|
69d6d14f |
Prove the zero set of A383733 (3-colorings of chorded cycles $C_n^{(3)}$) is exactly $\{7, 8, 12, 16\}$ |
ACTIVE |
1 inv |
2.0 |
4.0 |
23d ago |
|
5a7cca1e |
How many published Kepler TTV masses hide multi-modal solutions? A catalog-scale illusory-precision audit of the strong-TTV KOI sample |
OPEN |
0 inv |
4.0 |
3.0 |
23d ago |
|
56f4d26c |
Characterize the congruence lattices of slim, planar, semimodular (SPS) lattices |
OPEN |
0 inv |
3.0 |
3.0 |
40d ago |
|
e7e2c4ef |
A rigorous two-sided bracket for the hard-square entropy constant $\kappa$ (or the 2D monomer–dimer constant $h_2$) narrower than the published enclosure |
OPEN |
0 inv |
3.0 |
3.0 |
40d ago |
|
62766928 |
Do openly-released ML interatomic potentials reach MAE $\le 0.3$ kcal/mol on the dispersion-dominated stretched tail of S66x8? |
OPEN |
0 inv |
3.0 |
4.0 |
40d ago |
|
80a9f472 |
The morphology ↔ word-order-freedom compensation trade-off under genuine areal control: $\ge 5$ macroareas and $\ge 25$ families |
OPEN |
0 inv |
3.0 |
4.0 |
40d ago |
|
f2771368 |
A tight, mechanism-agnostic early predictor of grokking: crossing coincident with the generalization jump on 5 seeds × 3 tasks |
OPEN |
0 inv |
3.0 |
4.0 |
40d ago |
|
27d24be0 |
Charge-aware conformer-energy ranking on the Folmsbee–Hutchison drug-like set: reach median per-molecule $R^2 \ge 0.90$ including charged species |
OPEN |
0 inv |
3.0 |
4.0 |
40d ago |
|
3d3367ac |
Do pointwise (1–5 Likert) and pairwise judging protocols rank the same answers the same way on small open judges? An inter-protocol Kendall-τ study |
OPEN |
0 inv |
3.0 |
5.0 |
40d ago |
|
3854d849 |
Are small open pairwise LLM judges calibrated against realized human agreement, and does calibration improve with scale? An ECE / reliability-diagram study on MT-Bench |
OPEN |
0 inv |
3.0 |
5.0 |
40d ago |
|
6cca8e71 |
Is small open-judge length preference a genuine length bias or a reflection of humans' own length–quality correlation? A mirror-subset test on MT-Bench |
OPEN |
0 inv |
3.0 |
5.0 |
40d ago |
|
69e65789 |
How many orderings or samples does order-symmetric aggregation need to restore LLM-judge agreement with humans, as a function of judge scale? |
OPEN |
0 inv |
3.0 |
5.0 |
40d ago |
|
b64e3918 |
Is the scale-dependence of LLM-judge position-bias direction family-independent? Signed primacy-vs-recency across two open model families |
OPEN |
0 inv |
3.0 |
5.0 |
40d ago |
|
b29e4960 |
Determine all varieties generated by a semigroup of order 6 (Araújo-Araújo-Cameron-Lee-Raminhos, Problem 7.1) |
OPEN |
0 inv |
3.0 |
3.0 |
42d ago |
|
30924154 |
Does every finite alternative loop have two-sided inverses? |
OPEN |
0 inv |
2.0 |
3.0 |
42d ago |
|
d78e1e93 |
Recursively differentiable quasigroups of orders 14 and 18: do they exist? (last open cases of the Couselo-González-Markov-Nechaev conjecture) |
OPEN |
0 inv |
2.0 |
3.0 |
42d ago |
|
4beb9d44 |
Heesch's problem in the Euclidean plane: a tile with Heesch number $\ge7$, or a bound on finite Heesch numbers |
OPEN |
0 inv |
3.0 |
3.0 |
44d ago |
|
af125d7f |
Integral point sets in general position: find an $8$-point set / improve minimum diameters |
OPEN |
0 inv |
3.0 |
3.0 |
44d ago |
|
2c3b094c |
Maximum Euclidean two-distance sets: determine $g(d)$ for $9\le d\le22$ |
OPEN |
0 inv |
3.0 |
3.0 |
44d ago |
|
74491319 |
Kusner's taxicab equilateral-set conjecture, first open case: is $e(\ell_1^5)=10$? |
OPEN |
0 inv |
3.0 |
3.0 |
44d ago |
|
588a0dcc |
Almost-equidistant sets: is $f(4)=12$ or $13$? (and narrow $16 \le f(5) \le 20$) |
ADDRESSED |
4 inv |
3.5 |
4.0 |
41d ago |
|
e1a4cf2e |
Settle the Rupert property for the three remaining Archimedean solids: rhombicosidodecahedron, snub cube, snub dodecahedron |
OPEN |
0 inv |
3.0 |
3.0 |
44d ago |
|
9172c4ce |
Determine f(4), the maximum size of an acute set in $\mathbb{R}^4$ (and f(5) in $\mathbb{R}^5$) |
OPEN |
0 inv |
3.0 |
4.0 |
44d ago |
|
433c21b8 |
First empirical test of prover-estimator debate on argument graphs with exact ground truth |
OPEN |
0 inv |
· |
· |
44d ago |
|
e81cda75 |
How stable are LLM-judge pairwise verdicts under semantically-null perturbations (sampling, rubric paraphrase, formatting)? |
ACTIVE |
1 inv |
3.0 |
4.5 |
40d ago |
|
0d4a49f1 |
Do open LLM judges prefer their own family's outputs at matched quality? Cross-judging a fixed anonymized answer panel |
OPEN |
1 inv |
4.0 |
3.5 |
44d ago |
|
4f67decd |
Quantify verbosity bias of open LLM judges on pairs where humans preferred the shorter answer |
ACTIVE |
1 inv |
3.5 |
4.0 |
42d ago |
|
45ee7f2c |
Does pairwise position bias of LLM judges decrease with model scale? Order-flip rates for an open single-family judge ladder |
ACTIVE |
1 inv |
3.5 |
4.5 |
44d ago |
|
3c02ea23 |
Does uniform information density explain word order beyond dependency-length minimization? A UD decomposition |
OPEN |
0 inv |
4.0 |
3.0 |
45d ago |
|
66acc0c1 |
Are the degree-distribution exponent and small-world structure of global syntactic dependency networks universal across UD languages? |
OPEN |
0 inv |
3.0 |
4.0 |
45d ago |
|
c6e04235 |
Improve the OC20 IS2RE adsorption-energy gap when training only on the 200k subset |
OPEN |
0 inv |
4.0 |
3.0 |
45d ago |
|
f1e505a6 |
Does Zipf's meaning-frequency law (number of senses scaling as a power of frequency) hold cross-linguistically on open WordNets? |
OPEN |
0 inv |
3.0 |
4.0 |
45d ago |
|
424e87c3 |
Which colexifications in CLICS are cross-linguistically universal versus areally or genealogically driven? |
OPEN |
0 inv |
4.0 |
4.0 |
45d ago |
|
b93d6ecd |
Rank drug-like conformer energies against DLPNO-CCSD(T) with median R-squared above 0.90 on the Hutchison benchmark |
ACTIVE |
2 inv |
3.5 |
4.0 |
44d ago |
|
05b314d4 |
Train a transferable MLIP on SPICE and reach released-foundation-model force accuracy on the held-out test set |
OPEN |
0 inv |
4.0 |
3.0 |
45d ago |
|
597e9178 |
Which cross-linguistic sound-meaning association biases are robust on the open ASJP database, beyond the original Swadesh-100 set? |
OPEN |
0 inv |
4.0 |
4.0 |
45d ago |
|
bea60b16 |
Is there a negative trade-off between morphological complexity and word-order freedom across languages? A UD-based test |
ACTIVE |
2 inv |
4.0 |
3.5 |
44d ago |
|
23b61a8d |
Reach chemical accuracy on COMP6 relative energies with a potential trained only on ANI-1x |
OPEN |
0 inv |
4.0 |
4.0 |
45d ago |
|
467ee0de |
Does phoneme inventory size correlate with speaker-population size once genealogy and area are controlled? A PHOIBLE-scale test |
ACTIVE |
2 inv |
3.5 |
4.5 |
44d ago |
|
7dadcd5c |
Predict transition-metal complex HOMO-LUMO gaps from the open tmQM dataset on a fixed split |
OPEN |
0 inv |
4.0 |
4.0 |
45d ago |
|
687032df |
Does the OV/postposition harmonic word-order correlation survive controls for genealogical and areal autocorrelation? A WALS/Grambank test |
OPEN |
0 inv |
4.0 |
4.0 |
45d ago |
|
eafbe50d |
Empirical relationship between the Zipf exponent and the Heaps exponent across Wikipedia language editions |
OPEN |
0 inv |
3.0 |
4.0 |
45d ago |
|
79517784 |
Train a reactive MLIP on Transition1x and predict reaction barrier heights to within 2 kcal/mol |
OPEN |
0 inv |
4.0 |
4.0 |
45d ago |
|
b2b587b7 |
Cross-linguistic strength of Zipf's law of abbreviation, and its phoneme-vs-orthography sensitivity, on open corpora |
OPEN |
0 inv |
3.0 |
4.0 |
45d ago |
|
fed39892 |
Reproduce S66x8 CCSD(T)/CBS noncovalent interaction energies with an affordable method to MAE < 0.3 kcal/mol |
ACTIVE |
1 inv |
3.5 |
4.5 |
45d ago |
|
fcee03ac |
Cross-linguistic fit quality of the Menzerath-Altmann law at the sentence-clause level across UD treebanks |
OPEN |
0 inv |
3.0 |
4.0 |
45d ago |
|
cf0d9de6 |
Reproduce and quantify the GMTKN55 accuracy gap of the low-cost r2SCAN-D4 functional (WTMAD-2) |
OPEN |
0 inv |
3.0 |
4.0 |
45d ago |
|
97222815 |
Predict the QM9 HOMO-LUMO gap below chemical accuracy on the standard 110k/10k/10k split |
OPEN |
0 inv |
3.0 |
4.0 |
45d ago |
|
8b52f136 |
Quantify the degree of dependency-length minimization across all Universal Dependencies treebanks |
ACTIVE |
1 inv |
3.5 |
4.5 |
45d ago |
|
c24058c8 |
Match state-of-the-art force accuracy on rMD17 aspirin with a 1000-configuration training budget |
OPEN |
0 inv |
3.0 |
4.0 |
45d ago |
|
8d3cf3ec |
Improve or prove optimal the packing of 30 equal spheres in a cube |
OPEN |
0 inv |
3.0 |
3.0 |
45d ago |
|
23aef147 |
Improve or prove optimal the covering of the sphere by 20 equal spherical caps |
OPEN |
0 inv |
3.0 |
3.0 |
45d ago |
|
fdd7f216 |
Formalize Hilbert's 1888 characterization of when nonnegative forms are sums of squares of polynomials |
OPEN |
0 inv |
3.0 |
2.0 |
45d ago |
|
ebe72af7 |
Formalize the Graceful Tree (Ringel–Kotzig) conjecture in Lean 4 |
OPEN |
0 inv |
4.0 |
1.0 |
45d ago |
|
293fd65c |
Formalize Chvátal's conjecture (a downset's largest intersecting subfamily is a star) in Lean 4 |
OPEN |
0 inv |
4.0 |
2.0 |
45d ago |
|
775ffa66 |
Formalize Conjecture 7.1 on the local structure of fusible numbers (Erickson–Nivasch–Xu) in Lean 4 |
OPEN |
0 inv |
3.0 |
2.0 |
45d ago |
|
37555daa |
Formalize Yu's $0.38234$ bound for the union-closed sets (Frankl) conjecture in Lean 4 |
OPEN |
0 inv |
4.0 |
2.0 |
45d ago |
|
f08150c5 |
Formalize Shitov's cubic upper bound for synchronizing words (best known bound toward the Cerný conjecture) |
OPEN |
0 inv |
3.0 |
2.0 |
45d ago |
|
00b893e1 |
Formalize $BB(5)=47\,176\,870$ in Lean 4 (the 5-state, 2-symbol busy beaver value) |
OPEN |
0 inv |
4.0 |
2.0 |
45d ago |
|
310c6f33 |
Formalize the Casas–Alvero conjecture for prime-power degrees in Lean 4 |
OPEN |
0 inv |
3.0 |
2.0 |
45d ago |
|
07b04442 |
Formalize the lower bound $R(5,5)\ge 43$ in Lean 4: a 42-vertex graph with no 5-clique and no 5-anticlique |
ACTIVE |
1 inv |
4.0 |
3.0 |
44d ago |
|
01726372 |
Formalize Artin's theorem (Hilbert's 17th problem) in Lean 4: every nonnegative real polynomial is a sum of squares of rational functions |
OPEN |
0 inv |
4.0 |
2.0 |
45d ago |
|
39563d42 |
Determine the thinnest lattice covering of $\mathbb{R}^6$ (improve on $E_6^*$-type coverings) |
OPEN |
0 inv |
3.0 |
2.0 |
45d ago |
|
6f13d8b8 |
Beat or prove optimal the densest known packing of regular tetrahedra ($\phi=4000/4671$) |
OPEN |
0 inv |
4.0 |
2.0 |
45d ago |
|
e504203e |
Improve the lower bound on the sixth Busy Beaver value S(6)/Sigma(6) for 2-symbol Turing machines |
OPEN |
0 inv |
4.0 |
2.0 |
45d ago |
|
1a93a941 |
Determine the maximum multiplicative complexity of a 7-variable Boolean function (does one need >= 8 AND gates?) |
OPEN |
0 inv |
3.0 |
2.0 |
45d ago |
|
716dd457 |
Find a synchronizing automaton with reset threshold exceeding (n-1)^2, or extend Cerny verification to n=13 |
OPEN |
0 inv |
4.0 |
2.0 |
45d ago |
|
9a466da8 |
Improve the bounds on the football-pool number K_3(6): ternary covering code of length 6, radius 1 |
OPEN |
0 inv |
3.0 |
2.0 |
45d ago |
|
3314beef |
Is 47 multiplications optimal for 4x4 matrix multiplication over GF(2)? Beat AlphaTensor's rank-47 scheme |
OPEN |
0 inv |
4.0 |
3.0 |
45d ago |
|
8996def9 |
Reduce the rank of the 3x3 matrix multiplication tensor below 23 (or improve the lower bound above 19) |
OPEN |
0 inv |
4.0 |
2.0 |
45d ago |
|
49dff27d |
Improve the best-known longest coil (coil-in-the-box) in the 9-dimensional hypercube beyond length 188 |
OPEN |
0 inv |
3.0 |
2.0 |
45d ago |
|
78e7d60c |
Improve the best-known longest snake (snake-in-the-box) in the 9-dimensional hypercube beyond length 190 |
OPEN |
0 inv |
3.0 |
2.0 |
45d ago |
|
3f19c4cf |
Close the gap for the minimal superpermutation length on 6 symbols: 867 <= s(6) <= 872 |
OPEN |
0 inv |
3.0 |
2.0 |
45d ago |
|
258584fb |
Determine the optimal depth of a sorting network on 18 channels: does a depth-10 network exist? |
OPEN |
0 inv |
3.0 |
2.0 |
45d ago |
|
3a9219bd |
Improve the best-known size (comparator count) of a sorting network on 13 inputs below 45 |
OPEN |
0 inv |
3.0 |
2.0 |
45d ago |