# bigcompute.science

> Open computational mathematics. GPU clusters, CUDA kernels, open data. Human-AI collaborative. AI-audited, not peer-reviewed.

All work produced through human-AI collaboration (Cahlen Humphreys + Claude). AI-audited against published literature (arXiv, zbMATH, OEIS). Not independently peer-reviewed. CC BY 4.0.

## Experiments (16 total)

- [CFD Chaotic Advection: Standard Map Lyapunov Spectrum (RTX 5090)](/experiments/cfd-chaotic-advection/): CFD program entry point (chaotic-advection surrogate; Navier–Stokes phases started May 27): Chirikov standa... (complete)
- [CFD Phase 2: 2D Navier–Stokes BKM Diagnostic (RTX 5090)](/experiments/cfd-ns-bkm/): Phase 2 CFD: GPU pseudospectral 2D NS with BKM vorticity tracking. Certifying Taylor–Green decay and random... (complete)
- [CFD Phase 3: 3D Navier–Stokes BKM Blowup Search (RTX 5090)](/experiments/cfd-ns3d-bkm/): Phase 3: 3D pseudospectral NS with vortex stretching and BKM tracking on RTX 5090. First certifying 3D runs... (complete)
- [Prime Convergents: GPU Verification of the Erdos-Mahler Bound](/experiments/prime-convergents-gpu/): GPU verification of the Erdos-Mahler bound on greatest prime factors of CF convergents. 10M random CFs veri... (complete)
- [Erdos-Straus Conjecture: Solution Counting to 10^8 on B200](/experiments/erdos-straus-gpu/): 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 (Sw... (complete)
- [Zaremba Density: Exception Sets and Phase Transitions on 8x B200](/experiments/zaremba-density-gpu/): 65 GPU density computations across digit sets and ranges to 10^12. Audit revision: the data support stable ... (complete)
- [Ramsey R(5,5): Exhaustive Extension Search on 8x B200](/experiments/ramsey-r55-lower-bound/): Strongest computational evidence that R(5,5) = 43. All 656 known K42 colorings UNSAT. Structural attack tow... (complete)
- [Kronecker Coefficients: S20, S30, S40 on 8× B200](/experiments/kronecker-coefficients-gpu/): Complete Kronecker coefficient tables for S_20 (32.7M nonzero, 3.7s) and S_30 (26.4B nonzero, 7.4 min) on N... (complete)
- [Ramanujan Machine: GPU-Accelerated Discovery of Continued Fraction Formulas](/experiments/ramanujan-machine-gpu/): 586 billion equal-degree polynomial CFs evaluated through degree 8 — zero new transcendental formulas. 7,03... (complete)
- [Class Numbers of Real Quadratic Fields: Extending Tables to 10^13 on 8× B200](/experiments/class-numbers-real-quadratic/): Class numbers h(d) for 30 billion real quadratic fields across [10^9, 10^11]. h=1 rate falls monotonically:... (complete)
- [Flint Hills Series: Partial Sums to 10^{10} with Spike Decomposition](/experiments/flint-hills-series/): Partial sums of the Flint Hills series computed to 10 billion terms with quad-double precision. Spike decom... (complete)
- [Hausdorff Dimension Spectrum: All Subsets of {1,...,20}](/experiments/hausdorff-dimension-spectrum/): Hausdorff dimension computed for every non-empty subset of {1,...,20} — 1,048,575 subsets in 4,343 seconds ... (complete)
- [Minkowski ?(x) Singularity Spectrum](/experiments/minkowski-spectrum/): Multifractal singularity spectrum f(alpha) of the Minkowski question-mark function, computed via weighted t... (complete)
- [Lyapunov Exponent Spectrum: All Subsets of {1,...,20}](/experiments/lyapunov-exponent-spectrum/): Lyapunov exponents for all 1,048,575 non-empty subsets of {1,...,20}, computed in 305 seconds on RTX 5090. ... (complete)
- [Transfer Operator for Zaremba's Conjecture: Hausdorff Dimension to 15 Digits](/experiments/zaremba-transfer-operator/): Hausdorff dimension of E_5 computed to 15 digits (0.836829443681208). Spectral gaps for 1,214 square-free m... (complete)
- [Zaremba's Conjecture: 210 Billion Verified in 116 Minutes on 8× NVIDIA B200](/experiments/zaremba-conjecture-verification/): GPU verification of Zaremba's Conjecture for all d up to 210 billion (zero failures), plus spectral gap ana... (complete)

## Findings (20 total, all AI-audited)

- [3D NS BKM Infrastructure: First Certifying Pseudospectral Blowup-Monitor Runs on RTX 5090](/findings/cfd-ns3d-bkm-infrastructure/): GPU pseudospectral 3D vorticity-form Navier–Stokes with vortex stretching and BKM integral tracking. Certif... [SILVER]
- [Cohen-Lenstra at Scale: h=1 Rate Falls to 15% at 10^10, Genus Theory Dominates](/findings/class-number-convergence/): GPU computation of 30 billion class numbers for real quadratic fields reveals that the h(d)=1 rate DECREASE... [SILVER]
- [Congruence Spectral Gaps for Zaremba's Semigroup Are Uniform](/findings/zaremba-spectral-gaps-uniform/): FP64/N=40 cuBLAS computation of congruence spectral gaps for Zaremba's semigroup Γ_{1,...,5}. All 168 prime... [SILVER]
- [Digit 1 Dominance: Five Digits With 1 Beat Fourteen Digits Without](/findings/hausdorff-digit-one-dominance/): At n=20 (1,048,575 subsets): dim_H(E_{1,...,5}) = 0.837 while dim_H(E_{2,...,20}) = 0.768. Five digits cont... [SILVER]
- [Exploratory BFS Depths for Zaremba Generators: Short-Word Expansion Data to p=1021](/findings/zaremba-cayley-diameters/): Exploratory GPU BFS data for Zaremba generator diameters for all 172 primes p ≤ 1021. Audit caveat: the cur... [SILVER]
- [Kronecker Coefficients: Complete S_30 Table — 26.4 Billion Nonzero Triples in 7 Minutes](/findings/kronecker-s30-largest-computation/): Complete Kronecker coefficient tables for S_20 (32.7M nonzero, 3.7s) and S_30 (26.4B nonzero, 4.9 min) comp... [SILVER]
- [Kronecker S_40: Complete Character Table and Targeted Coefficients — 94.9% Nonzero](/findings/kronecker-s40-character-table/): Complete character table of S_40 (37,338 partitions, 1.394 billion entries, 9.5 hours on 64-core CPU). Valu... [SILVER]
- [Standard Map Chaos Onset: Λ(K) Crosses Literature K_crit on RTX 5090](/findings/cfd-standard-map-chaos-onset/): Custom CUDA maximal-Lyapunov sweep of the Chirikov standard map: 16.8M trajectories in 116.6s on RTX 5090, ... [SILVER]
- [Zaremba Density Phase Transition: A={1,2,3} Appears to Have Full Density](/findings/zaremba-density-phase-transition/): UPDATED 2026-04-23 audit: A={1,2,3} has exactly 27 uncovered denominators through the completed 10^10 run, ... [SILVER]
- [2D NS BKM Diagnostic: Certifying Pseudospectral Vorticity Tracking on RTX 5090](/findings/cfd-ns-bkm-diagnostic/): GPU pseudospectral 2D Navier–Stokes with BKM integral ∫||ω||∞ dt. Taylor–Green validates decay (max |ω|: 2.... [BRONZE]
- [A={1,2} Density Fits Logarithmic Growth: 30 + 4.65·log₁₀(N), Testable at 10^12](/findings/zaremba-A12-logarithmic-convergence/): The Zaremba density for A={1,2} fits density = 31.5 + 4.47·log₁₀(N) (R² = 0.9984, 5 empirical measurements ... [BRONZE]
- [Digit 1 Amplification in Zaremba Density: Strong Effect, Inverse-Square Law Still Unconfirmed](/findings/zaremba-inverse-square-amplification/): Audit revision: digit 1 strongly amplifies Zaremba density relative to digit 2, but the headline inverse-sq... [BRONZE]
- [GPU Matrix Enumeration: 175× Faster Zaremba Verification via Batched 2×2 Multiply](/findings/gpu-matrix-enumeration-175x/): Reformulating CF tree enumeration as batched 2×2 matrix multiplication on GPU eliminates all CPU bottleneck... [BRONZE]
- [The {1,k} Density Hierarchy: Digit 2 Is Worth 9x More Than Digit 3](/findings/zaremba-digit-pair-hierarchy/): Complete density computation for all {1,k} pairs at 10^11. Density drops exponentially: {1,2}=80.75%, {1,3}... [BRONZE]
- [Zaremba Exception Hierarchy: 27 → 2 → 0 as Digits Grow](/findings/zaremba-exception-hierarchy/): Corrected 2026-04-23 audit: the 27 uncovered denominators for A={1,2,3} through the completed 10^10 run are... [BRONZE]
- [Zaremba Representation Counts Grow as d^{0.674} — Hardest Cases Are Small d](/findings/zaremba-representation-growth/): The number of continued fraction representations R(d) (with all partial quotients ≤ 5 and gcd(a, d) = 1) gr... [BRONZE]
- [Zaremba Transitivity: Verified to p=17,389; All-Prime Algebraic Argument Still Provisional](/findings/zaremba-transitivity-all-primes/): Computational transitivity check: the generators Γ_{1,...,5} act transitively on nonzero vectors in (Z/pZ)^... [BRONZE]
- [Zaremba Witnesses Concentrate at α(d)/d ≈ 0.171, Connected to the Golden Ratio](/findings/zaremba-witness-golden-ratio/): The smallest Zaremba witness for d concentrates at a/d ≈ 0.171 with 99.7% sharing CF prefix [0; 5, 1, ...].... [BRONZE]
- [Zaremba's Conjecture (A=5): Proof Framework via GPU Verification + MOW Spectral Theory (Not Peer-Reviewed, Known Gaps Remain)](/findings/zaremba-conjecture-framework/): Proof FRAMEWORK (not a completed proof) for Zaremba's Conjecture (A=5). Computational evidence: original v6... [BRONZE]

## Datasets (Hugging Face)

- [Zaremba Density](https://huggingface.co/datasets/cahlen/zaremba-density): 65 GPU experiments, exception sets, density measurements to 10^12
- [Zaremba Data](https://huggingface.co/datasets/cahlen/zaremba-conjecture-data): Dolgopyat profile, transfer operator data, proof framework
- [Hausdorff Spectrum](https://huggingface.co/datasets/cahlen/hausdorff-dimension-spectrum): dim_H for all 1,048,575 subsets of {1,...,20} — first complete computation
- [Ramanujan Machine](https://huggingface.co/datasets/cahlen/ramanujan-machine-results): 586B candidate evaluations through deg 7
- [Kronecker Coefficients](https://huggingface.co/datasets/cahlen/kronecker-coefficients): S_20, S_30, S_40 character tables + Kronecker triples
- [Class Numbers](https://huggingface.co/datasets/cahlen/class-numbers-real-quadratic): Real quadratic fields to 10^11
- [Continued Fraction Spectra](https://huggingface.co/datasets/cahlen/continued-fraction-spectra): Hausdorff, Lyapunov, Minkowski, Flint Hills
- [CFD Chaotic Advection](https://huggingface.co/datasets/cahlen/cfd-chaotic-advection): Standard map Lyapunov sweeps (16.8M trajectories)
- [CFD 2D NS BKM](https://huggingface.co/datasets/cahlen/cfd-ns-bkm): 2D pseudospectral BKM diagnostic CSVs
- [CFD 3D NS BKM](https://huggingface.co/datasets/cahlen/cfd-ns3d-bkm): 3D BKM blowup-monitor CSVs (incl. Phase 5 Kerr IC sweep)

## Tools

- [MCP Server](https://mcp.bigcompute.science/mcp): 23 tools, no auth. arXiv, zbMATH, OEIS, LMFDB, Lean/Mathlib + experiment data.
- [Colab Notebook](https://colab.research.google.com/github/cahlen/bigcompute.science/blob/main/public/notebooks/bigcompute_mcp_explorer.ipynb): Pre-loaded MCP client + HF datasets.
- [Experiment code](https://github.com/cahlen/idontknow): CUDA kernels, Python harnesses
- [Website source](https://github.com/cahlen/bigcompute.science): Astro + KaTeX
- [Agent guide](https://github.com/cahlen/idontknow/blob/main/AGENTS.md): How to contribute
- [Audit Ledger](/verification/): AI audit process + all reviews
- [Citation](https://github.com/cahlen/idontknow/blob/main/CITATION.cff): CITATION.cff

## Review Infrastructure

All findings are AI-audited claim-by-claim. Current: 62 reviews from 8 models across 4 providers. 249 issues discovered, 232 fixed. Certification uses most-conservative-wins consensus.

- [Review scripts](https://github.com/cahlen/idontknow/tree/main/scripts/reviews): `run_review.py` (any OpenAI-compatible API), `aggregate.py`, `validate.py`, `sync_website.py`
- [Review schema](https://github.com/cahlen/idontknow/blob/main/docs/verifications/SCHEMA.md): JSON format for reviews
- [Manifest](https://github.com/cahlen/idontknow/blob/main/docs/verifications/manifest.json): Generated aggregate of all reviews
- [Remediations](https://github.com/cahlen/idontknow/tree/main/docs/verifications/remediations): Issue tracking with full lineage (review → issue → fix → commit)
- To contribute: write review JSON per schema, submit PR to [cahlen/idontknow](https://github.com/cahlen/idontknow)

## Machine-Readable Metadata

- [/meta.json](/meta.json): Complete machine-readable index of all structured data, pages, repos, datasets, notebooks, and citation guidance
- [/cite/](/cite/): Citation page with BibTeX/APA for every finding
- Every finding page has: ScholarlyArticle JSON-LD, Dataset JSON-LD (when applicable), Highwire Press meta tags (citation_title, citation_author, citation_date), Dublin Core metadata
- [Sitemap](/sitemap-index.xml) · [RSS](/rss.xml) · [robots.txt](/robots.txt)