Open computational mathematics. AI-audited, not peer-reviewed. All code and data open for independent verification.
17 computational results from GPU-accelerated mathematics research. Each finding is AI-audited claim-by-claim against published literature (53 reviews from 7 models). Not a substitute for formal peer review. How to cite →
Complete character table of S_40 (37,338 partitions, 1.394 billion entries, 9.5 hours on 64-core CPU). Values exceed int64 (max |chi| = 5.9 x 10^22). To our knowledge, the first publicly archived expl...
Complete Kronecker coefficient tables for S_20 (32.7M nonzero, 3.7s) and S_30 (26.4B nonzero, 4.9 min) computed on a single NVIDIA B200 GPU. S_30 recomputed 2026-04-06 with Kahan summation kernel: 26,...
UPDATED 2026-04-23 audit: A={1,2,3} has exactly 27 uncovered denominators through the completed 10^10 run, all ≤ 6,234. Several {1,2,k} exception counts are stable across available completed ranges, b...
GPU computation of 30 billion class numbers for real quadratic fields reveals that the h(d)=1 rate DECREASES from 42% at d~10^4 to 15.35% at d~10^10 and is still falling. This is NOT non-monotone conv...
At n=20 (1,048,575 subsets): dim_H(E_{1,...,5}) = 0.837 while dim_H(E_{2,...,20}) = 0.768. Five digits containing 1 produce a larger Cantor set than fourteen digits without it. Removing digit 1 from {...
Exploratory GPU BFS data for Zaremba generator diameters for all 172 primes p ≤ 1021. Audit caveat: the current kernel uses determinant -1 generators and stops when total_visited reaches |SL₂(p)|, so ...
FP64/N=40 cuBLAS computation of congruence spectral gaps for Zaremba's semigroup Γ_{1,...,5}. All 168 primes to p=1000 have σ_p ≥ 0.344. The three smallest gaps occur at p=491 (σ=0.344), p=877 (σ=0.35...
Audit revision: digit 1 strongly amplifies Zaremba density relative to digit 2, but the headline inverse-square law is not established by the current data. At matched N = 10^10 for {1,k} and {2,k}, k=...
The Zaremba density for A={1,2} fits density = 31.5 + 4.47·log₁₀(N) (R² = 0.9984, 5 empirical measurements at N = 10^6, 10^9, 10^10, 10^11, 10^12; forecasted values such as for N > 10^12 are extrapola...
Complete density computation for all {1,k} pairs at 10^11. Density drops exponentially: {1,2}=80.75%, {1,3}=9.11%, {1,4}=1.07%, ..., {1,10}=0.0085%. Only {1,2} has Hausdorff dimension above 1/2. Updat...
Corrected 2026-04-23 audit: the 27 uncovered denominators for A={1,2,3} through the completed 10^10 run are 6,20,28,38,42,54,96,150,156,164,216,228,318,350,384,558,770,876,1014,1155,1170,1410,1870,205...
Reformulating CF tree enumeration as batched 2×2 matrix multiplication on GPU eliminates all CPU bottlenecks. The fused expand+mark+compact kernel verifies 100M values in 7.5 seconds on a single B200,...
Proof FRAMEWORK (not a completed proof) for Zaremba's Conjecture (A=5). Computational evidence: original v6 GPU brute-force run reported zero uncovered denominators to 2.1×10^11, but it is not certifi...
The number of continued fraction representations R(d) (with all partial quotients ≤ 5 and gcd(a, d) = 1) grows empirically as d^{0.674}. This was established by ordinary least-squares regression of lo...
Computational transitivity check: the generators Γ_{1,...,5} act transitively on nonzero vectors in (Z/pZ)^2 for each of the first 2,000 primes, up to p=17,389. Audit revision: the all-prime Dickson-c...
The smallest Zaremba witness for d concentrates at a/d ≈ 0.171 with 99.7% sharing CF prefix [0; 5, 1, ...]. The concentration lies between the convergents 1/6 and 2/11, with a heuristic connection to ...