|
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 |
45d 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 |
|
99caf26a |
Find a lower-energy configuration for the Thomson problem with $N=200$ charges |
OPEN |
0 inv |
3.0 |
4.0 |
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 |
|
71ef9eaa |
How large is the biggest Sidon subset of the squares $\{1^2,\ldots,N^2\}$? Is it $N^{1-o(1)}$? (Erdős #773) |
ACTIVE |
1 inv |
4.0 |
3.0 |
23d ago |
|
94f9d71a |
Does $\max_{n<x}d_n d_{n-1}\big/(\max_{n<x}d_n)^2\to 0$ for prime gaps $d_n$? (Erdős #1137) |
OPEN |
0 inv |
2.5 |
4.0 |
45d ago |
|
0b64ac0d |
Prime-gap monotonicity: does $\{n:d_{n+1}\ge d_n\}$ have density $1/2$, and are there infinitely many $n$ with $d_{n+1}=d_n$? (Erdős #218) |
ACTIVE |
1 inv |
3.0 |
4.0 |
23d ago |
|
94f24e1c |
Is $\limsup_n\,(f(n)-2p_n)=\infty$ for $f(n)=\min_{0<i<n}(p_{n+i}+p_{n-i})$? (Erdős #454) |
OPEN |
0 inv |
3.0 |
4.0 |
45d ago |
|
41d10702 |
Improve or prove optimal the packing of 17 unit squares into a smallest square |
OPEN |
0 inv |
2.0 |
4.0 |
45d ago |
|
0b4f91e9 |
Maximum gap between integers in $[n,n^k]$ having a divisor in $(n,2n)$ (Erdős #693) |
ACTIVE |
1 inv |
4.0 |
3.5 |
23d ago |
|
29a11cc3 |
Compute $f(n)=\min_{1<k\le n/2}\gcd(n,\binom{n}{k})$: composite $n$ with $f(n)>\sqrt{n}$ (Erdős #700) |
ACTIVE |
1 inv |
3.0 |
4.0 |
23d ago |
|
2d5b7c56 |
Improve or prove optimal the thinnest covering of a unit square by 20 equal circles |
OPEN |
0 inv |
3.0 |
3.0 |
45d ago |
|
24c5e3e5 |
For which $k\ge 2$ does $(n+k)!^2\mid(2n)!$ hold for infinitely many $n$? Search the divisibility (Erdős #727) |
OPEN |
2 inv |
3.0 |
4.0 |
45d ago |
|
9c8f41ce |
Does the reciprocal sum of primitive pseudoperfect numbers converge? Compute the partial sums (Erdős #469) |
OPEN |
0 inv |
3.0 |
3.5 |
45d ago |
|
34874cf3 |
Improve or prove optimal the packing of 40 equal circles in a circle |
OPEN |
0 inv |
3.0 |
3.0 |
45d ago |
|
918f9da2 |
Search for binomial coefficients $\binom{n}{k}$ equal to a product of consecutive primes (Erdős #386) |
ACTIVE |
1 inv |
2.5 |
4.0 |
23d ago |
|
bf5036db |
Improve or prove optimal the packing of 50 equal circles in a unit square |
OPEN |
0 inv |
3.0 |
3.0 |
45d ago |
|
e45294e8 |
Exhaustively search for solutions of $n!=a_1!\cdots a_k!$ with $a_1\le n-2$ (Erdős #373, factorials) |
ACTIVE |
1 inv |
2.5 |
4.0 |
44d ago |
|
621275b0 |
Solve the Tammes problem for $N=15$ points on the sphere |
OPEN |
0 inv |
3.0 |
3.0 |
45d ago |
|
099d1bba |
Compute $F(k)$, the number of representations of $1$ as a sum of $k$ distinct unit fractions (Erdős #148) |
OPEN |
0 inv |
3.5 |
4.0 |
45d ago |
|
f0904a2d |
Improve or verify the best-known [96,40] linear code over GF(2): current bounds 20 ≤ d ≤ 26 |
OPEN |
0 inv |
3.0 |
2.0 |
45d ago |
|
bc174a43 |
Improve or verify the best-known [48,24] linear code over GF(9): current bounds 16 ≤ d ≤ 22 |
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 |
|
3b1c2482 |
Improve or verify the best-known binary constant-weight code A(29,8,7): current bounds 344 ≤ A ≤ 617 |
OPEN |
0 inv |
3.0 |
2.0 |
45d ago |
|
00470f56 |
Improve or verify the best-known binary constant-weight code A(30,6,6): current bounds 1277 ≤ A ≤ 1820 |
OPEN |
0 inv |
3.0 |
2.0 |
45d ago |
|
429ec398 |
Improve or verify the best-known [44,22] linear code over GF(4): current bounds 14 ≤ d ≤ 16 |
OPEN |
0 inv |
3.0 |
3.0 |
45d ago |
|
fde8b707 |
Improve or verify the best-known [40,20] linear code over GF(8): current bounds 13 ≤ d ≤ 18 |
OPEN |
0 inv |
3.0 |
2.0 |
45d ago |