs cluster	known-unknowns/disease-research/camelyon16-test-froc-and-slide-auc.md	CAMELYON16 lymph-node metastasis detection: beat the best lesion-level FROC on the public 129-slide test reference
cami2-genome-binning-recovered-genomes	Genomes	harvest	laptop-days	known-unknowns/genomics/cami2-genome-binning-recovered-genomes.md	CAMI II genome binning: recover more near-complete genomes from the gold-standard co-assembly than any binner on the CAMI Benchmarking Portal (marine, strain-madness, plant-associ…
care-enzyme-reaction-retrieval-hard	Biology	harvest	laptop-hours	known-unknowns/biology/care-enzyme-reaction-retrieval-hard.md	CARE benchmark: beat the best published accuracy for retrieving the enzyme class (EC number) of an unseen reaction
flusight-ed-visits-beat-ensemble-wis	Disease research	harvest	laptop-hours	known-unknowns/disease-research/flusight-ed-visits-beat-ensemble-wis.md	CDC FluSight emergency-department visits: beat the FluSight-ensemble's season WIS on the newer ED-visit target
flusight-retrospective-beat-ensemble-wis	Disease research	harvest	laptop-hours	known-unknowns/disease-research/flusight-retrospective-beat-ensemble-wis.md	CDC FluSight hub: beat the FluSight-ensemble's season-average WIS retrospectively on a completed season
centered-maximal-c47-lower-bound	Erdős problems and proofs	harvest	laptop-hours	known-unknowns/erdos-and-proofs/centered-maximal-c47-lower-bound.md	Centred Hardy-Littlewood maximal constant for squares in the plane (C_47): a measure beating Lin's 1.6855099933
chc-comp-2026-unknown-status-first-solve	Optimization benchmarks	harvest	laptop-hours to laptop-…	known-unknowns/optimization-benchmarks/chc-comp-2026-unknown-status-first-solve.md	CHC-COMP 2026: first validated model or refutation for a Horn-clause task no solver answered and whose verdict is only a placeholder
jarvis-chipsff-umlip-defect-surface-elastic-mae	Chemistry and materials	harvest	laptop-hours to evaluat…	known-unknowns/chemistry-materials/jarvis-chipsff-umlip-defect-surface-elastic-mae.md	CHIPS-FF on JARVIS-Leaderboard: a universal force field with lower MAE than all 16 listed for vacancy energy, surface energy, C11, bulk modulus or formation energy (104 materials)
chvatal-sankoff-binary-lcs-constant-bounds	Erdős problems and proofs	standard	laptop-days	known-unknowns/erdos-and-proofs/chvatal-sankoff-binary-lcs-constant-bounds.md	Chvatal-Sankoff constant (C_31a): a certified bound on the expected LCS of two random binary strings beating 0.792665992 <= gamma_2 <= 0.821963
cifar10-speedrun-94-single-a100	Machine learning	standard	needs cluster	known-unknowns/machine-learning/cifar10-speedrun-94-single-a100.md	CIFAR-10 speedrun: 94% mean test accuracy on one A100 faster than Hiverge (1.98 s) and Fulcrum's Fable-5 E1 recipe (1.828 s), or 96% under 27.3 s
classic-online-bin-packing-asymptotic-ratio	Algorithms	standard	laptop-days	known-unknowns/algorithms/classic-online-bin-packing-asymptotic-ratio.md	Classic online bin packing: a deterministic lower bound above Balogh-Bekesi-Dosa-Epstein-Levin's 1.54278, or an algorithm at most 1.57821 (Advanced Harmonic, retuned by Martin in…
code-test-ecg-abnormality-f1	Disease research	harvest	laptop-hours	known-unknowns/disease-research/code-test-ecg-abnormality-f1.md	CODE-test 12-lead ECG: beat the published per-abnormality F1 on the 827-exam annotated test set
sigtyp2022-cognate-reflex-prediction-surprise	Ancient texts and fragments	harvest	laptop-hours	known-unknowns/ancient-texts/sigtyp2022-cognate-reflex-prediction-surprise.md	Cognate reflex prediction (SIGTYP 2022 surprise data): beat FeVeT and CogTran on normalized edit distance and B-Cubed F at the 0.10, 0.30 and 0.50 test proportions
main-belt-asteroid-new-activity-archival	Sky archives	standard	laptop-hours	known-unknowns/sky-archives/main-belt-asteroid-new-activity-archival.md	Cometary activity in archival survey images of a main-belt asteroid with no cometary designation and no reported activity
top-tagging-landscape-rejection-record	Particle physics	standard	laptop-days	known-unknowns/particle-physics/top-tagging-landscape-rejection-record.md	Community top-tagging dataset (Kasieczka et al.): beat OmniLearned-l's background rejection 3486 at 30% signal efficiency
condorcet-dimension-four-profile	Wildcard	moonshot	laptop-hours to laptop-…	known-unknowns/wildcard/condorcet-dimension-four-profile.md	Condorcet dimension 4: an election in which no three candidates form a Condorcet winning set (refutes Charikar et al. Conjecture 1)
cpap-consecutive-primes-ap-records	Number hunts	harvest	laptop-days	known-unknowns/number-hunts/cpap-consecutive-primes-ap-records.md	Consecutive primes in arithmetic progression (CPAP-k, k = 3..10): beat a largest, smallest or largest-difference known record
rings-of-order-32	Wildcard	standard	laptop-days	known-unknowns/wildcard/rings-of-order-32.md	Count the rings of order 32: the smallest unknown value of OEIS A027623 (only a(32) > 18,590 is known)
life-nxn-still-life-and-vanishing-counts	Graphs, games and automata	harvest	laptop-days	known-unknowns/graphs-games-automata/life-nxn-still-life-and-vanishing-counts.md	Counting n x n Life configurations: still lifes in the 16 x 16 square (A136278 a(16)) and patterns that vanish in one step in the 15 x 15 square (A134963 a(15))
covering-array-living-table-upper-bounds	Record tables	harvest	laptop-hours	known-unknowns/record-tables/covering-array-living-table-upper-bounds.md	Covering arrays CA(N;t,k,v), t = 2..6, v = 2..25: fewer rows than the best known in the living covering-array table
ecf-cubature-fewer-points	Record tables	standard	laptop-hours	known-unknowns/record-tables/ecf-cubature-fewer-points.md	Cubature: a positive-interior (PI) rule with fewer points than the best known for a standard region and degree
cvrplib-vrptw-gh-dimacs-bks	Optimization benchmarks	harvest	laptop-hours	known-unknowns/optimization-benchmarks/cvrplib-vrptw-gh-dimacs-bks.md	CVRPLIB VRPTW (Gehring-Homberger, DIMACS truncated-distance objective): beat an open best-known solution
cvrplib-x-xl-xxl-bks	Optimization benchmarks	harvest	laptop-hours	known-unknowns/optimization-benchmarks/cvrplib-x-xl-xxl-bks.md	CVRPLIB: beat a best-known solution on an open X, XL or Arnold-XXL CVRP instance
darkmachines-unsupervised-median-total-improvement	Particle physics	standard	laptop-days	known-unknowns/particle-physics/darkmachines-unsupervised-median-total-improvement.md	Dark Machines unsupervised anomaly detection: beat the best median total improvement (15.0, spline-flow likelihood) over the 19 BSM signals
jarvis-ocp10k-is2re-adsorption-energy-mae	Physics	standard	laptop-days	known-unknowns/physics/jarvis-ocp10k-is2re-adsorption-energy-mae.md	Data-efficient catalysis on Open Catalyst (JARVIS ocp10k): predict OC20 relaxed adsorption energies on the 24,943 val-ID systems from 10,000 training systems with MAE below ALIGNN…
de-bruijn-newman-upper-bound-certified	Number hunts	moonshot	laptop-days	known-unknowns/number-hunts/de-bruijn-newman-upper-bound-certified.md	de Bruijn-Newman constant: a certified upper bound below every claim on Tao's C_21 page (refereed record 0.2; unrefereed claims down to 0.107964910079)
bb6-holdout-certificates	Number hunts	harvest	laptop-hours	known-unknowns/number-hunts/bb6-holdout-certificates.md	Decide official BB(6) holdout machines with independently checkable certificates
gw-memory-20-mode-stacked-bayes-factor	Earth and sky	standard	needs cluster	known-unknowns/earth-and-sky/gw-memory-20-mode-stacked-bayes-factor.md	Decisive stacked evidence for the (l=2, m=0) memory-carrying mode across all GWTC-4.0 and GWTC-5.0 binary black holes
deepvariant-case-study-accuracy-records	Genomes	harvest	laptop-hours for a chr2…	known-unknowns/genomics/deepvariant-case-study-accuracy-records.md	DeepVariant case-study accuracy: beat DeepVariant 1.10's documented F1 on its own public held-out inputs, above all ONT R10.4.1 indels (0.9302) and RNA-seq
perm4-determinantal-complexity-below-15	Algorithms	moonshot	laptop-days	known-unknowns/algorithms/perm4-determinantal-complexity-below-15.md	Determinantal complexity of the 4x4 permanent: a determinantal expression smaller than Grenet's 15 x 15
diagonal-latin-square-spectra-vatutin	Record tables	harvest	laptop-minutes to lapto…	known-unknowns/record-tables/diagonal-latin-square-spectra-vatutin.md	Diagonal Latin squares (Vatutin's proving lists): fewer transversals, fewer or more diagonal transversals, or fewer intercalates than the best known for n = 10..28
mint-digital-nets-lower-t	Record tables	harvest	laptop-hours	known-unknowns/record-tables/mint-digital-nets-lower-t.md	Digital (t,m,s)-nets: a smaller quality parameter t than MinT's best known digital net (bases 2-9)
dimacs-colouring-open-upper-bounds	Optimization benchmarks	harvest	laptop-hours to laptop-…	known-unknowns/optimization-benchmarks/dimacs-colouring-open-upper-bounds.md	DIMACS graph colouring: a proper colouring with fewer colours than the best known for an open benchmark graph (DSJC, flat1000_76_0, latin_square_10, C2000/C4000)
directed-percolation-square-lattice-threshold-digits	Physics	standard	laptop-days	known-unknowns/physics/directed-percolation-square-lattice-threshold-digits.md	Directed percolation on the square lattice: more digits of p_c than Jensen's series values 0.644700185(5) (bond) and 0.70548522(4) (site)
dna-codes-gc-king-table	Biology	harvest	laptop-hours	known-unknowns/biology/dna-codes-gc-king-table.md	DNA codes with constant GC-content: beat a lower bound in the Gaborit-King A_4^GC(n,d,w) table
dna-codes-gc-rc-king-table	Biology	harvest	laptop-hours	known-unknowns/biology/dna-codes-gc-rc-king-table.md	DNA codes with GC-content and reverse-complement constraint: beat a lower bound in the A_4^GC,RC(n,d,w) table
queens-graph-domatic-numbers	Graphs, games and automata	harvest	laptop-hours	known-unknowns/graphs-games-automata/queens-graph-domatic-numbers.md	Domatic, idomatic and total domatic numbers of the n x n queens graph for n = 10..12 (close Lauri's gaps)
domineering-12x12	Graphs, games and automata	standard	needs cluster	known-unknowns/graphs-games-automata/domineering-12x12.md	Domineering on the 12x12 board (largest solved square board is 11x11, Uiterwijk 2016)
doubling-construction-subspace-codes	Record tables	standard	laptop-days	known-unknowns/record-tables/doubling-construction-subspace-codes.md	Doubling construction for mixed dimension subspace codes: decide whether A_q(2k+1,2k-1) = 2q^(k+1)+2 for (q,k) = (3,3) or (2,4)
earthquakenpp-beat-etas-test-loglik	Earth and sky	standard	laptop-hours	known-unknowns/earth-and-sky/earthquakenpp-beat-etas-test-loglik.md	EarthquakeNPP: beat the ETAS benchmark's per-event test log-likelihood on a real California catalog
edit-metric-dna-codes-gc	Biology	standard	laptop-hours	known-unknowns/biology/edit-metric-dna-codes-gc.md	Edit-distance DNA codes with GC/homopolymer constraints: beat a published lower bound
checkers-perft-ply-30	Graphs, games and automata	standard	needs cluster, or sever…	known-unknowns/graphs-games-automata/checkers-perft-ply-30.md	English checkers from the start: the number of move sequences of 30 plies (OEIS A133046 a(30))
eaqecc-qutrit-codetables-gaps	Physics	harvest	laptop-hours	known-unknowns/physics/eaqecc-qutrit-codetables-gaps.md	Entanglement-assisted qutrit codes [[n,k,d;c]]_3 with c >= 1: raise a lower bound in Grassl's EAQECC qutrit table
eslp-min-terms-k7-to-k32	Number hunts	harvest	laptop-days	known-unknowns/number-hunts/eslp-min-terms-k7-to-k32.md	Equal sums of like powers for k = 7..32: a k.m.n solution with fewer terms than Meyrignac's EulerNet records
equiangular-lines-dims-18-20-42	Record tables	standard	laptop-hours	known-unknowns/record-tables/equiangular-lines-dims-18-20-42.md	Equiangular lines: more equiangular lines in R^18, R^19, R^20 or R^42 than the best known
equidistant-subspace-codes-b2-8-1-4	Record tables	standard	laptop-hours	known-unknowns/record-tables/equidistant-subspace-codes-b2-8-1-4.md	Equidistant subspace codes: more than 40 four-dimensional subspaces of F_2^8 pairwise meeting in exactly a point (B_2(8,1;4))
erdos-1033-triangle-degree-sum-constant	Erdős problems and proofs	standard	laptop-hours	known-unknowns/erdos-and-proofs/erdos-1033-triangle-degree-sum-constant.md	Erdos #1033 (Bollobas-Erdos): a construction below 1.463877226961 n, or a certified lower bound of at least 1.453 n, for the forced triangle degree sum
erdos-1063-binomial-divisibility-nk-next-terms	Erdős problems and proofs	harvest	laptop-hours to laptop-…	known-unknowns/erdos-and-proofs/erdos-1063-binomial-divisibility-nk-next-terms.md	Erdos #1063 (Erdos-Selfridge): n_k for k >= 76 (OEIS A389360 beyond the forum's k = 75)
erdos-213-integral-8-points-general-position	Erdős problems and proofs	standard	laptop-hours	known-unknowns/erdos-and-proofs/erdos-213-integral-8-points-general-position.md	Erdos #213: eight points in the plane, no three on a line, no four on a circle, all distances integers
erdos-513-maximum-term-constant	Erdős problems and proofs	standard	laptop-hours	known-unknowns/erdos-and-proofs/erdos-513-maximum-term-constant.md	Erdos #513 (maximum-term constant C_51): a transcendental entire function with liminf mu(r)/M(r) above the record
erdos-580-efls-small-cases	Erdős problems and proofs	standard	laptop-days	known-unknowns/erdos-and-proofs/erdos-580-efls-small-cases.md	Erdos #580 (Erdos-Furedi-Loebl-Sos n/2-n/2-n/2 conjecture): a counterexample, or certified verification for n = 20
erdos-156-saturated-sidon-next-terms	Erdős problems and proofs	standard	laptop-days to needs cl…	known-unknowns/erdos-and-proofs/erdos-156-saturated-sidon-next-terms.md	Erdős #156 small cases: minimum size of a maximal (saturated) Sidon set in {1..n}: settle a(189) in {9, 10}, and the nine-mark threshold
erdos-20-sunflower-numbers-small	Erdős problems and proofs	harvest	laptop-hours	known-unknowns/erdos-and-proofs/erdos-20-sunflower-numbers-small.md	Erdős #20 small cases (Erdős-Rado sunflower numbers): beat Abbott et al.'s 38 three-sets with no 4-sunflower, 54 four-sets with no 3-sunflower, or 88 three-sets with no 5-sunflowe…
erdos-203-two-dimensional-sierpinski	Erdős problems and proofs	moonshot	laptop-days	known-unknowns/erdos-and-proofs/erdos-203-two-dimensional-sierpinski.md	Erdős #203: an m coprime to 6 with every 2^k 3^l m + 1 composite (a two-dimensional Sierpiński number)
erdos-21-cover-number-q6	Erdős problems and proofs	standard	laptop-days	known-unknowns/erdos-and-proofs/erdos-21-cover-number-q6.md	Erdős #21 small cases (Erdős-Lovász): an intersecting 6-uniform family with cover number 6 and at most 17 edges (best known 18, lower bound 14)
erdos-23-triangle-free-bipartite-deletion	Erdős problems and proofs	moonshot	laptop-days	known-unknowns/erdos-and-proofs/erdos-23-triangle-free-bipartite-deletion.md	Erdős #23: a triangle-free graph on 5n vertices needing more than n^2 deletions to be bipartite, or a certified extension of Ferudun's n <= 40 range
erdos-273-covering-moduli-p-minus-1	Erdős problems and proofs	standard	laptop-days	known-unknowns/erdos-and-proofs/erdos-273-covering-moduli-p-minus-1.md	Erdős #273: a covering system with distinct moduli of the form p - 1, p >= 5 prime
erdos-313-primary-pseudoperfect-new	Number hunts	standard	laptop-hours	known-unknowns/number-hunts/erdos-313-primary-pseudoperfect-new.md	Erdős #313: a new primary pseudoperfect number (1/p_1 + ... + 1/p_k = 1 - 1/m), beyond the 11 known
erdos-366-two-full-three-full-pair	Number hunts	moonshot	laptop-days	known-unknowns/number-hunts/erdos-366-two-full-three-full-pair.md	Erdős #366: a 2-full n with n+1 3-full (or two consecutive 3-full integers)
erdos-773-sidon-squares-next-term	Erdős problems and proofs	standard	laptop-hours to laptop-…	known-unknowns/erdos-and-proofs/erdos-773-sidon-squares-next-term.md	Erdős #773 small cases: largest Sidon subset of the first n squares, a(72) and beyond (OEIS A390813)
friedman-mathmagic-archive-records	Recreational math	harvest	laptop-hours	known-unknowns/recreational-math/friedman-mathmagic-archive-records.md	Erich Friedman's Math Magic archive: beat a best-known entry on a monthly-problem page (non-packing categories)
gtopx-interplanetary-trajectory-records	Engineering and chips	harvest	laptop-days	known-unknowns/engineering/gtopx-interplanetary-trajectory-records.md	ESA GTOP / GTOPX interplanetary trajectory benchmarks: beat a best-known Delta-v, mass or mission time (Messenger full 1.9579 km/s, Cassini2 8.3830 km/s, Rosetta 1.34334 km/s, GTO…
mertens-function-exact-values-next-terms	Number hunts	harvest	needs cluster	known-unknowns/number-hunts/mertens-function-exact-values-next-terms.md	Exact Mertens function values: M(10^24) (A084237) or M(2^76) (A084236), with new terms of A084235 (first k with |M(k)| = 2^n) as partial wins
square-grid-lattice-gas-exact-counts-oeis	Physics	harvest	laptop-hours	known-unknowns/physics/square-grid-lattice-gas-exact-counts-oeis.md	Exact partition functions of lattice gases on n x n boards: the next term of OEIS A028420 (monomer-dimer), A006506 (hard squares), A063443 (kings/1x1-2x2 tilings), A054759 (square…
extremal-doubly-even-self-dual-96-120-128	Record tables	moonshot	needs cluster for a sea…	known-unknowns/record-tables/extremal-doubly-even-self-dual-96-120-128.md	Extremal doubly-even self-dual binary codes at lengths 96, 120 and 128 (beyond the famous 72)
fault-free-domino-tilings-a124997-n13	Graphs, games and automata	standard	laptop-hours to laptop-…	known-unknowns/graphs-games-automata/fault-free-domino-tilings-a124997-n13.md	Fault-free domino tilings of the 2n x 2n square: the next term A124997(13) (the 26 x 26 board), open since 2016
feigenbaum-constants-and-accumulation-point-digits	Physics	standard	laptop-days	known-unknowns/physics/feigenbaum-constants-and-accumulation-point-digits.md	Feigenbaum constants and the period-doubling accumulation point: more verified digits than the published records
fibonacci-lucas-composite-factors	Number hunts	harvest	laptop-hours	known-unknowns/number-hunts/fibonacci-lucas-composite-factors.md	Fibonacci and Lucas numbers F_n, L_n (n < 10,000): a new factor of a listed composite cofactor
ccd-finnis-sinclair-mo-fe-clusters	Packings and physics	harvest	laptop-hours	known-unknowns/packings-physics/ccd-finnis-sinclair-mo-fe-clusters.md	Finnis-Sinclair molybdenum and iron clusters (N = 3..100): lower a putative global minimum in the Elliott-Shibuta-Wales tables
five-voter-tournaments-n5	Graphs, games and automata	harvest	laptop-hours to laptop-…	known-unknowns/graphs-games-automata/five-voter-tournaments-n5.md	Five voters: a tournament on at most 21 alternatives that no five voters can induce by majority (13 <= N(5) <= 22, Chindelevitch-Harutyunyan Question 1)
bipartite-ramsey-b5-quadrilateral	Graphs, games and automata	standard	laptop-days to needs cl…	known-unknowns/graphs-games-automata/bipartite-ramsey-b5-quadrilateral.md	Five-colour bipartite Ramsey number b5(2) (26-28): a rectangle-free 5-colouring of the 26 x 26 grid, or a proof that none exists
fixed-polyominoes-a001168-n71	Graphs, games and automata	standard	needs cluster	known-unknowns/graphs-games-automata/fixed-polyominoes-a001168-n71.md	Fixed polyominoes: the exact count of 71-cell polyominoes (next term of OEIS A001168 after Barequet and Ben-Shachar's n = 70)
fjsplib-flexible-jobshop-open-ub	Optimization benchmarks	harvest	laptop-hours	known-unknowns/optimization-benchmarks/fjsplib-flexible-jobshop-open-ub.md	Flexible job shop (FJSPLib: Brandimarte mk10, Dauzere-Peres-Paulli, Behnke-Geiger, Hurink): lower the best known makespan of an open instance
fc-graffiti-oeis-solved-sorries	Formal proofs	harvest	laptop-hours	known-unknowns/formal-proofs/fc-graffiti-oeis-solved-sorries.md	Formal Conjectures WrittenOnTheWallII (Graffiti) and OEIS collections: research-solved conjectures without any Lean proof
fc-finite-witness-sorries	Formal proofs	harvest	laptop-hours	known-unknowns/formal-proofs/fc-finite-witness-sorries.md	Formal Conjectures: research-solved sorries closable by an explicit finite witness (R(5,5) > 42 graph, small Hadamard orders, ...)
three-heap-wythoff-fraenkel-a1-11	Graphs, games and automata	standard	laptop-hours	known-unknowns/graphs-games-automata/three-heap-wythoff-fraenkel-a1-11.md	Fraenkel's N-heap Wythoff conjectures: prove the three-heap case with smallest heap 11 (Sun-Zeilberger stopped at 10)
turan-k4-minus-3-graph-density	Erdős problems and proofs	standard	needs cluster	known-unknowns/erdos-and-proofs/turan-k4-minus-3-graph-density.md	Frankl-Füredi K4^- problem: a certified upper bound on pi(K4^-) below 0.286504, or a K4^--free 3-graph denser than 2/7
free-polyforms-catch-up-with-fixed-counts	Graphs, games and automata	harvest	laptop-days	known-unknowns/graphs-games-automata/free-polyforms-catch-up-with-fixed-counts.md	Free polyominoes, polyhexes and polyiamonds: close the gap to the fixed counts (A000105 beyond n = 59, A000228 beyond 36, A000577 beyond 52)
full-flag-codes-binary-a2f-5-2	Record tables	standard	laptop-hours	known-unknowns/record-tables/full-flag-codes-binary-a2f-5-2.md	Full flag codes over F_2: beat A^f_2(5,2) >= 3120 (upper bound 3255) or A^f_2(6,6) >= 224
fullerene-isomer-counts-beyond-c400	Chemistry and materials	standard	laptop-days via the pub…	known-unknowns/chemistry-materials/fullerene-isomer-counts-beyond-c400.md	Fullerene isomer counts: the number of fullerenes (OEIS A007894) or IPR fullerenes (A046880) with 402 carbon atoms or more
jet-tagging-fundamental-limit-gpt-jets-gap	Particle physics	standard	needs cluster	known-unknowns/particle-physics/jet-tagging-fundamental-limit-gpt-jets-gap.md	Fundamental limit of jet tagging (GPT-generated top/QCD jets with known likelihood ratio): beat the best tagger's rejection 553 at 50% top efficiency
furstenberg-sarkozy-c4b-lower-bound	Erdős problems and proofs	harvest	laptop-hours	known-unknowns/erdos-and-proofs/furstenberg-sarkozy-c4b-lower-bound.md	Furstenberg-Sarkozy exponent C_4b: a larger square-difference-free set exponent
life-smaller-orphan	Graphs, games and automata	standard	laptop-hours	known-unknowns/graphs-games-automata/life-smaller-orphan.md	Game of Life orphan with a smaller bounding box
life-still-life-counts-35-cells	Graphs, games and automata	harvest	laptop-days	known-unknowns/graphs-games-automata/life-still-life-counts-35-cells.md	Game of Life still-life enumeration: the number of strict and pseudo still lifes with 35 cells (A019473, A056613), or quasi still lifes with 23 cells (A330283)
gcw-cullen-woodall-composites	Number hunts	harvest	laptop-hours	known-unknowns/number-hunts/gcw-cullen-woodall-composites.md	Generalized Cullen and Woodall numbers n*a^n +- 1 (a <= 12, n <= 1000): factor a listed composite cofactor
generalized-offdiagonal-schur-s3-stu	Number hunts	harvest	laptop-hours	known-unknowns/number-hunts/generalized-offdiagonal-schur-s3-stu.md	Generalized off-diagonal Schur numbers S(3; s,t,u): refute Ahmed–Schaal's S = stu - tu - u - 1 or settle a new cell with a certificate
generalized-wilson-primes-open-orders	Number hunts	harvest	laptop-days	known-unknowns/number-hunts/generalized-wilson-primes-open-orders.md	Generalized Wilson primes: the first prime of order n for the 24 orders n < 100 with none known (OEIS A128666)
genernib-grn-inference-beat-leaderboard	Biology	standard	laptop-hours	known-unknowns/biology/genernib-grn-inference-beat-leaderboard.md	geneRNIB: beat the best listed gene-regulatory-network inference scores on a perturbation dataset
massbalancemachine-norway-test-glaciers-rmse	Earth and sky	standard	laptop-minutes to lapto…	known-unknowns/earth-and-sky/massbalancemachine-norway-test-glaciers-rmse.md	Glacier point mass balance in Norway: beat the Mass Balance Machine RMSE on the 14 withheld test glaciers
go-small-rectangular-boards	Graphs, games and automata	harvest	laptop-days for the 24-…	known-unknowns/graphs-games-automata/go-small-rectangular-boards.md	Go on small rectangular boards: an exact first-player score for a blank or ' > =6' cell of van der Werf's m x n table (3x10, 2x12, 4x8, 5x7, 6x6, ...)
graph-design-spectra-possible-exceptions	Record tables	harvest	laptop-hours	known-unknowns/record-tables/graph-design-spectra-possible-exceptions.md	Graph-design spectra: decompose K_16 into 12 copies of a 6-vertex 10-edge graph, K_21 into 7 icosahedra, or settle another listed possible exception
long-run-gray-code-r8	Algorithms	standard	laptop-days	known-unknowns/algorithms/long-run-gray-code-r8.md	Gray codes with long bit runs: an 8-bit Gray code whose bit runs all have length at least 6, or a proof that r(8) = 5
grothendieck-kg3-werner-locality-bounds	Physics	standard	laptop-days	known-unknowns/physics/grothendieck-kg3-werner-locality-bounds.md	Grothendieck constant of order 3 / two-qubit Werner nonlocality threshold: improve 1.43670 <= K_G(3) <= 1.4546
ccd-gupta-murrell-mottram-metal-clusters	Packings and physics	harvest	laptop-hours	known-unknowns/packings-physics/ccd-gupta-murrell-mottram-metal-clusters.md	Gupta and Murrell-Mottram metal clusters (Zn, Cd <= 125; Pb <= 150; Na <= 379/380): lower a putative global minimum in the Doye tables
ccd-gupta-cobalt-clusters-n200	Packings and physics	harvest	laptop-hours	known-unknowns/packings-physics/ccd-gupta-cobalt-clusters-n200.md	Gupta cobalt clusters (N = 2..200): lower a putative global minimum on the Cambridge Cluster Database cobalt table or its posted improvements
guy-hill-cycle-complement-crossing	Graphs, games and automata	standard	laptop-days	known-unknowns/graphs-games-automata/guy-hill-cycle-complement-crossing.md	Guy-Hill conjecture for the complement of a cycle: determine cr(complement of C_11) (conjectured 36)
torus-grid-crossing-c8-c8	Graphs, games and automata	standard	laptop-days	known-unknowns/graphs-games-automata/torus-grid-crossing-c8-c8.md	Harary-Kainen-Schwenk conjecture: is cr(C_8 x C_8) = 48? (smallest open toroidal grid)
hard-square-critical-activity-digits	Physics	standard	laptop-days	known-unknowns/physics/hard-square-critical-activity-digits.md	Hard-square lattice gas: more digits of the critical activity z_c = 3.7962551739... (Guo-Blote 2002) or of the negative-activity singularity -0.1193388818... (Todo 1999)
vesuvius-ink9um-validation-masks-buffered	Herculaneum scrolls	harvest	laptop-hours	known-unknowns/herculaneum-scrolls/vesuvius-ink9um-validation-masks-buffered.md	Herculaneum 9 µm ink detection within a scroll: beat every public model's average precision on the three official ink_9um validation masks (384 px buffer rule)
vesuvius-frag4-ink-f05-holdout	Herculaneum scrolls	harvest	laptop-hours	known-unknowns/herculaneum-scrolls/vesuvius-frag4-ink-f05-holdout.md	Herculaneum fragment ink detection: beat the 2023 Kaggle winners' own weights on the released hidden-test Fragment 4 (PHercParis1Fr39) under one pinned full-fragment F0.5 protocol…
vesuvius-profilometer-ink-dice	Herculaneum scrolls	harvest	laptop-hours	known-unknowns/herculaneum-scrolls/vesuvius-profilometer-ink-dice.md	Herculaneum optical-profilometry ink segmentation: beat the Sci. Rep. 2026 nnU-Net held-out Dice on the shipped 5-fold splits of scrollprize/profilometer, topography only
hex-10x10-opening-moves	Graphs, games and automata	standard	needs cluster	known-unknowns/graphs-games-automata/hex-10x10-opening-moves.md	Hex 10x10: solve a second opening move (only the central f5/e6 pair is solved, since 2013)
hexadecimal-games-unsolved-periodicity	Graphs, games and automata	moonshot	laptop-days	known-unknowns/graphs-games-automata/hexadecimal-games-unsolved-periodicity.md	Hexadecimal games: certify the (arithmetic) periodicity of one game on Nowakowski's unsolved list (.f6, .7f, .9, .e, .b6, ...)
hg002-ont-read-correction-gqc-error-rate	Genomes	standard	needs cluster or a GPU…	known-unknowns/genomics/hg002-ont-read-correction-gqc-error-rate.md	HG002 nanopore read correction scored against the Q100 genome: corrected ONT reads with fewer errors per megabase than HERRO's 88 (GQC readbench)
symmetric-polyomino-holeless-tetrad	Graphs, games and automata	standard	laptop-days	known-unknowns/graphs-games-automata/symmetric-polyomino-holeless-tetrad.md	Holeless tetrad from a symmetric polyomino with at most 33 cells (record: 34-ominoes, Rubin and Scherer)
homfam-msa-total-column-score	Biology	standard	laptop-days	known-unknowns/biology/homfam-msa-total-column-score.md	HomFam multiple sequence alignment: beat learnMSA2's best 66.92% mean total-column score over the 94 HomFam families
homogeneous-cunningham-composites	Number hunts	harvest	laptop-days	known-unknowns/number-hunts/homogeneous-cunningham-composites.md	Homogeneous Cunningham numbers a^n +- b^n: a new factor of one of the 565 listed composites
iccad2022-3d-placement-d2d-wirelength	Engineering and chips	harvest	laptop-hours	known-unknowns/engineering/iccad2022-3d-placement-d2d-wirelength.md	ICCAD 2022 CAD Contest Problem B (3D placement with D2D vertical connections): a shorter legal 3D placement than the best published
iccad2023-3d-mixed-size-placement-score	Engineering and chips	harvest	laptop-hours	known-unknowns/engineering/iccad2023-3d-mixed-size-placement-score.md	ICCAD 2023 CAD Contest Problem B (3D placement with macros): a lower HPWL + 10 x HBT score than the best published
iea37-cs4-borssele-81-turbine-layout	Engineering and chips	standard	laptop-hours	known-unknowns/engineering/iea37-cs4-borssele-81-turbine-layout.md	IEA Wind Task 37 case study 4 (Borssele III/IV, 81 x 10 MW): a feasible layout with higher AEP than DEBO's 2,913,220.604 MWh
inatsounds-test-map	Ecology and bioacoustics	standard	needs cluster	known-unknowns/ecology/inatsounds-test-map.md	iNatSounds 2024: beat the best published test mAP (65.4) for file-level species ID across 1,212 species of birds, frogs, insects and mammals
integer-complexity-conjecture-a	Number hunts	moonshot	laptop-days	known-unknowns/number-hunts/integer-complexity-conjecture-a.md	Integer complexity Conjecture A: ||2^a 3^b 5^c|| = 2a + 3b + 5c for c < 6 (Selfridge's ||2^a|| = 2a); a counterexample, or a proof beyond Altman's a <= 48
integer-complexity-smallest-complexity-90	Number hunts	standard	laptop-days	known-unknowns/number-hunts/integer-complexity-smallest-complexity-90.md	Integer complexity: the smallest number of complexity 90, A005520(90), beyond the 10^12 computation of Iraids et al.
isic2017-part3-melanoma-sk-mean-auc	Disease research	standard	laptop-hours	known-unknowns/disease-research/isic2017-part3-melanoma-sk-mean-auc.md	ISIC 2017 Part 3 (melanoma and seborrheic keratosis): beat the challenge-best mean AUC of 0.911 on the public 600-image test labels
isic2018-lesion-segmentation-thresholded-jaccard	Disease research	standard	laptop-hours	known-unknowns/disease-research/isic2018-lesion-segmentation-thresholded-jaccard.md	ISIC 2018 skin-lesion segmentation: beat the challenge-winning thresholded Jaccard on the public test ground truth
isic2018-task3-lesion-diagnosis-balanced-accuracy	Disease research	standard	laptop-hours	known-unknowns/disease-research/isic2018-task3-lesion-diagnosis-balanced-accuracy.md	ISIC 2018 Task 3 (HAM10000 diagnosis, 7 classes): beat the best balanced multiclass accuracy on the 1,512-image public test ground truth
itc2007-exam-timetabling-bks	Optimization benchmarks	harvest	laptop-hours	known-unknowns/optimization-benchmarks/itc2007-exam-timetabling-bks.md	ITC-2007 examination timetabling (track 1): beat the best known penalty on one of the 12 competition instances
itc2021-sports-timetabling-ub	Optimization benchmarks	harvest	laptop-hours	known-unknowns/optimization-benchmarks/itc2021-sports-timetabling-ub.md	ITC2021 sports timetabling: lower the best known penalty of an open instance
iwls2026-aig-delay-area-pareto	Algorithms	harvest	laptop-hours per benchm…	known-unknowns/algorithms/iwls2026-aig-delay-area-pareto.md	IWLS 2026 Programming Contest: an AIG off the virtual-best delay/area Pareto frontier for one of the 100 released truth tables (ex200-ex299)
jarvis-single-entry-perovskite-mxene-phonon-dos	Chemistry and materials	harvest	laptop-hours	known-unknowns/chemistry-materials/jarvis-single-entry-perovskite-mxene-phonon-dos.md	JARVIS-Leaderboard single-entry materials tasks: halide perovskites (5 properties), MXene formation energy and phonon DOS spectra: beat the only listed model
kalah-6-6-standard-exact-value	Graphs, games and automata	standard	needs cluster	known-unknowns/graphs-games-automata/kalah-6-6-standard-exact-value.md	Kalah(6,6) under standard capture rules: the exact perfect-play margin (proven only 'first player wins by at least 4')
knights-tour-counts-10x10-closed-9x9-open	Graphs, games and automata	moonshot	needs cluster	known-unknowns/graphs-games-automata/knights-tour-counts-10x10-closed-9x9-open.md	Knight's tour enumeration: the number of closed tours on the 10 x 10 board (A001230(5)) or open tours on the 9 x 9 board (A165134(9))
knotinfo-mosaic-number-twelve-crossing	Wildcard	harvest	laptop-hours	known-unknowns/wildcard/knotinfo-mosaic-number-twelve-crossing.md	Knot mosaics: the first mosaic, or a 7-mosaic, for one of the 854 11- and 12-crossing knots with no known mosaic in KnotInfo
knotinfo-bridge-index-13-crossing	Wildcard	harvest	laptop-hours	known-unknowns/wildcard/knotinfo-bridge-index-13-crossing.md	KnotInfo bridge index: settle one of the 536 13-crossing knots listed [3,4] by a 3-bridge diagram or a rank-4 Coxeter quotient
knotinfo-concordance-genus-unknown	Wildcard	harvest	laptop-days	known-unknowns/wildcard/knotinfo-concordance-genus-unknown.md	KnotInfo concordance genus: a certified concordance to a lower-genus knot for one of the 208 11- and 12-crossing knots listed as intervals (incl. the Conway knot 11n_34 at [1,3])
knotinfo-nonorientable-4genus-bounds	Wildcard	harvest	laptop-hours	known-unknowns/wildcard/knotinfo-nonorientable-4genus-bounds.md	KnotInfo smooth 4D crosscap numbers: a nonorientable band certificate beating an upper bound for an 11-13 crossing knot (3,525 intervals)
knotinfo-turaev-genus-twelve-crossing	Wildcard	standard	laptop-hours	known-unknowns/wildcard/knotinfo-turaev-genus-twelve-crossing.md	KnotInfo Turaev genus: a Turaev-genus-1 diagram for one of the 25 non-alternating knots (11n_118 and 24 at 12 crossings) listed [1,2]
knotinfo-smooth-4genus-slice-unknown	Wildcard	harvest	laptop-hours	known-unknowns/wildcard/knotinfo-smooth-4genus-slice-unknown.md	KnotInfo: close one of the last interval-valued smooth 4-genus entries (13 crossings) by an explicit ribbon disk or genus-1 cobordism
knotinfo-unknotting-number-unknown	Wildcard	harvest	laptop-hours	known-unknowns/wildcard/knotinfo-unknotting-number-unknown.md	KnotInfo: determine an unknotting number currently listed as an interval
kotzig-nim-tan-ward-conjectures	Graphs, games and automata	standard	laptop-days	known-unknowns/graphs-games-automata/kotzig-nim-tan-ward-conjectures.md	Kotzig's Nim: refute a Tan-Ward periodicity conjecture or extend its verified range (G(1,5;n) beyond n = 140, G(3,5;n) beyond 111, ...)
perfect-1-factorisation-open-orders	Graphs, games and automata	harvest	laptop-days	known-unknowns/graphs-games-automata/perfect-1-factorisation-open-orders.md	Kotzig's perfect 1-factorisation conjecture: a perfect 1-factorisation of K_64 (or K_66, 70, 76, 78, 88, 96, 100)
kourovka-20-21-isomorphic-normal-subgroups-c12-a4	Wildcard	standard	laptop-days	known-unknowns/wildcard/kourovka-20-21-isomorphic-normal-subgroups-c12-a4.md	Kourovka 20.21 (Verret/Conder): isomorphic normal subgroups K and L of index 12 with G/K = C12 and G/L = A4
burnside-b34-fewer-fourth-powers	Wildcard	standard	laptop-days to needs cl…	known-unknowns/wildcard/burnside-b34-fewer-fourth-powers.md	Kourovka 20.36 (Havas-Newman): define B(3,4) with fewer than a million fourth powers
vandiver-beyond-2-31	Number hunts	harvest	needs cluster for the f…	known-unknowns/number-hunts/vandiver-beyond-2-31.md	Kummer-Vandiver conjecture: extend the verified range past 2^31 (Hart-Harvey-Ong, 2016)
landau-constant-lower-bound	Erdős problems and proofs	standard	laptop-days	known-unknowns/erdos-and-proofs/landau-constant-lower-bound.md	Landau's constant L (C_57b): a certified lower bound above Wikstrom's 0.51 (covering radius 0.51003; upper bound 0.5433)
langford-skolem-pairings-next-counts	Recreational math	harvest	needs cluster	known-unknowns/recreational-math/langford-skolem-pairings-next-counts.md	Langford's problem: the number of Langford pairings L(2,31) or L(2,32), or the next Nickerson-Skolem (V(2,32), V(2,33)) or planar (P(43), P(44)) counts
rk-ap-free-next-terms-k4-k5-k6	Number hunts	harvest	laptop-days	known-unknowns/number-hunts/rk-ap-free-next-terms-k4-k5-k6.md	Largest k-AP-free subsets of [1..n] for k = 4, 5, 6: the next exact terms of A003003 (n = 143), A003004 (n = 116) and A003005 (n = 148)
latin-no-disjoint-transversals-no-pinned-small-even	Record tables	harvest	laptop-days	known-unknowns/record-tables/latin-no-disjoint-transversals-no-pinned-small-even.md	Latin squares of even order 10..26, or odd order, whose transversals pairwise intersect yet share no common cell (Ghafari-Wanless Conjecture 3 small orders)
lattice-animals-hypercubic-d4-plus-exact-counts	Physics	harvest	laptop-days	known-unknowns/physics/lattice-animals-hypercubic-d4-plus-exact-counts.md	Lattice animals in 4 to 9 dimensions: the next exact count of fixed polycubes beyond Luther and Mertens (OEIS A151830-A151835, unchanged since 2011)
ppi-bernett-gold-standard-auprc	Biology	standard	laptop-hours	known-unknowns/biology/ppi-bernett-gold-standard-auprc.md	Leakage-free protein-protein interaction prediction: beat the best published AUPR on the Bernett gold-standard human dataset
lennard-jones-ccd-doye-table	Packings and physics	standard	laptop-hours	known-unknowns/packings-physics/lennard-jones-ccd-doye-table.md	Lennard-Jones clusters: lower a putative global minimum in the Cambridge Cluster Database / Doye tables (N = 3..150, 310..1000)
linear-trimer-coverings-a139772-24x24	Graphs, games and automata	standard	needs cluster	known-unknowns/graphs-games-automata/linear-trimer-coverings-a139772-24x24.md	Linear trimer (I-tromino) tilings of the 3n x 3n square: the next term A139772(8), the 24 x 24 board
local-cyclicity-centers-m3-thirteen	Wildcard	harvest	laptop-days	known-unknowns/wildcard/local-cyclicity-centers-m3-thirteen.md	Local cyclicity M(n): 13 small-amplitude limit cycles from one cubic equilibrium, or beat M(4) >= 21, M(5) >= 33, M(6) >= 48, M(7) >= 61, M(8) >= 76, M(9) >= 88
uncrossed-knight-path-10x10	Recreational math	harvest	laptop-days	known-unknowns/recreational-math/uncrossed-knight-path-10x10.md	Longest uncrossed knight's path: settle the open 10 x 10 value (OEIS A003192, best known 61) or the closed 11 x 11 value (A157416, best known 70)
mnk-game-five-in-a-row-9x9	Graphs, games and automata	standard	needs cluster	known-unknowns/graphs-games-automata/mnk-game-five-in-a-row-9x9.md	m,n,k-games: settle five-in-a-row (k = 5) on 9x9 or another board between 8x8 (draw) and 15x15 (win)
m3-competition-beat-best-published-smape	Machine learning	standard	laptop-hours	known-unknowns/machine-learning/m3-competition-beat-best-published-smape.md	M3 competition (3,003 series): an out-of-sample average sMAPE below the best published 12.37
mahler-problem-littlewood-large-measure-records	Record tables	harvest	laptop-hours	known-unknowns/record-tables/mahler-problem-littlewood-large-measure-records.md	Mahler's problem for Littlewood polynomials: beat the skew-symmetric record Mahler measure at an even degree 32-60 in Mossinghoff's tables
masser-gramain-constant-certified-bracket	Number hunts	standard	laptop-days	known-unknowns/number-hunts/masser-gramain-constant-certified-bracket.md	Masser-Gramain constant delta: a certified bracket narrower than Melquiond-Nowak-Zimmermann's 1.819776 < delta < 1.819833 (2013)
matbench-medium-structure-tasks-cpu	Physics	harvest	laptop-days	known-unknowns/physics/matbench-medium-structure-tasks-cpu.md	Matbench v0.1 medium tasks (phonons, dielectric, expt_is_metal, log_gvrh, log_kvrh, perovskites): beat the verified leaderboard score with CPU-trained models
matbench-small-data-tasks	Physics	harvest	laptop-hours	known-unknowns/physics/matbench-small-data-tasks.md	Matbench v0.1: beat the per-task leaderboard on a small-data task (steels, jdft2d, expt_gap, glass) with CPU-only models
meanders-semimeanders-next-terms	Graphs, games and automata	standard	laptop-days	known-unknowns/graphs-games-automata/meanders-semimeanders-next-terms.md	Meanders and semi-meanders: the next exact term of OEIS A005316 (open meanders, known to n = 58) or A000682 (semi-meanders, known to n = 49)
meunier-stable-kneser-odd-s-small-n	Graphs, games and automata	harvest	laptop-hours to laptop-…	known-unknowns/graphs-games-automata/meunier-stable-kneser-odd-s-small-n.md	Meunier's s-stable Kneser conjecture: certify chi = n - sk + s for open small cases with odd s (e.g. all of (k, s) = (3, 5), n = 16..21)
sinitic-protoform-reconstruction-wikihan	Ancient texts and fragments	harvest	laptop-hours	known-unknowns/ancient-texts/sinitic-protoform-reconstruction-wikihan.md	Middle Chinese protoform reconstruction (WikiHan, WikiHan-aug, Hóu): beat the Lu-Wang-Mortensen 2024 reranked systems on accuracy and token edit distance
sloane-hard-sphere-clusters-second-moment	Packings and physics	harvest	laptop-hours	known-unknowns/packings-physics/sloane-hard-sphere-clusters-second-moment.md	Minimal-energy clusters of hard spheres: N unit spheres in R^3 (N <= 99) or R^4 (N <= 32) with smaller second moment than the Sloane-Hardin-Duff-Conway table
min-comparison-sorting-s23-s24	Algorithms	moonshot	needs cluster	known-unknowns/algorithms/min-comparison-sorting-s23-s24.md	Minimum-comparison sorting: settle S(23) in {75, 76} or S(24) in {80, 81} (OEIS A036604), or raise the n = 28 lower bound
miplib2017-open-primal-bound	Optimization benchmarks	harvest	laptop-hours	known-unknowns/optimization-benchmarks/miplib2017-open-primal-bound.md	MIPLIB 2017: improve the best known objective of an open collection instance
mlgwsc1-dataset3-sensitive-distance	Earth and sky	standard	laptop-days	known-unknowns/earth-and-sky/mlgwsc1-dataset3-sensitive-distance.md	MLGWSC-1 gravitational-wave search challenge: beat the best published sensitive distance at a false-alarm rate of 1 per month on dataset 3
moabb-within-session-benchmark-cells	Neuroscience	harvest	laptop-hours per dataset	known-unknowns/neuroscience/moabb-within-session-benchmark-cells.md	MOABB EEG-BCI benchmark: one pipeline that beats the published best within-session score on at least three datasets of a paradigm table
mondrian-art-problem-defect-records	Recreational math	harvest	laptop-hours	known-unknowns/recreational-math/mondrian-art-problem-defect-records.md	Mondrian Art Problem: a smaller defect than the best known for some n = 67..96 (OEIS A276523), or the exact a(67)
mint-net-below-digital-bound	Record tables	moonshot	laptop-days	known-unknowns/record-tables/mint-net-below-digital-bound.md	MOONSHOT - A (t,m,s)-net that beats every digital net: t below MinT's proven digital lower bound, e.g. a (2,8,7)-net in base 2
truncated-tetrahedra-snub-solids-packing	Packings and physics	moonshot	laptop-days	known-unknowns/packings-physics/truncated-tetrahedra-snub-solids-packing.md	MOONSHOT - Archimedean solids without central symmetry: beat 207/208 for truncated tetrahedra (Jiao-Torquato), or the lattice records 0.787699 / 0.788640 for the chiral snub cube…
beckett-gray-code-n9	Algorithms	moonshot	needs cluster for exhau…	known-unknowns/algorithms/beckett-gray-code-n9.md	MOONSHOT - Beckett-Gray codes: does a 9-bit Beckett-Gray code exist? (open for every n >= 9)
polycube-genus0-edge-unfolding-counterexample	Recreational math	moonshot	laptop-days	known-unknowns/recreational-math/polycube-genus0-edge-unfolding-counterexample.md	MOONSHOT - Edge-unfolding polycubes (TOPP Problem 64): a genus-0 polycube with no edge unfolding along cube edges
odd-weird-primitive-weird-erdos-470	Number hunts	moonshot	laptop-days	known-unknowns/number-hunts/odd-weird-primitive-weird-erdos-470.md	MOONSHOT - Erdős #470: an odd weird number, or primitive weird numbers with more than 16 prime factors or a cubed odd prime factor
erdos-straus-beyond-1e18	Number hunts	moonshot	laptop-days for a range…	known-unknowns/number-hunts/erdos-straus-beyond-1e18.md	MOONSHOT - Erdős–Straus conjecture (Erdős #242): 4/n with no 3-term Egyptian fraction, or verification beyond 10^18
eulerian-synchronizing-szykula-vorel-bound	Graphs, games and automata	moonshot	laptop-days	known-unknowns/graphs-games-automata/eulerian-synchronizing-szykula-vorel-bound.md	MOONSHOT - Eulerian synchronizing automata: a reset threshold above floor((n^2-3)/2) (refuting the Szykuła-Vorel conjecture), or binary Eulerian records
firing-squad-five-state-minimal-time	Graphs, games and automata	moonshot	laptop-days	known-unknowns/graphs-games-automata/firing-squad-five-state-minimal-time.md	MOONSHOT - Firing squad synchronization: a 5-state minimal-time solution, or a certified proof that none exists (Mazoyer's 6 states have stood since 1987)
harmonious-tree-conjecture-beyond-31	Graphs, games and automata	moonshot	needs cluster	known-unknowns/graphs-games-automata/harmonious-tree-conjecture-beyond-31.md	MOONSHOT - Graham-Sloane harmonious tree conjecture: a tree that is not harmonious, a formal proof, or the first verification past Fang's 31 vertices
leanapap-kelley-meka-integer-bound	Formal proofs	moonshot	laptop-days	known-unknowns/formal-proofs/leanapap-kelley-meka-integer-bound.md	MOONSHOT - LeanAPAP: formal proof of the Kelley-Meka bound for 3AP-free sets of integers (corrected form of theorem `int`)
ore-harmonic-number-conjectures	Number hunts	moonshot	laptop-days	known-unknowns/number-hunts/ore-harmonic-number-conjectures.md	MOONSHOT - Ore's harmonic numbers: an odd one (Ore's conjecture), or a counterexample to the practical, Mersenne-factor or completeness conjectures recorded in OEIS A001599
hypercubic-percolation-1-over-d-series-next-term	Physics	moonshot	needs cluster	known-unknowns/physics/hypercubic-percolation-1-over-d-series-next-term.md	MOONSHOT - Percolation threshold of Z^d in powers of 1/(2d-1): the first coefficient beyond Mertens-Moore's 119077/96 (site) and 4855/12 (bond)
ps-minus-ground-state-energy-digits	Physics	moonshot	laptop-days	known-unknowns/physics/ps-minus-ground-state-energy-digits.md	MOONSHOT - Positronium negative ion Ps- (e- e+ e-): a variational ground-state energy below Frolov's 2023 record -0.26200507023298010777040211998
binary-q-fano-plane-s2-2-3-7	Record tables	moonshot	needs cluster	known-unknowns/record-tables/binary-q-fano-plane-s2-2-3-7.md	MOONSHOT - The binary q-analog of the Fano plane S_2[2,3,7] (fallback: a (7,4;3)_2 subspace code with more than 333 planes)
moonstone-lunar-benchmark-beat-mg-mae	Planets and moons	standard	laptop-days	known-unknowns/planetary-science/moonstone-lunar-benchmark-beat-mg-mae.md	Moonstone lunar benchmark: beat MG-MAE on crater segmentation, mare segmentation or geologic-unit classification on the fixed split
mrs-perkins-quilt-large-sides	Recreational math	harvest	laptop-hours	known-unknowns/recreational-math/mrs-perkins-quilt-large-sides.md	Mrs Perkins's quilt: a coprime squared square with at most n squares and a larger side than the best known (OEIS A089047/A089046, n >= 19)
multicolour-cycle-ramsey-small	Record tables	harvest	laptop-hours for lower…	known-unknowns/record-tables/multicolour-cycle-ramsey-small.md	Multicolour Ramsey numbers of short cycles: close R5(C4) 27-29, R6(C4) 34-38, R4(C6) 18-20, R(C3,C3,C4,C4) 30-36, R(C4,C4,K4) 20-21 or a similar DS1 cell
antipodal-gray-code-n10	Algorithms	standard	laptop-days	known-unknowns/algorithms/antipodal-gray-code-n10.md	n-antipodal Gray codes: is there a 10-bit Gray code in which every word's complement is exactly 10 steps away? (Killian-Savage, open for even n >= 10)
nanogpt-slowrun-100m-token-val-loss	Machine learning	harvest	needs cluster	known-unknowns/machine-learning/nanogpt-slowrun-100m-token-val-loss.md	NanoGPT Slowrun: lowest FineWeb val loss from a fixed 100M-token training set (1-hour track 3.183, unlimited 2.987)
ccmc-flare-scoreboard-m-bss-2023-2024	Earth and sky	standard	laptop-hours	known-unknowns/earth-and-sky/ccmc-flare-scoreboard-m-bss-2023-2024.md	NASA CCMC Flare Scoreboard: a reproducible 24-hour M-class flare forecast that beats every scoreboard model's Brier skill score over 2023-2024
nasa-tropical-storm-wind-speed-rmse	Earth and sky	standard	laptop-days	known-unknowns/earth-and-sky/nasa-tropical-storm-wind-speed-rmse.md	NASA/Radiant Earth tropical-storm wind-speed challenge: beat the winning RMSE from GOES infrared imagery on the released test labels
tsp-national-bm33708-ch71009	Optimization benchmarks	standard	laptop-days	known-unknowns/optimization-benchmarks/tsp-national-bm33708-ch71009.md	National TSPs: a shorter tour for Burma (bm33708) or China (ch71009), the two unsolved Waterloo country instances
near-extremal-self-dual-weight-enumerators	Record tables	harvest	laptop-hours: negacircu…	known-unknowns/record-tables/near-extremal-self-dual-weight-enumerators.md	Near-extremal self-dual codes with new weight enumerators: realize an admissible ternary (lengths 36-72) or quaternary Hermitian (lengths 24-36) enumerator not yet known to exist
kamada-near-repdigit-sequences-without-prime	Number hunts	harvest	laptop-days	known-unknowns/number-hunts/kamada-near-repdigit-sequences-without-prime.md	Near-repdigit-related sequences with no known prime (Kamada): 298...89, 25...567, 45...529, 54...427, 454...41
nlb21-released-test-cobps	Neuroscience	harvest	laptop-hours	known-unknowns/neuroscience/nlb21-released-test-cobps.md	Neural Latents Benchmark '21 (test data now public): beat the final EvalAI leaderboard's top co-smoothing bits/spike on an NLB dataset split
kepler-eb-circumbinary-transit-candidate	Sky archives	standard	laptop-hours to laptop-…	known-unknowns/sky-archives/kepler-eb-circumbinary-transit-candidate.md	New circumbinary transit candidate in a Kepler eclipsing binary (Villanova EB catalog)
xmm-chandra-archival-new-xray-periodicity	Sky archives	harvest	laptop-hours to laptop-…	known-unknowns/sky-archives/xmm-chandra-archival-new-xray-periodicity.md	New coherent X-ray periodicity in an archival XMM-Newton or Chandra source (5XMM-DR15 / CSC 2.2), confirmed independently and absent from period catalogues
gwosc-o4-missed-cbc-candidate	Earth and sky	standard	laptop-days for one mon…	known-unknowns/earth-and-sky/gwosc-o4-missed-cbc-candidate.md	New compact-binary merger candidate in public O4a/O4b LIGO-Virgo strain that GWTC-4.1, GWTC-5.0 and the community catalogs do not list
apollo-moonquake-missed-vs-pds-catalog	Earth and sky	harvest	laptop-hours	known-unknowns/earth-and-sky/apollo-moonquake-missed-vs-pds-catalog.md	New deep moonquake or impact in open Apollo Passive Seismic Experiment data, absent from the PDS expanded lunar event catalogue
tess-exocomet-dip-candidate	Sky archives	harvest	laptop-hours	known-unknowns/sky-archives/tess-exocomet-dip-candidate.md	New exocomet-transit candidate (asymmetric single dip) in public TESS light curves
degree-diameter-table	Graphs, games and automata	harvest	laptop-hours	known-unknowns/graphs-games-automata/degree-diameter-table.md	New largest known (Delta,D) graph in the degree-diameter table
kmtnet-2024-2025-planetary-anomaly-candidate	Sky archives	harvest	laptop-days	known-unknowns/sky-archives/kmtnet-2024-2025-planetary-anomaly-candidate.md	New planetary-anomaly candidate in public KMTNet 2024-2025 microlensing light curves, absent from the KMTNet planet list and the archives
small-body-satellite-archival-not-in-johnston	Planets and moons	standard	laptop-hours	known-unknowns/planetary-science/small-body-satellite-archival-not-in-johnston.md	New satellite of a TNO, Centaur, Jupiter Trojan or asteroid resolved in public archival HST, JWST or adaptive-optics images, absent from Johnston's Archive
kepler-tess-single-transit-long-period-candidate	Sky archives	harvest	laptop-hours	known-unknowns/sky-archives/kepler-tess-single-transit-long-period-candidate.md	New single-/duo-transit long-period candidate in Kepler or TESS light curves
gaia-stellar-stream-not-in-galstreams	Sky archives	standard	laptop-days	known-unknowns/sky-archives/gaia-stellar-stream-not-in-galstreams.md	New stellar stream in Gaia DR3 absent from the galstreams library (v1.2.1) and the STREAMFINDER atlas
wd-debris-transit-new-candidate	Sky archives	harvest	laptop-hours	known-unknowns/sky-archives/wd-debris-transit-new-candidate.md	New white dwarf with transiting planetary debris in public ZTF or TESS light curves
nim-dimension-clobber-amazons	Graphs, games and automata	standard	laptop-days	known-unknowns/graphs-games-automata/nim-dimension-clobber-amazons.md	Nim-dimension of Amazons: a position equal to *8 (only *4 is known)
nogo-fraction-one-sixteenth	Graphs, games and automata	standard	laptop-hours to laptop-…	known-unknowns/graphs-games-automata/nogo-fraction-one-sixteenth.md	NoGo: a position on a Go board with value 1/16 (only 1, 1/2, 1/4 and 1/8 are known)
kings-hard-core-entropy-a247413-digits	Physics	harvest	laptop-hours	known-unknowns/physics/kings-hard-core-entropy-a247413-digits.md	Non-attacking kings (hard-core gas with diagonal exclusion) at unit activity: more correct digits of the entropy constant OEIS A247413
sprouts-normal-play-63-spots	Graphs, games and automata	standard	needs cluster	known-unknowns/graphs-games-automata/sprouts-normal-play-63-spots.md	Normal-play Sprouts: settle the 63-spot game or another open n <= 105 (SPOTS frontier, 2026)
chess-legal-positions-upper-bound	Recreational math	standard	laptop-hours	known-unknowns/recreational-math/chess-legal-positions-upper-bound.md	Number of legal chess positions: a provable upper bound well below Tromp's 8.7279e45 ranking
games-born-by-day-4-count	Graphs, games and automata	standard	laptop-hours to laptop-…	known-unknowns/graphs-games-automata/games-born-by-day-4-count.md	Number of short games born by day 4: tighten Suetsugu's bounds 10^28.2 < |G4| < 4.0e184 (OEIS A065401 a(4))
obelix-li-electrolyte-ionic-conductivity-mae	Physics	harvest	laptop-minutes	known-unknowns/physics/obelix-li-electrolyte-ionic-conductivity-mae.md	OBELiX experimental Li solid-electrolyte ionic conductivity: beat the published best test MAE of 1.59 log10(S/cm) on the official 121-entry test split
ssh-mapping-ose-2021a-resolution	Earth and sky	harvest	laptop-hours	known-unknowns/earth-and-sky/ssh-mapping-ose-2021a-resolution.md	Ocean data challenge 2021a (SSH mapping OSE): beat the leaderboard effective resolution or RMSE score on real altimetry
odd-graceful-trees-beyond-12	Graphs, games and automata	harvest	laptop-hours	known-unknowns/graphs-games-automata/odd-graceful-trees-beyond-12.md	Odd-graceful tree conjecture (Gnanajothi): extend the verification past 12 vertices, or a tree that is not odd-graceful
ogbg-molpcba-beat-leaderboard-ap	Drug discovery	standard	laptop-days	known-unknowns/drug-discovery/ogbg-molpcba-beat-leaderboard-ap.md	OGB ogbg-molpcba: beat the leaderboard's top test AP (0.3204) on 128 PubChem bioassays
ogbg-ppa-beat-leaderboard-accuracy	Machine learning	standard	laptop-days	known-unknowns/machine-learning/ogbg-ppa-beat-leaderboard-accuracy.md	OGB ogbg-ppa: beat the leaderboard's top test accuracy (0.8258) for classifying protein-association graphs by taxonomic group
ogbl-vessel-beat-leaderboard-roc-auc	Machine learning	standard	laptop-hours	known-unknowns/machine-learning/ogbl-vessel-beat-leaderboard-roc-auc.md	OGB ogbl-vessel: beat the leaderboard's top test ROC-AUC (0.9838) for mouse-brain vessel link prediction
ogbn-arxiv-no-ext-beat-leaderboard-accuracy	Machine learning	harvest	laptop-hours	known-unknowns/machine-learning/ogbn-arxiv-no-ext-beat-leaderboard-accuracy.md	OGB ogbn-arxiv: beat the top no-external-data test accuracy (0.7611) for arXiv CS subject classification
ogbn-mag-beat-leaderboard-venue-accuracy	Machine learning	standard	laptop-days	known-unknowns/machine-learning/ogbn-mag-beat-leaderboard-venue-accuracy.md	OGB ogbn-mag: beat the leaderboard's top test accuracy (0.5801) for heterogeneous-graph paper venue prediction
s2-cloud-cover-challenge-private-jaccard	Earth and sky	standard	laptop-days	known-unknowns/earth-and-sky/s2-cloud-cover-challenge-private-jaccard.md	On Cloud N (Sentinel-2 cloud cover challenge): beat the winning 0.8974 Jaccard on the released private test split
online-bin-stretching-computer-lower-bounds	Algorithms	harvest	laptop-days	known-unknowns/algorithms/online-bin-stretching-computer-lower-bounds.md	Online bin stretching: a computer-certified adversary tree beating the best lower bound for some m in 3..12 (41/30, 19/14, 15/11 cells), with randomized and upper-bound cells as p…
aliquot-open-sequence-termination	Number hunts	harvest	laptop-days	known-unknowns/number-hunts/aliquot-open-sequence-termination.md	Open aliquot sequences below 5,000,000: terminate one (reach a prime) or close it into a cycle
openproblems-predict-modality-cite-rmse	Biology	standard	laptop-hours	known-unknowns/biology/openproblems-predict-modality-cite-rmse.md	Open Problems predict modality: beat the best listed RMSE for predicting protein abundance from RNA (and RNA from ATAC) on NeurIPS 2021/2022 data
openproblems-scrna-denoising-beat-leaderboard	Biology	harvest	laptop-hours	known-unknowns/biology/openproblems-scrna-denoising-beat-leaderboard.md	Open Problems single-cell denoising: beat every listed method on the molecular-cross-validation leaderboard
openproblems-spatial-decomposition-r2	Biology	harvest	laptop-hours	known-unknowns/biology/openproblems-spatial-decomposition-r2.md	Open Problems spatial decomposition: beat the best listed R^2 for cell-type proportions on a benchmark dataset
openkbp-dose-prediction-test-dose-dvh-score	Disease research	standard	laptop-hours	known-unknowns/disease-research/openkbp-dose-prediction-test-dose-dvh-score.md	OpenKBP radiotherapy dose prediction: beat the challenge winner's dose score 2.429 Gy or DVH score 1.478 Gy on the 100 released test patients
orientable-sequences-binary-n17-and-kary	Record tables	harvest	laptop-hours to laptop-…	known-unknowns/record-tables/orientable-sequences-binary-n17-and-kary.md	Orientable sequences: a binary orientable cycle of order 18-20 longer than the best claimed period, or a k-ary period beating the Mitchell-Wild tables
packomania-hyperspheres-hsp4-hsp6	Packings and physics	harvest	laptop-hours	known-unknowns/packings-physics/packomania-hyperspheres-hsp4-hsp6.md	Packomania: equal 4D/5D/6D hyperspheres in a hypersphere (hsp4, hsp5, hsp6), beat a per-N record radius
packomania-cci-equal-circles-in-circle	Packings and physics	harvest	laptop-hours	known-unknowns/packings-physics/packomania-cci-equal-circles-in-circle.md	Packomania: equal circles in a circle (cci), beat a per-N record radius
packomania-csq-equal-circles-in-square	Packings and physics	harvest	laptop-hours	known-unknowns/packings-physics/packomania-csq-equal-circles-in-square.md	Packomania: equal circles in a square (csq), beat a per-N record radius
pannuke-three-fold-mpq	Disease research	standard	laptop-days	known-unknowns/disease-research/pannuke-three-fold-mpq.md	PanNuke pan-cancer nucleus segmentation and classification: beat the best published three-split mPQ (0.5123, PromptNucSeg-H)
parameter-golf-16mb-fineweb-bpb	Machine learning	standard	needs cluster	known-unknowns/machine-learning/parameter-golf-16mb-fineweb-bpb.md	Parameter Golf (finished): a 16 MB language-model artifact trained in 10 min on 8xH100 that beats 1.0565 bits per byte on FineWeb val
pcam-patchcamelyon-from-scratch-accuracy	Disease research	standard	laptop-hours	known-unknowns/disease-research/pcam-patchcamelyon-from-scratch-accuracy.md	PatchCamelyon (lymph-node metastasis patches): beat 89.8% accuracy / 0.963 AUC on the official test split without external pretraining
involutions-avoiding-1324-4231-next-terms	Recreational math	standard	needs cluster	known-unknowns/recreational-math/involutions-avoiding-1324-4231-next-terms.md	Pattern-avoiding involutions: the next exact count of involutions avoiding 1324 (n = 35) or 4231 (n = 41)
penetrable-disks-continuum-percolation-discrepancy	Physics	standard	laptop-days	known-unknowns/physics/penetrable-disks-continuum-percolation-discrepancy.md	Penetrable disks in the plane: settle the 3-sigma clash between Mertens-Moore's eta_c = 1.12808737(6) and the critical-polynomial 1.12808706(8)
obtuse-triangle-billiards-periodic-beyond-112-3	Wildcard	standard	laptop-days	known-unknowns/wildcard/obtuse-triangle-billiards-periodic-beyond-112-3.md	Periodic billiard paths in obtuse triangles: extend the 112.3-degree theorem (Tokarsky-Garber-Marinov-Moore 2018)
permutation-snark-6-mod-8	Graphs, games and automata	standard	laptop-days for cycle-p…	known-unknowns/graphs-games-automata/permutation-snark-6-mod-8.md	Permutation snarks: a first one of order 6 mod 8 (at least 54 vertices) or a first one of girth at least 6
two-stack-series-sortable-count-n20	Recreational math	standard	laptop-days	known-unknowns/recreational-math/two-stack-series-sortable-count-n20.md	Permutations sortable by two stacks in series: the exact count for n = 20 (first term beyond Elvey Price-Guttmann)
petersen-colouring-smallest-counterexample	Graphs, games and automata	standard	laptop-days for gadget/…	known-unknowns/graphs-games-automata/petersen-colouring-smallest-counterexample.md	Petersen colouring conjecture (refuted 2026): a counterexample on fewer than 52 vertices (minimum is in [40, 52]) or a cyclically 5-edge-connected one
pglib-opf-v2307-ac-cheaper-dispatch	Optimization benchmarks	harvest	laptop-hours	known-unknowns/optimization-benchmarks/pglib-opf-v2307-ac-cheaper-dispatch.md	PGLib-OPF v23.07: an AC-feasible dispatch cheaper than the published baseline on a large case with an open relaxation gap
plant-genomic-benchmark-agront-expression-strength	Biology	harvest	laptop-hours for promot…	known-unknowns/biology/plant-genomic-benchmark-agront-expression-strength.md	Plants Genomic Benchmark (AgroNT): beat the published R^2 for plant gene expression on held-out gene families or for promoter and terminator strength
polaris-novartis-cyp3a4-aafe	Drug discovery	harvest	laptop-hours	known-unknowns/drug-discovery/polaris-novartis-cyp3a4-aafe.md	Polaris novartis/adme-novartis-cyp3a4-reg: beat the listed absolute-average-fold-error on 368 test compounds
polaris-pkis2-kinase-small-leaderboards	Drug discovery	harvest	laptop-hours	known-unknowns/drug-discovery/polaris-pkis2-kinase-small-leaderboards.md	Polaris PKIS2/PKIS1 kinase benchmarks (EGFR, KIT, RET, LOK-SLK): beat shallow leaderboards on 74-144 test compounds
polaris-tdcommons-mirror-admet-leaderboards	Drug discovery	harvest	laptop-hours	known-unknowns/drug-discovery/polaris-tdcommons-mirror-admet-leaderboards.md	Polaris tdcommons/* ADMET mirrors: beat the top listed score on a single-fold public split (offline-scorable)
tetromino-multiples-next-terms	Graphs, games and automata	harvest	laptop-days	known-unknowns/graphs-games-automata/tetromino-multiples-next-terms.md	Polyomino number theory: the next count of free polyominoes tiled by n copies of a tetromino (I: A397019, T: A397020, L: A397021, S: A397022)
polyomino-oddities-open-cells	Graphs, games and automata	harvest	laptop-hours	known-unknowns/graphs-games-automata/polyomino-oddities-open-cells.md	Polyomino oddities (Sillke figures): settle a '?' or 'Unsolved' cell, or beat a minimal known tile count on George Sicherman's oddity tables
polyomino-order-6-or-odd	Graphs, games and automata	standard	laptop-hours	known-unknowns/graphs-games-automata/polyomino-order-6-or-odd.md	Polyomino of order 6, or of odd order 5 or more
posebusters-redock-pb-valid-rate	Drug discovery	harvest	laptop-hours	known-unknowns/drug-discovery/posebusters-redock-pb-valid-rate.md	PoseBusters benchmark set (428 complexes): raise the PB-valid RMSD<=2A redocking rate above the published classical-docking rate
spherical-quadrature-s2-positive-fewest-nodes	Packings and physics	standard	laptop-hours	known-unknowns/packings-physics/spherical-quadrature-s2-positive-fewest-nodes.md	Positive-weight quadrature on the sphere S^2: exact to degree t with fewer nodes than Graef's and Lebedev-Laikov's rules
precisionfda-truth-challenge-v2-difficult-mhc	Genomes	harvest	laptop-days per sample…	known-unknowns/genomics/precisionfda-truth-challenge-v2-difficult-mhc.md	precisionFDA Truth Challenge V2 (finished, answers released): beat the best submission's F1 in difficult-to-map regions or the MHC for HG003/HG004 from the challenge reads
prime-gap-list-merit-improvement	Recreational math	harvest	laptop-hours	known-unknowns/recreational-math/prime-gap-list-merit-improvement.md	Prime Gap List: improve the record merit for some gap size
prime-counting-pi-10-30-and-siblings	Number hunts	harvest	needs cluster	known-unknowns/number-hunts/prime-counting-pi-10-30-and-siblings.md	Prime-counting records: pi(10^30) (A006880), or a new pi(2^n), pi(e^n), pi(10^(n/2)) or 10^n-th prime value beyond Baugh and Walisch
primes-between-consecutive-powers-legendre-cubes-frontier	Number hunts	standard	needs cluster	known-unknowns/number-hunts/primes-between-consecutive-powers-legendre-cubes-frontier.md	Primes between consecutive squares and cubes: extend Legendre's conjecture past n = 7.05 x 10^13 or the cube result past n^3 = 1.649 x 10^40
property-b-m5-upper-bound	Erdős problems and proofs	standard	laptop-days	known-unknowns/erdos-and-proofs/property-b-m5-upper-bound.md	Property B: a non-2-colourable 5-uniform hypergraph with at most 50 edges (m(5) <= 51 since 1969)
protein-engineering-tournament-supervised-spearman	Biology	harvest	laptop-hours	known-unknowns/biology/protein-engineering-tournament-supervised-spearman.md	Protein Engineering Tournament pilot (supervised track): beat the best team Spearman on a released enzyme property
protein-engineering-tournament-zeroshot-spearman	Biology	harvest	laptop-hours	known-unknowns/biology/protein-engineering-tournament-zeroshot-spearman.md	Protein Engineering Tournament pilot (zero-shot track): beat the best team score on an unseen enzyme
proteingym-clinical-substitutions-auc	Disease research	harvest	laptop-hours	known-unknowns/disease-research/proteingym-clinical-substitutions-auc.md	ProteinGym clinical substitutions (ClinVar benign/pathogenic): beat the leaderboard's best average AUC
proteingym-per-assay-zero-shot	Biology	standard	laptop-hours	known-unknowns/biology/proteingym-per-assay-zero-shot.md	ProteinGym zero-shot substitutions: beat every listed model's Spearman on a single DMS assay
ptbxl-ecg-macro-auc-fold10	Disease research	standard	laptop-hours	known-unknowns/disease-research/ptbxl-ecg-macro-auc-fold10.md	PTB-XL ECG classification: beat the best published macro-AUC on the fixed fold-10 test set
pythagorean-triples-three-colour-record	Erdős problems and proofs	standard	laptop-hours	known-unknowns/erdos-and-proofs/pythagorean-triples-three-colour-record.md	Pythagorean triples with three colours: a triple-free 3-colouring of {1..N} for N above 25,000,000
qaplib-open-instances-bkv	Optimization benchmarks	harvest	laptop-hours to laptop-…	known-unknowns/optimization-benchmarks/qaplib-open-instances-bkv.md	QAPLIB: a permutation beating the best known value of one of the 28 unsolved instances (tai a/b, tai256c, sko, tho, wil)
qoblib-network-design-max-flow	Optimization benchmarks	standard	laptop-hours	known-unknowns/optimization-benchmarks/qoblib-network-design-max-flow.md	QOBLIB network design (Bienstock-Gunluk demands): a 2-in/2-out digraph and routing with lower maximum edge load for an open instance network11..network24
c4-versus-star-ramsey-open-values	Record tables	harvest	laptop-days	known-unknowns/record-tables/c4-versus-star-ramsey-open-values.md	Quadrilateral versus star (and wheel): settle an open value of R(C4, K_{1,n}) such as n = 39 (46-47) or n = 51-54, 71, 72
quantum-chromatic-orthogonal-rank-separation-under-21	Physics	standard	laptop-days	known-unknowns/physics/quantum-chromatic-orthogonal-rank-separation-under-21.md	Quantum chromatic number vs rank-1 quantum chromatic number: a graph on at most 20 vertices with chi_q(G) < chi_q^(1)(G) (smallest known: Lalonde's 21-vertex G21)
quaternary-hadamard-bh-n-4-open-orders	Record tables	harvest	laptop-days	known-unknowns/record-tables/quaternary-hadamard-bh-n-4-open-orders.md	Quaternary Hadamard matrices BH(n,4): settle an open even order below 2000 (smallest 334, then 438, 446, 478)
racks-quandles-next-order	Wildcard	harvest	laptop-days for the kei…	known-unknowns/wildcard/racks-quandles-next-order.md	Racks and quandles: count those of order 14 (OEIS A181770/A181769), or the connected quandles of order 48 (A181771)
ramsey-complete-bipartite-small-cells	Record tables	harvest	laptop-hours for lower…	known-unknowns/record-tables/ramsey-complete-bipartite-small-cells.md	Ramsey numbers of small complete bipartite graphs R(K_{m,n}, K_{p,q}): close a gap in DS1 Tables IVb/IVc (R(K3,5,K3,4) 25-29, R(K2,10,K2,7) 29-31, R(K2,2,K2,19) 28-29, R(K4,4,K4,4…
randomized-metric-distortion-lower-bound	Wildcard	moonshot	laptop-hours	known-unknowns/wildcard/randomized-metric-distortion-lower-bound.md	Randomized metric distortion: certify a lower bound above Charikar-Ramakrishnan's 2.11264 (current window [2.11264, 2.13713])
rectilinear-crossing-kn	Graphs, games and automata	harvest	laptop-hours	known-unknowns/graphs-games-automata/rectilinear-crossing-kn.md	Rectilinear crossing number of K_n: resolve n=28 (7233 vs 7234) or beat a best-known drawing
regular-hadamard-order-8836	Record tables	standard	laptop-days	known-unknowns/record-tables/regular-hadamard-order-8836.md	Regular Hadamard matrix (Menon design) of order 4u^2 with u = 47 (order 8836), the first unknown order
asteroid-rotation-period-not-in-lcdb	Sky archives	harvest	laptop-hours	known-unknowns/sky-archives/asteroid-rotation-period-not-in-lcdb.md	Reliable rotation periods for asteroids with no entry in the Asteroid Lightcurve Database, from public survey photometry
rnagym-ncrna-fitness-zero-shot-macro	Biology	harvest	laptop-hours	known-unknowns/biology/rnagym-ncrna-fitness-zero-shot-macro.md	RNAGym ncRNA fitness: beat the top signed-Spearman macro score on the live zero-shot leaderboard
romanoff-constant-c45-upper-bound	Erdős problems and proofs	harvest	laptop-hours	known-unknowns/erdos-and-proofs/romanoff-constant-c45-upper-bound.md	Romanoff's constant C_45: a smaller certified upper bound for the density of odd n = p + 2^k
rubiks-cube-htm-distance-distribution	Graphs, games and automata	moonshot	needs cluster for the d…	known-unknowns/graphs-games-automata/rubiks-cube-htm-distance-distribution.md	Rubik's Cube, half-turn metric: the exact number of positions at distance 16 (next term of OEIS A080601), or new distance-20 positions
sage-global-sdm-test-auroc	Ecology and bioacoustics	standard	laptop-days	known-unknowns/ecology/sage-global-sdm-test-auroc.md	SAGE global species distribution benchmark: beat the best overall test AUROC (85.9, random forest) on sPlotOpen presence-absence plots
satbird-usa-encounter-rates	Ecology and bioacoustics	standard	needs cluster	known-unknowns/ecology/satbird-usa-encounter-rates.md	SatBird USA-summer bird encounter rates: one model that beats every published test metric (top-10, top-30, top-k, MAE, MSE)
scholz-brauer-unrepaired-non-hansen	Number hunts	standard	laptop-hours	known-unknowns/number-hunts/scholz-brauer-unrepaired-non-hansen.md	Scholz-Brauer conjecture: an addition chain for 2^n - 1 of length n - 1 + l(n) at one of the six unrepaired non-Hansen numbers (33167549, 33247629, 33573479, 33580601, 33626279, 4…
schwartz-teq-counterexample-below-24	Graphs, games and automata	standard	laptop-hours to laptop-…	known-unknowns/graphs-games-automata/schwartz-teq-counterexample-below-24.md	Schwartz's conjecture: a tournament on at most 23 alternatives with two minimal TEQ-retentive sets (the smallest known has 24)
saw-hypercubic-exact-enumeration	Physics	harvest	laptop-days	known-unknowns/physics/saw-hypercubic-exact-enumeration.md	Self-avoiding walks: an exact count c_n beyond the published record on the 4D/5D hypercubic, bcc, fcc or simple cubic lattice
addition-chain-c48-d46	Number hunts	standard	needs cluster	known-unknowns/number-hunts/addition-chain-c48-d46.md	Shortest addition chains: compute c(48), the smallest n with l(n) = 48, or d(46) (Clift's c(r)/d(r) tables)
shorthand-universal-tori-permutations-n7	Algorithms	standard	laptop-days	known-unknowns/algorithms/shorthand-universal-tori-permutations-n7.md	Shorthand universal tori for permutations of [7]: an R x C torus with 2x3 windows for some R >= 3 (only 2-row tori are known)
nea-yarkovsky-detection-not-in-sbdb-neocc	Planets and moons	harvest	laptop-hours	known-unknowns/planetary-science/nea-yarkovsky-detection-not-in-sbdb-neocc.md	Significant Yarkovsky drift for a near-Earth asteroid that neither the JPL SBDB nor ESA NEOCC orbit solves for
single-deletion-codes-length-12	Record tables	standard	laptop-days to needs cl…	known-unknowns/record-tables/single-deletion-codes-length-12.md	Single-deletion-correcting binary codes of length 12: is the Varshamov-Tenengolts code (316 words) optimal? (bounds 316-320)
sintef-lilim-pdptw-bks	Optimization benchmarks	harvest	laptop-hours	known-unknowns/optimization-benchmarks/sintef-lilim-pdptw-bks.md	SINTEF Li & Lim PDPTW benchmark: hierarchically beat a best-known solution on a 600/800/1000-task instance
sintef-vrptw-gh-hierarchical-bks	Optimization benchmarks	harvest	laptop-hours	known-unknowns/optimization-benchmarks/sintef-vrptw-gh-hierarchical-bks.md	SINTEF VRPTW (Gehring-Homberger, hierarchical objective): fewer vehicles, or equal vehicles and shorter distance, on a 200-1000 customer instance
square-site-percolation-rigorous-bounds	Physics	standard	laptop-minutes to lapto…	known-unknowns/physics/square-site-percolation-rigorous-bounds.md	Site percolation on the square lattice Z^2: a certified lower bound on p_c above van den Berg-Ermakov's 0.556 (1996) or an upper bound below Wierman-Oberly's 0.666894 (2024)
prime-ktuple-skewes-numbers-next	Number hunts	harvest	laptop-days for the sex…	known-unknowns/number-hunts/prime-ktuple-skewes-numbers-next.md	Skewes numbers for prime k-tuples: A210439(10), A332493(9), or the sexy-prime (p, p+6) Skewes number
hypercube-edge-slicing-s-n	Record tables	harvest	laptop-days	known-unknowns/record-tables/hypercube-edge-slicing-s-n.md	Slicing the hypercube: fewer hyperplanes than ceil(4n/5) cutting every edge of Q_n (e.g. 5 for Q_7), or new S(n,k) edge records
binary-sink-automata-reset-threshold-record	Graphs, games and automata	standard	laptop-hours to laptop-…	known-unknowns/graphs-games-automata/binary-sink-automata-reset-threshold-record.md	Slowly synchronizing binary automata with a sink: beat Ananichev-Vorel's n^2/4 + 2n - 9 reset threshold (n = 16, 28) or the best known value for another n
turan-3-graph-density-table-lidicky-volec	Record tables	harvest	laptop-days for the low…	known-unknowns/record-tables/turan-3-graph-density-table-lidicky-volec.md	Small 3-graph Turán and codegree-squared densities: beat a bound in the Lidický-Volec 2026 table (K6, K7, K5^-, K5^=, K5^ < , J4, J5, F4,2, F4^-,2)
small-t-designs-unknown-existence	Record tables	harvest	laptop-hours to laptop-…	known-unknowns/record-tables/small-t-designs-unknown-existence.md	Small simple t-designs of unknown existence: 3-(20,5,2), 3-(21,7,15), 4-(16,8,15), 4-(18,9,14), 4-(19,9,21), 5-(16,7,5), 5-(17,8,20), 2-(55,10,3) and kin
pg2q-smallest-complete-arcs	Record tables	harvest	laptop-hours	known-unknowns/record-tables/pg2q-smallest-complete-arcs.md	Smallest complete arcs in PG(2,q), q >= 37: beat a smallest known size in the Bartoli-Davydov-Faina-Kreshchuk-Marcugini-Pambianco tables
edge-ununfoldable-polyhedra-smallest-records	Recreational math	harvest	laptop-hours	known-unknowns/recreational-math/edge-ununfoldable-polyhedra-smallest-records.md	Smallest edge-ununfoldable polyhedra in restricted classes: triangulated with fewer than 20 vertices, convex-faced with fewer than 13 faces, or stacked with acute triangles
hypohamiltonian-smallest-planar-and-girth	Graphs, games and automata	harvest	laptop-days for planar…	known-unknowns/graphs-games-automata/hypohamiltonian-smallest-planar-and-girth.md	Smallest hypohamiltonian graphs with extra properties: a planar one below Tsai's 34 vertices, a planar one of order 35, a planar cubic one below 70, or a first one of girth 8
smallest-k-chromatic-girth-g-table	Graphs, games and automata	harvest	laptop-days for structu…	known-unknowns/graphs-games-automata/smallest-k-chromatic-girth-g-table.md	Smallest k-chromatic graphs of given girth: beat an upper bound in the Exoo-Goedgebeur n_g(k) table (incl. the triangle-free 6-chromatic gap 32..40)
mertens-smallest-counterexample-upper-bound	Number hunts	standard	laptop-days	known-unknowns/number-hunts/mertens-smallest-counterexample-upper-bound.md	Smallest Mertens counterexample: a certified bound below exp(3.485 x 10^18) (2026 claim under review), or below Kim-Nguyen's published exp(1.96 x 10^19)
multimagic-squares-smaller-orders	Recreational math	harvest	pure thought	known-unknowns/recreational-math/multimagic-squares-smaller-orders.md	Smallest multimagic squares and cubes: a tetramagic square below order 243, a pentamagic below 729, a hexamagic below 4096, a trimagic of order 13 or 15, or a bimagic cube below o…
rbibd-45-5-1-smallest-open-resolvable	Record tables	standard	laptop-days	known-unknowns/record-tables/rbibd-45-5-1-smallest-open-resolvable.md	Smallest open resolvable Steiner 2-designs: a resolvable S(2,5,45) (also v = 345, 465, 645) or a resolvable S(2,6,66)
strong-pseudoprime-psi14-zhang	Number hunts	standard	laptop-days	known-unknowns/number-hunts/strong-pseudoprime-psi14-zhang.md	Smallest strong pseudoprime to the first 14 prime bases: beat Zhang's conjectured psi_14 = 6003094289670105800312596501 (OEIS A014233)
smtlib-qf-nia-unknown-certificates	Optimization benchmarks	harvest	laptop-hours per benchm…	known-unknowns/optimization-benchmarks/smtlib-qf-nia-unknown-certificates.md	SMT-LIB nonlinear integer arithmetic (QF_NIA): a checked answer for an unknown-status benchmark no SMT-COMP solver ever decided
sokoban-max-moves-small-boards	Graphs, games and automata	harvest	laptop-hours	known-unknowns/graphs-games-automata/sokoban-max-moves-small-boards.md	Sokoban maximum moves: a board with n floor squares and k boxes whose shortest solution beats the DeStefano-qqwref archive
higher-dimensional-partitions-next-terms	Recreational math	harvest	needs cluster for A0002…	known-unknowns/recreational-math/higher-dimensional-partitions-next-terms.md	Solid and higher-dimensional partitions: the next term of A000293 (solid, n = 73) or A000334 (4D, n = 41), or of the 5- to 8-dimensional counts
spherical-codes-cohn-table	Packings and physics	harvest	laptop-hours	known-unknowns/packings-physics/spherical-codes-cohn-table.md	Spherical codes (Tammes problem and higher dimensions): beat an entry in Cohn's spherical-codes.org table
sloane-cohn-spherical-coverings-s2	Packings and physics	harvest	laptop-hours	known-unknowns/packings-physics/sloane-cohn-spherical-coverings-s2.md	Spherical coverings: N points on the sphere with a smaller covering radius than the Hardin-Sloane-Smith table (N = 4..130, kept by Henry Cohn)
spherical-designs-s2-fewest-points	Packings and physics	harvest	laptop-days	known-unknowns/packings-physics/spherical-designs-s2-fewest-points.md	Spherical t-designs on S^2 with fewer points: beat the smallest known N for a degree t (Hardin-Sloane, Graef-Potts and Womersley tables)
elliptic-quadric-q7-3-spread	Record tables	moonshot	laptop-days to needs cl…	known-unknowns/record-tables/elliptic-quadric-q7-3-spread.md	Spread of the elliptic quadric Q^-(7,3): 82 generator planes partitioning its 1066 points, or a rerunnable nonexistence proof
squared-rectangle-census-next-order	Recreational math	harvest	needs cluster	known-unknowns/recreational-math/squared-rectangle-census-next-order.md	Squared-rectangle census: the next complete count of perfect squared rectangles (order 27), squared squares (order 38) or compound perfect squares (order 40)
jarvis-ssub-experimental-formation-enthalpy-mae	Chemistry and materials	standard	laptop-hours	known-unknowns/chemistry-materials/jarvis-ssub-experimental-formation-enthalpy-mae.md	SSUB experimental formation enthalpies on JARVIS-Leaderboard (1,726 compounds, composition only): beat ElemNet2-TL's test MAE of 0.0924
steiner-tree-bcr-integrality-gap-lower-bound	Algorithms	standard	laptop-days	known-unknowns/algorithms/steiner-tree-bcr-integrality-gap-lower-bound.md	Steiner tree bidirected cut relaxation: an explicit instance with integrality gap above Vicari's 6/5 (hypergraphic 8/7 and BCR+ 36/31 as partial wins)
strongly-regular-configurations-open	Record tables	harvest	laptop-days	known-unknowns/record-tables/strongly-regular-configurations-open.md	Strongly regular configurations: construct a (v_k; lambda, mu) configuration marked '?' in the Abreu-Funk-Krcadinac-Labbate table (smallest (41_5; 9,10))
sudoku-x-11-clues	Recreational math	standard	laptop-days	known-unknowns/recreational-math/sudoku-x-11-clues.md	Sudoku-X with 11 clues: beat the 12-clue minimum (known since 2007; 558,981 12-clue puzzles known, 552,952 public)
ccd-sutton-chen-clusters	Packings and physics	harvest	laptop-hours	known-unknowns/packings-physics/ccd-sutton-chen-clusters.md	Sutton-Chen metal clusters (12-6, 9-6, 10-8; N <= 80): lower a putative global minimum in the Doye-Wales tables
swot-error-calibration-2022c-gulf-stream	Earth and sky	harvest	laptop-hours	known-unknowns/earth-and-sky/swot-error-calibration-2022c-gulf-stream.md	SWOT correlated-error calibration data challenge 2022c (Gulf Stream OSSE): beat the leaderboard's best on-swath RMSE
symmetric-hadamard-undecided-orders	Record tables	harvest	laptop-days	known-unknowns/record-tables/symmetric-hadamard-undecided-orders.md	Symmetric Hadamard matrices: an order 4v where none is known (smallest 428 = 4*107, then 476, 652, 668, 716)
t2t-human-genome-compression-record	Biology	standard	laptop-days	known-unknowns/biology/t2t-human-genome-compression-record.md	T2T human genome compression: beat the best bits-per-base entry in the public human-genome compression table
tabarena-v01-per-dataset-best-error	Machine learning	harvest	laptop-hours per small…	known-unknowns/machine-learning/tabarena-v01-per-dataset-best-error.md	TabArena-v0.1: beat the best mean test error of all 94 leaderboard entries on one of the 51 curated tabular datasets
tdc-docking-drd3-oracle-budgeted-generation	Drug discovery	harvest	laptop-hours	known-unknowns/drug-discovery/tdc-docking-drd3-oracle-budgeted-generation.md	TDC Docking Benchmark Group (DRD3, 5,000-call docking oracle): beat the Graph-GA top-100/top-10/top-1 records
det3-tensor-rank-17-or-18	Algorithms	moonshot	laptop-days	known-unknowns/algorithms/det3-tensor-rank-17-or-18.md	Tensor rank of the 3x3 determinant as a 9x9x9 tensor: 17 or 18? (Shitov's Question 11.1)
fermi-gbm-offline-tgf-missed	Earth and sky	standard	laptop-hours	known-unknowns/earth-and-sky/fermi-gbm-offline-tgf-missed.md	Terrestrial gamma-ray flash in public Fermi GBM TTE data, absent from the GBM TGF catalog
tgb-dynamic-link-mrr-leaderboards	Machine learning	harvest	laptop-hours for tgbl-w…	known-unknowns/machine-learning/tgb-dynamic-link-mrr-leaderboards.md	TGB dynamic link prediction (tgbl-wiki-v2, review-v2, coin-v2, comment, flight-v2): beat a leaderboard's top test MRR
maximal-prime-gap-86th	Number hunts	standard	needs cluster	known-unknowns/number-hunts/maximal-prime-gap-86th.md	The 86th maximal prime gap: the first gap above 1854 (rank 85 confirmed at 1.0141 x 10^20 in May 2026)
equal-circle-coverings-square-disk	Packings and physics	harvest	laptop-hours	known-unknowns/packings-physics/equal-circle-coverings-square-disk.md	Thinnest coverings by n equal circles: cover the unit square (Nurmela-Ostergard table, n <= 30) or a disk (Tan, n = 21..25) with smaller circles
thomson-problem-live-tables	Packings and physics	harvest	laptop-hours	known-unknowns/packings-physics/thomson-problem-live-tables.md	Thomson problem: lower the best known Coulomb energy for some N (Deeter / Cambridge Cluster Database / Riesz s=1 tables)
three-colour-rado-numbers-ax-by-cz	Number hunts	harvest	laptop-hours	known-unknowns/number-hunts/three-colour-rado-numbers-ax-by-cz.md	Three-colour Rado numbers R_3(ax + by = cz): refute an Ahmed–Zaman–Bright conjecture or settle a cell beyond the SAT tables
ghz-nonlocality-robustness-below-049143	Physics	harvest	laptop-days	known-unknowns/physics/ghz-nonlocality-robustness-below-049143.md	Three-qubit GHZ nonlocality robustness: a certified Bell violation at white-noise visibility below 0.49143 (Designolle-Vertesi-Pokutta)
turan-tight-5-cycle-3-graph-density	Erdős problems and proofs	standard	needs cluster	known-unknowns/erdos-and-proofs/turan-tight-5-cycle-3-graph-density.md	Tight 5-cycle C5^(3) (Mubayi-Rödl conjecture): a certified upper bound on pi(C5^(3)) below 0.46503, or a C5^(3)-free construction above 2*sqrt(3)-3
timpasslib-integrated-timetabling-routing	Optimization benchmarks	harvest	laptop-hours	known-unknowns/optimization-benchmarks/timpasslib-integrated-timetabling-routing.md	TimPassLib: a periodic timetable with lower total passenger travel time than the best known for an open integrated timetabling-and-routing instance
toads-and-frogs-erickson-conjecture-5	Graphs, games and automata	standard	laptop-hours to laptop-…	known-unknowns/graphs-games-automata/toads-and-frogs-erickson-conjecture-5.md	Toads and Frogs: values of T^a [ ]^b F^a beyond Thanatipanonda's table, or a counterexample to Erickson's Conjecture 5
tptp-unknown-rating-1-problems	Formal proofs	harvest	laptop-hours	known-unknowns/formal-proofs/tptp-unknown-rating-1-problems.md	TPTP: prove (or refute) a problem with status Unknown/Open or rating 1.00, with an independently checked proof
plmfit-trastuzumab-cdrh3-binding-mcc	Biology	standard	laptop-hours	known-unknowns/biology/plmfit-trastuzumab-cdrh3-binding-mcc.md	Trastuzumab CDR-H3 variant binding (PLMFit herH3 one-vs-rest): beat the scoreboard MCC of 0.3898
robinx-ttp-traveling-tournament-ub	Optimization benchmarks	harvest	laptop-hours	known-unknowns/optimization-benchmarks/robinx-ttp-traveling-tournament-ub.md	Traveling Tournament Problem (RobinX repository): shorter total travel for an open NL, NFL, GAL, CIRC, SUP, BRA or CON instance
triangular-peg-solitaire-shortest-11-12	Graphs, games and automata	harvest	laptop-hours	known-unknowns/graphs-games-automata/triangular-peg-solitaire-shortest-11-12.md	Triangular peg solitaire: shorter single-vacancy solutions on Triangle(11) and Triangle(12) (OEIS A127500 bounds 19..28 and 21..29)
tribone-tilings-triangle-a334875-n45	Graphs, games and automata	standard	laptop-hours to laptop-…	known-unknowns/graphs-games-automata/tribone-tilings-triangle-a334875-n45.md	Tribone (T_2 stone) tilings of the triangle T_n (Conway-Lagarias, Propp's Problem 20): the next nonzero term A334875(45), unknown since 2020
tsp-art-bosch-five-instances	Optimization benchmarks	standard	laptop-days	known-unknowns/optimization-benchmarks/tsp-art-bosch-five-instances.md	TSP Art (Bosch): a shorter tour for vangogh120K, venus140K, pareja160K, courbet180K or earring200K
tsptw-lopez-ibanez-open-cells	Optimization benchmarks	standard	laptop-hours to laptop-…	known-unknowns/optimization-benchmarks/tsptw-lopez-ibanez-open-cells.md	TSPTW makespan (Lopez-Ibanez collection): beat the best-known makespan 917.83 of rc_204.1, the last open makespan cell
turan-pure-power-sum-c42-upper-bound	Erdős problems and proofs	standard	laptop-hours	known-unknowns/erdos-and-proofs/turan-pure-power-sum-c42-upper-bound.md	Turan's pure power-sum constant (C_42, Erdos #519): a certified upper bound below 0.6873358063 or an explicit lower bound above 1/2
turan-k5-3-graph-density	Erdős problems and proofs	standard	needs cluster	known-unknowns/erdos-and-proofs/turan-k5-3-graph-density.md	Turán's K5^(3) conjecture: a certified upper bound on pi(K5^(3)) below 0.757017, or a K5^(3)-free construction above 3/4
hcp-fcc-ice-diamond-percolation-twins	Physics	standard	laptop-hours to laptop-…	known-unknowns/physics/hcp-fcc-ice-diamond-percolation-twins.md	Twin-lattice percolation: are the hcp and fcc bond thresholds equal (both 0.120164 within 1e-6), and how far apart are ice Ih and diamond?
univalent-bloch-constant-upper-bound	Erdős problems and proofs	harvest	laptop-hours	known-unknowns/erdos-and-proofs/univalent-bloch-constant-upper-bound.md	Univalent Bloch-Landau constant B_u (C_57c): a slit domain with certified inradius/conformal-radius ratio below van Staden's 0.65628589
regular-graph-counts-next-order	Graphs, games and automata	harvest	laptop-hours to laptop-…	known-unknowns/graphs-games-automata/regular-graph-counts-next-order.md	Unlabeled regular graph counts: the next unknown term for cubic, quintic, sextic or 7-regular graphs (A002851, A006821, A006822, A014377), or quartic beyond order 50
heesch-polyform-hc5	Graphs, games and automata	standard	laptop-hours	known-unknowns/graphs-games-automata/heesch-polyform-hc5.md	Unmarked polyform with Heesch number 5 or more
uranus-neptune-coorbital-unrecognised	Sky archives	harvest	laptop-hours	known-unknowns/sky-archives/uranus-neptune-coorbital-unrecognised.md	Unrecognised Uranus or Neptune co-orbital (Trojan, horseshoe or quasi-satellite) among catalogued small bodies, shown by clone integration
soho-ccor-archival-sungrazer-comet	Earth and sky	harvest	laptop-hours	known-unknowns/earth-and-sky/soho-ccor-archival-sungrazer-comet.md	Unreported sungrazing comet in archival SOHO/LASCO or GOES-19 CCOR coronagraph images, absent from Sungrazer lists
brouwer-binary-unrestricted-a-n-d	Record tables	harvest	laptop-hours	known-unknowns/record-tables/brouwer-binary-unrestricted-a-n-d.md	Unrestricted binary codes A(n,d), n <= 28: new lower bound in Brouwer's table
usgs-oaf-aftershock-1week-m4-brier-2024-2025	Earth and sky	standard	laptop-hours	known-unknowns/earth-and-sky/usgs-oaf-aftershock-1week-m4-brier-2024-2025.md	USGS operational aftershock forecasts 2024-2025: lower Brier score than USGS for 'at least one M4+ aftershock within a week'
vertex-minor-ramsey-rvm5	Graphs, games and automata	standard	laptop-hours	known-unknowns/graphs-games-automata/vertex-minor-ramsey-rvm5.md	Vertex-minor Ramsey numbers: a 13-vertex graph with no 5-vertex edgeless vertex-minor (R_vm(5) >= 14), or beat Bae's explicit bounds for k = 6..9
random-fibonacci-viswanath-embree-trefethen-digits	Number hunts	standard	laptop-days	known-unknowns/number-hunts/random-fibonacci-viswanath-embree-trefethen-digits.md	Viswanath's random Fibonacci constant 1.1319882487943...: a rigorous enclosure to 17 or more decimals
volcano-thermal-unrest-not-in-gvp	Earth and sky	harvest	laptop-hours	known-unknowns/earth-and-sky/volcano-thermal-unrest-not-in-gvp.md	Volcanic thermal anomaly in open Sentinel-2 imagery at a volcano with no corresponding Smithsonian GVP eruption record
magic-square-water-retention-records	Recreational math	harvest	laptop-hours	known-unknowns/recreational-math/magic-square-water-retention-records.md	Water retention of magic squares (Knecht): a normal magic square of order 10-15 retaining more water than the OEIS A201126 lower bounds, or better order 16-28, semi-magic and asso…
integer-square-dissections-count-a045846	Recreational math	standard	laptop-days for A224239…	known-unknowns/recreational-math/integer-square-dissections-count-a045846.md	Ways to cut an n x n square into integer squares: the next term a(26) of OEIS A045846, or new terms of the inequivalent count A224239
rectangle-dissections-square-a182275-n13	Recreational math	harvest	laptop-hours	known-unknowns/recreational-math/rectangle-dissections-square-a182275-n13.md	Ways to divide an n x n square into integer-sided rectangles: the next term A182275(13) (known to n = 12 since Butler 2014)
wheel-and-fan-ramsey-small	Record tables	harvest	laptop-hours for lower…	known-unknowns/record-tables/wheel-and-fan-ramsey-small.md	Wheels and fans: close a gap in DS1 Table VIII (R(W7,W8) 19-21, R(W8,W8) 22-25, R(W4,W8) 22-26, ...) or R(F4,F4) 18-24
wilf-conjecture-verification-beyond-genus-100	Number hunts	standard	needs cluster	known-unknowns/number-hunts/wilf-conjecture-verification-beyond-genus-100.md	Wilf's conjecture on numerical semigroups: extend the computer verification beyond genus 100, or find a counterexample