GPU-accelerated computational mathematics — exploring open conjectures with custom CUDA kernels, interval arithmetic, and heavy compute on NVIDIA B200 + RTX 5090.
Human–AI collaborative research. CUDA kernels, mathematical arguments, review infrastructure, and documentation developed jointly by Cahlen Humphreys and AI agents (Claude Opus 4.6, o3-pro, GPT-5.2, Grok). Not peer-reviewed. All claims grounded in computational evidence and reproducible code. Everything open for independent verification.
Results: bigcompute.science · Data: Hugging Face · MCP: mcp.bigcompute.science (23 tools, no auth)
# Run the research agent (needs one API key: Gemini free, or OpenAI, or Anthropic)
export GEMINI_API_KEY='AIza...' # free at aistudio.google.com/apikey
./scripts/run_agent.sh # one cycle: monitor → harvest → analyze → review → deploy
./scripts/run_agent.sh --loop 10m # autonomous loopOr open a Colab notebook — free T4 GPU, auto-compile, run experiments on open conjectures.
| Experiment | Key Result | Status |
|---|---|---|
| Zaremba Conjecture | Proof framework (not complete proof). 210B verified, ρ_η ≤ 0.7606 (arb-certified, 77 digits). 4 gaps remain. | Paper |
| Zaremba Density | 5 closed exception sets ({1,2,3}=27 through {1,2,7}=7,178). A={1,2} logarithmic convergence (31.5 + 4.47·log₁₀N). Inverse-square amplification law. | In progress |
| Ramsey R(5,5) | 656/656 K₄₂ colorings UNSAT. Strongest computational evidence R(5,5) = 43. | Complete |
| Kronecker Coefficients | S₂₀, S₃₀ (26.4B nonzero), S₄₀ char table (37,338 partitions). 94.9% nonzero. S₄₅ infeasible (63 TB). | S₄₀ complete |
| Class Numbers | Complete to 10¹¹. h=1 rate falls to 0 (genus theory). Extending to 10¹³. | In progress |
| Hausdorff Spectrum | First complete dim_H for all 2²⁰-1 subsets of {1,...,20}. | Complete |
| Ramanujan Machine | 586B+ equal-degree CFs exhausted (0 new formulas, 7K false positives disproven via PSLQ). v2 asymmetric-degree kernel built — deg(b)≈2×deg(a) required. | Pivoting to v2 |
| Prime Convergents | 10M random CFs verified Erdős-Mahler bound. Worst-case ratio 4.87, constant ~10 suffices. | Complete |
| Erdős-Straus | Solution counts f(p) for 4/p = 1/x + 1/y + 1/z. All primes to 10⁸. | In progress |
| Lyapunov Spectrum | All 1,048,575 Lyapunov exponents. | Complete |
| Minkowski ?(x) | First numerical singularity spectrum f(α). | Complete |
| Flint Hills | Partial sums to 10¹⁰. | Complete |
Every finding is AI-audited claim-by-claim by multiple models. Currently 53 reviews from 7 models across 3 providers. 210 issues discovered, 207 resolved (98.6%).
# Run a review (any OpenAI-compatible API)
export API_KEY='...'
python3 scripts/reviews/run_review.py --slug kronecker-s40-character-table --model gemini-2.5-flash --provider google --api-base https://generativelanguage.googleapis.com/v1beta/openai
# Rebuild manifest + website data
python3 scripts/reviews/aggregate.py
python3 scripts/reviews/sync_website.py- Review scripts:
scripts/reviews/— run, aggregate, validate, sync - Manifest:
docs/verifications/manifest.json— single source of truth - Remediations:
docs/verifications/remediations/— per-finding issue tracking with commit links - PR Bot:
.github/workflows/pr-review.yml— auto-validates PRs, scans for secrets, labels
Autonomous loop: Monitor → Harvest → Analyze → Review → Remediate → Deploy → Plan.
./scripts/run_agent.sh # one cycle
./scripts/run_agent.sh --loop 10m # autonomous
./scripts/run_agent.sh --loop 10m --auto-launch # + launch experiments on free GPUsWorks with any ONE of: Claude Code (no key needed), Anthropic API, OpenAI API, or Gemini API (free). Auto-detects what's available. Default: creates branch + PR (safe). --direct-push for repo owner.
Source: scripts/research_agent.py
scripts/experiments/ CUDA kernels and Python harnesses per experiment
scripts/reviews/ AI peer review infrastructure
scripts/research_agent.py Autonomous research loop
docs/verifications/ Review JSONs, manifest, remediations
docs/verifications/remediations/ Per-finding issue tracking with commit links
paper/ Zaremba proof paper (LaTeX + PDF)
data/ Raw computation output (large files on HF)
logs/ Computation logs
.github/workflows/ PR bot (auto-validate, scan for secrets, label)
| Environment | GPUs | VRAM | Role |
|---|---|---|---|
| B200 Cluster | 8× NVIDIA B200 | 1.43 TB (NVLink 5) | Primary compute |
| Local | RTX 5090 | 32 GB | Development + smaller experiments |
| Colab | T4 (free) / A100 / L4 | 16-80 GB | Distributed contributions |
- Colab — Open notebook, compile kernels on free GPU, run experiments
- Agent — Clone, set one API key,
./scripts/run_agent.sh - PR — Add review JSONs or experiment logs, PR bot validates automatically
See AGENTS.md for the full contribution guide.
- bigcompute.science — Results + audit dashboard
- MCP Server — 23 tools, no auth (arXiv, zbMATH, OEIS, LMFDB, Lean/Mathlib)
- Hugging Face — Datasets (class numbers, Kronecker, spectra, Zaremba)
- llms.txt — Agent-consumable structured index