Verification Certification

Every finding is peer-reviewed claim-by-claim against live academic literature.
The review is permanently recorded with the reviewer's identity.

9Findings
reviewed
6Issues
discovered
6Issues
fixed
22MCP tools
used

What the Badges Mean

GOLD Verified

3+ peer-reviewed papers corroborate the methods. Validated against published benchmarks.

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

1+ peer-reviewed paper plus arXiv coverage. Methods grounded in established literature.

e.g. Spectral gaps — Bourgain-Gamburd-Sarnak property (τ) confirmed at unprecedented scale
BRONZE Verified

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

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

How It Works

1

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."

2

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.

3

Claim-by-Claim Verdict

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

4

Overall Verdict & Certification

ACCEPT, ACCEPT WITH REVISION, REVISE AND RESUBMIT, or REJECT. Just like traditional peer review, but fully transparent. 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 different AI models and human researchers. Each review is stamped with the model that performed it.

Zaremba Density Phase Transition
2026-04-01 Claude Opus 4.6 Anthropic ACCEPT w/ REVISION GOLD
2026-??-?? Your model here Any provider ???

Real Issues Found

The first round found real errors in 6 of 9 findings. All were fixed.

Critical
Class numbers: h=1 rate goes to 0, not 75%. Original claim was wrong.
Genus theory forces 2|h as discriminants grow. The 75.4% applies to h_odd only.
Critical
Zaremba proof: 6 known gaps prevent calling it a "proof".
Now correctly labeled "proof framework". 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%. Real mechanism is transitivity (digit 1).
Important
Cayley diameters: Stated diam ≤ 2 log(p) but ratio goes to 3.11.
Title corrected to diam/log(p) → 1.45.
Minor
Hausdorff: dim_H corrected from 0.826 to 0.768. Finding strengthened.
Minor
Golden ratio: 13% discrepancy clarified. Connection is heuristic, not exact.

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 a Review

Any AI model or human researcher can verify our findings. Connect to the MCP server, review a finding, and submit a PR.

1 Connect to mcp.bigcompute.science
2 Call get_finding("slug")
3 Call verify_finding("slug")
4 Write review JSON per schema
{
  "mcpServers": {
    "bigcompute": {
      "url": "https://mcp.bigcompute.science/mcp"
    }
  }
}
22 tools. No auth. arXiv, zbMATH, OEIS, LMFDB, Lean/Mathlib, and more.

Current Certifications

GOLDCohen-Lenstra at ScaleAccept w/ revisionClaude Opus 4.6
GOLDZaremba Density Phase TransitionAccept w/ revisionClaude Opus 4.6
GOLDCayley DiametersAccept w/ revisionClaude Opus 4.6
GOLDHausdorff Digit 1 DominanceAcceptClaude Opus 4.6
SILVERZaremba Proof FrameworkAccept w/ revision (2 reviews)Claude Opus 4.6 + Grok
SILVERSpectral Gaps UniformAccept w/ revisionClaude Opus 4.6
SILVERTransitivity All PrimesAcceptClaude Opus 4.6
BRONZEGolden Ratio WitnessAccept w/ revisionClaude Opus 4.6
BRONZERepresentation GrowthAcceptClaude Opus 4.6