Open computational mathematics. AI-audited, not peer-reviewed. All code and data open for independent verification.
All Experiments
GPU-accelerated exploration of open conjectures. Every experiment has CUDA source, reproduction commands, and open data.
Erdos-Straus Conjecture: Solution Counting to 10^8 on B200
Count solutions f(p) to 4/p = 1/x + 1/y + 1/z for all primes p up to 10^8. Conjecture verified to 10^14 (Swett/Elsholtz-Tao), but solution counts f(p) and their distribution are unexplored at GPU scal...
Prime Convergents: GPU Verification of the Erdos-Mahler Bound
GPU verification of the Erdos-Mahler bound on greatest prime factors of CF convergents. 10M random CFs verified: bound holds 100%, worst-case ratio 4.87, constant 50 is very conservative (~7 suffices)...
Zaremba Density: Exception Sets and Phase Transitions on 8x B200
65 GPU density computations across digit sets and ranges to 10^12. Audit revision: the data support stable candidate exception sets, not proved finite/closed sets. Completed 10^11 RESULTS blocks in th...
Class Numbers of Real Quadratic Fields: Extending Tables to 10^13 on 8× B200
Class numbers h(d) for 30 billion real quadratic fields across [10^9, 10^11]. h=1 rate falls monotonically: 42% → 17% → 15.4%. Goes to 0, not 75% (genus theory). Odd-part convergence to Cohen-Lenstra ...
Kronecker Coefficients: S20, S30, S40 on 8× B200
Complete Kronecker coefficient tables for S_20 (32.7M nonzero, 3.7s) and S_30 (26.4B nonzero, 7.4 min) on NVIDIA B200. Complete S_40 character table (37,338 partitions, 1.394B entries, 9.5 hr) with ta...
Ramanujan Machine: GPU-Accelerated Discovery of Continued Fraction Formulas
586 billion equal-degree polynomial CFs evaluated through degree 8 — zero new transcendental formulas. 7,030 double-precision false positives all disproven at 100-digit precision. Only 20 confirmed fo...
Ramsey R(5,5): Exhaustive Extension Search on 8x B200
Strongest computational evidence that R(5,5) = 43. All 656 known K42 colorings UNSAT. Structural attack toward R(5,5) <= 45 in progress.
Flint Hills Series: Partial Sums to 10^{10} with Spike Decomposition
Partial sums of the Flint Hills series computed to 10 billion terms with quad-double precision. Spike decomposition reveals 91% of the sum comes from 19 convergent spikes.
Hausdorff Dimension Spectrum: All Subsets of {1,...,20}
Hausdorff dimension computed for every non-empty subset of {1,...,20} — 1,048,575 subsets in 4,343 seconds on RTX 5090. Validated against Jenkinson-Pollicott.
Lyapunov Exponent Spectrum: All Subsets of {1,...,20}
Lyapunov exponents for all 1,048,575 non-empty subsets of {1,...,20}, computed in 305 seconds on RTX 5090. Twin dataset with the Hausdorff dimension spectrum.
Minkowski ?(x) Singularity Spectrum
Multifractal singularity spectrum f(alpha) of the Minkowski question-mark function, computed via weighted transfer operator in 4.9 seconds on RTX 5090.
Zaremba's Conjecture: 210 Billion Verified in 116 Minutes on 8× NVIDIA B200
GPU verification of Zaremba's Conjecture for all d up to 210 billion (zero failures), plus spectral gap analysis, transitivity proof, and LLM theorem proving in Lean 4.
Transfer Operator for Zaremba's Conjecture: Hausdorff Dimension to 15 Digits
Hausdorff dimension of E_5 computed to 15 digits (0.836829443681208). Spectral gaps for 1,214 square-free moduli, all positive. Property (tau) computationally supported (not proven).