# 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 AI-audited, not peer-reviewed.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

- [Zaremba 210B Verification](/experiments/zaremba-conjecture-verification/): 210B denominators verified, zero failures. Proof framework (not completed proof). (complete)
- [Zaremba Transfer Operator](/experiments/zaremba-transfer-operator/): Hausdorff dimension, spectral gaps, property (tau). (complete)
- [Zaremba Density](/experiments/zaremba-density-phase-transition/): Phase transition, 3 closed exception sets, {1,k} hierarchy. (in-progress)
- [Ramsey R(5,5)](/experiments/ramsey-r55-lower-bound/): 656/656 K42 colorings UNSAT. (in-progress)
- [Class Numbers](/experiments/class-numbers-real-quadratic/): 30B discriminants. h=1 rate falls to 0 (genus theory). (in-progress)
- [Kronecker Coefficients](/experiments/kronecker-coefficients-gpu/): S_20, S_30 (26.4B nonzero), S_40 char table done. (in-progress)
- [Ramanujan Machine](/experiments/ramanujan-machine-gpu/): 586B candidates through deg 7, zero transcendentals. (in-progress)
- [Hausdorff Spectrum](/experiments/hausdorff-dimension-spectrum/): dim_H for all 2^20-1 subsets of {1,...,20}. (complete)
- [Lyapunov Spectrum](/experiments/lyapunov-exponent-spectrum/): Lyapunov exponents for all 2^20-1 subsets. (complete)
- [Minkowski Spectrum](/experiments/minkowski-spectrum/): Multifractal singularity spectrum of ?(x). (complete)
- [Flint Hills Series](/experiments/flint-hills-series/): Partial sums to 10^10, spike decomposition. (complete)

## Findings (15 total, all AI-audited)

- [Zaremba Density Phase Transition](/findings/zaremba-density-phase-transition/): A={1,2,3} exactly 27 exceptions. delta > 1/2 PLUS transitivity needed. [GOLD]
- [A={1,2} Logarithmic Convergence](/findings/zaremba-A12-logarithmic-convergence/): 5 data points, density = 31.5 + 4.47*log10(N). [BRONZE]
- [Digit Pair Hierarchy](/findings/zaremba-digit-pair-hierarchy/): {1,k} decays as k^(-3.5). Digit 1 amplifies 42-243x. 4 closed sets (27, 64, 374, 1834). [SILVER]
- [Exception Hierarchy](/findings/zaremba-exception-hierarchy/): 27 -> 2 -> 0 as digits grow. d=54, d=150 need digit 5. [BRONZE]
- [Kronecker S_30](/findings/kronecker-s30-largest-computation/): 26.4B nonzero triples, 7.4 min on B200. [GOLD]
- [Kronecker S_40](/findings/kronecker-s40-character-table/): Complete char table (37,338 partitions, 1.394B entries). 94.9% nonzero (sampled). Hooks multiplicity-free. [GOLD]
- [Cohen-Lenstra at Scale](/findings/class-number-convergence/): h=1 rate falls to 0 (genus theory), NOT 75%. [GOLD]
- [Zaremba Proof Framework](/findings/zaremba-conjecture-proved/): D0=3.4e10, 3 AI reviews (Claude + Grok + GPT-5.2). NOT a completed proof. [SILVER]
- [Spectral Gaps Uniform](/findings/zaremba-spectral-gaps-uniform/): All 1214 moduli positive, min 0.237. [SILVER]
- [Transitivity All Primes](/findings/zaremba-transitivity-all-primes/): Dickson classification, AI-assisted. [SILVER]
- [Cayley Diameters](/findings/zaremba-cayley-diameters/): diam/log(p) -> 1.45 for 172 primes. [GOLD]
- [Digit 1 Dominance](/findings/hausdorff-digit-one-dominance/): dim_H(E_{1,...,5}) > dim_H(E_{2,...,20}). [GOLD]
- [Witness Golden Ratio](/findings/zaremba-witness-golden-ratio/): a/d concentrates near 0.171. [BRONZE]
- [GPU 175x Speedup](/findings/gpu-matrix-enumeration-175x/): Batched 2x2 matrix multiply. [BRONZE]
- [Representation Growth](/findings/zaremba-representation-growth/): R(d) grows as d^0.674. [BRONZE]

## Datasets (Hugging Face)

- [Zaremba Data](https://huggingface.co/datasets/cahlen/zaremba-conjecture-data): Density logs, Dolgopyat profile, {1,k} hierarchy, closed exception sets
- [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
- [Continued Fraction Spectra](https://huggingface.co/datasets/cahlen/continued-fraction-spectra): Hausdorff, Lyapunov, Minkowski, Flint Hills

## Tools

- [MCP Server](https://mcp.bigcompute.science/mcp): 22 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: 41 reviews from 4 models (Claude Opus 4.6, o3-pro, Grok, GPT-5.2) across 3 providers (Anthropic, OpenAI, xAI). 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)