Open computational mathematics. AI-audited, not peer-reviewed. All code and data open for independent verification.

Audit Log

Every finding is checked claim-by-claim by AI models against published literature and mathematical databases. This is not a substitute for formal peer review — it is an informal error-catching process.
Each review logs which model performed the check.

17 Findings audited

44 Reviews total

164 Issues discovered

91% Issues resolved

What the Badges Mean

Gold literature-supported

3+ published papers corroborate the methods. Validated against published benchmarks.

e.g. Hausdorff digit 1 dominance — validated against Jenkinson-Pollicott, Hensley, and Falk-Nussbaum

Silver literature-supported

1+ published paper plus arXiv coverage. Methods grounded in established literature.

e.g. Spectral gaps — Bourgain-Gamburd-Sarnak property (τ) computationally supported at large scale

Bronze novel observation

Novel observation. Related preprints exist but no direct literature precedent.

e.g. Golden ratio witness — no prior report of this concentration

How It Works

Claim Extraction

Each finding's specific numerical claims are identified — not vague descriptions, but checkable statements like "A={1,2,3} has exactly 27 exceptions, all ≤ 6234."

Literature Cross-Reference

Each claim is checked against live academic databases via our MCP server: arXiv, zbMATH, Semantic Scholar, OEIS, LMFDB, and Lean/Mathlib. Not a keyword search — an actual comparison of our numbers against published theorems and bounds.

Claim-by-Claim Verdict

Each claim receives: VERIFIED, NEEDS CLARIFICATION, DISPUTED, or UNVERIFIABLE. The reviewer explains reasoning and cites specific papers.

Overall Verdict & Certification

ACCEPT, ACCEPT WITH REVISION, REVISE AND RESUBMIT, or REJECT. This is not a substitute for traditional peer review — it is a transparent pre-review process. The review is saved with the reviewer's model identity.

As AI models get smarter, findings get re-reviewed. The ledger grows. Confidence compounds.

The Living Ledger

Findings accumulate reviews over time from various AI models and occasional manual checks. Each review logs which model performed it.

Date Model Provider Verdict Finding

2026-04-04 gpt-4.1 openai ACCEPT WITH REVISION Zaremba Density Phase Transition: A={1,...

2026-04-04 o3-pro openai REVISE AND RESUBMIT Zaremba Density Phase Transition: A={1,...

2026-04-03 o3-pro OpenAI ACCEPT WITH REVISION Cayley Graph Diameters of Zaremba's Sem...

2026-04-03 o3-pro OpenAI ACCEPT WITH REVISION Cohen-Lenstra at Scale: h=1 Rate Falls ...

2026-04-03 o3-pro OpenAI ACCEPT WITH REVISION Congruence Spectral Gaps for Zaremba's ...

2026-04-03 o3-pro OpenAI ACCEPT WITH REVISION Digit 1 Dominance: Five Digits With 1 B...

2026-04-03 o3-pro OpenAI ACCEPT WITH REVISION Kronecker Coefficients: Complete S_30 T...

2026-04-03 o3-pro OpenAI ACCEPT WITH REVISION Kronecker S_40: Complete Character Tabl...

Real Issues Found

Across 17 findings, reviewers discovered 164 issues in 15 findings. 150 resolved, 14 remaining.

9Critical

92Important

63Minor

Critical

Transitivity proof: Circular dependency in Step 3 — used orbit size to bound |H|, which is what the proof tries to establish.
Rewritten with non-circular resultant-based argument. Borel exclusion strengthened to check all bases.

Critical

Zaremba proof: MOW constant-tracking unverified — no explicit constants in published paper.
Retitled "proof framework". Six known gaps enumerated. rho_eta needs interval certification.

Important

Zaremba density: δ > 1/2 threshold contradicted by our own data.
{2,3,4,5} has δ=0.605 but only 97%. Reframed as two necessary conditions (digit 1 + transitivity).

Important

Digit pair hierarchy: "Closed" exception sets declared without completeness certificate.
Rephrased as conjectural. No branch-and-bound argument provided for finiteness.

Minor

Hausdorff: 3-decimal accuracy claimed without truncation error analysis.
Precision hedged. Convergence study (N=15, 25, 35, ...) added to show resolution above numerical noise.

Community Verification

Anyone can submit computation results via our Colab notebooks. Every new submission is automatically re-run on our GPU cluster to confirm the numbers match. Fake or tampered results are flagged instantly.

Submit

Run an experiment on Colab (free T4). Click “Submit to GitHub” — results are pre-filled.

Triage

Bot checks against known frontiers. Already computed? Auto-closed. New data? Labeled for verification.

Verify

Research agent re-runs the exact same experiment on our cluster. Numbers match? Labeled verified.

Submissions are free. Verification costs GPU time. That’s what Guerrilla Mathematics™ funds.

What This Is NOT

Not traditional peer review

No human referee panel. This is AI-assisted literature cross-referencing with claim-by-claim analysis.

Not proof verification

We check mathematical context, not formal correctness. For formal proofs, use Lean 4.

Not infallible

AI reviewers make errors. That's why the ledger accumulates reviews from multiple models.

Contribute

Any AI model or human researcher can verify our findings, run new experiments, and submit reviews.

Fastest: The Research Agent

If you have Claude Code and a GPU, the research agent handles everything — monitoring experiments, harvesting results, running multi-model peer reviews, fixing issues, and deploying updates.

git clone https://github.com/cahlen/idontknow && cd idontknow
export OPENAI_API_KEY='sk-...'
./scripts/run_agent.sh              # one cycle
./scripts/run_agent.sh --loop 10m   # autonomous loop

Uses your Claude Code account for analysis. OpenAI key optional (for multi-model reviews). Source · Guide

Manual: Review a Finding

1 Connect to mcp.bigcompute.science

2 Call get_finding("slug")

3 Call verify_finding("slug")

4 Write review per schema

5 Submit PR

{
  "mcpServers": {
    "bigcompute": {
      "url": "https://mcp.bigcompute.science/mcp"
    }
  }
}

22 tools. No auth. arXiv, zbMATH, OEIS, LMFDB, Lean/Mathlib, and more.

Audit Dashboard

17 findings · 44 reviews · 164 issues tracked (150 resolved)

SILVER 7 findings

Cayley Graph Diameters of Zaremba's Semigroup: diam(p)/log(p) ... +

Claude + o3-pro · Accept w/ revision (3 reviews)

7/7 resolved

Review Ledger

2026-04-03 o3-pro OpenAI SILVER ACCEPT WITH REVISION

2026-04-01 Claude Opus 4.6 Anthropic GOLD ACCEPT WITH REVISION

Issues

important Clarify which moduli were processed and correct the stated count. resolved

important The prime count 172 is correct (π(1021)=172); the reviewer's '669' ... resolved

minor Cite a proof or give a careful argument for the mod-p to integer lift. resolved

minor Report measured throughput, GPU model specs, and validation checks ... resolved

important Add measured throughput and validation details to the Method sectio... resolved

minor Provide quantitative trend analysis and error bars; temper the asym... resolved

+1 more