{"resourceId":"anthropic-formal-math-eth-refutation-claude-lean-readme-202610","versions":[{"version":"external-cf68d476b41b8ce2059130955ab26d7be9977064552a13fe195a16d6d7d40eae","resource":{"id":"anthropic-formal-math-eth-refutation-claude-lean-readme-202610","title":"Anthropic publishes Claude's claimed 2^o(n) 3-SAT algorithm refuting ETH with an AI-written Lean proof, noting no machine checks that the formal statement matches the paper","organization":"Anthropic","sector":"AI model provider; research","geography":"Global","publishedAt":"Undated repository README (claim announced late October 2026, per Papex)","publicationDate":null,"eventDate":null,"sourceName":"GitHub: anthropics/formal-math","sourceLabel":"Vendor research artifact","sourceUrl":"https://raw.githubusercontent.com/anthropics/formal-math/main/eth/README.md","evidenceClass":"vendor-claim","outcomeClass":"emerging","topics":["knowledge-work","developers-agents"],"finding":"Anthropic's repository states that an internal research Claude model found a deterministic 2^o(n) algorithm for 3-SAT, refuting the Exponential Time Hypothesis, with a paper credited to Claude and a Lean 4 formalization written by AI models. It says the result is purely asymptotic with no practical effect, and that Lean checks the proofs but no machine checks that the formal statement matches the paper.","sledRelevance":"This is the primary vendor source for a research claim that universities, CS faculty and research offices are already discussing and citing (cross-tagged research). It is useful for showing how a vendor states verification limits alongside a headline claim. Why now: not archived; the independent examination reported Oct. 31 makes the vendor's own stated limits relevant to how campuses discuss the result.","evidence":"Vendor claim with a public formal proof artifact; independent kernel replays reported by third parties; no expert verdict.","architectureImplications":"Shows a reproducible pattern for AI-assisted formal work: pinned toolchain, multi-kernel checking and a short human-readable statement file.","governanceImplications":"Authorship credited to an AI model raises questions for institutional authorship and integrity policies.","securityPrivacyImplications":"No direct data-security effect.","caveats":"Vendor claim. The README is undated. The result has no practical algorithmic effect by Anthropic's own account.","streamIds":["anthropic","research"],"roles":{"sales":"Sales should treat this as a capability signal, not a proof point. Anthropic claims an internal Claude model refuted ETH, and its own README limits the claim: purely asymptotic, no practical effect, and the formal statement needs human reading. Use it to start conversations about research verification, not to sell discovery. Do not describe the result as confirmed or as available in commercial models.","engineering":"For engineers, the repository is a model for reproducible AI-assisted formal work: pinned Lean and Mathlib versions, a short statement file, axiom checks and a second independent kernel in CI. Rebuilding needs moderate compute (about 8 minutes on 24 vCPUs, about 7 GB memory, per the README). The step machines cannot do is checking that the statement matches the paper. Campus groups can replay the build to learn the workflow.","delivery":"Delivery can use the repository as a reference when designing research workflows for AI-produced proofs: provenance, pinned builds and a human statement review. Acceptance criteria are proposals: a campus replay documented and a statement-review checklist agreed with faculty. Wait for the expert examination before using the result as a teaching example of a settled theorem. Record AI authorship and tool versions for any local work built on it."},"roleDetails":{"sales":{"customerProblem":"Research customers hear AI discovery claims and need to separate vendor claims from verified results.","stakeholders":["CS faculty","Research computing director","Research-integrity officer"],"discoveryQuestions":["How would your institution evaluate an AI-produced research claim?","Who can review formal statements?","Do authorship policies address AI-credited work?"],"valueHypothesis":"Interpretation: positioning around verification practice is more durable than positioning around headline claims.","potentialEngagement":"A research-AI verification workflow review using this repository as a worked example.","unsupportedClaims":["That ETH is refuted","That commercial Claude models produce comparable results routinely","Any practical speedup"]},"engineering":{"fit":"Relevant to research computing and formal-methods groups.","architectureIntegration":"Pinned Lean toolchain with Comparator and independent-kernel checks in CI.","prerequisites":["Lean toolchain","About 24 vCPUs and 7 GB memory for builds per README"],"constraints":["No machine check of statement-to-paper correspondence","Repository not maintained"],"security":"No direct security concern.","proofOfValue":["Reproduce the build and axiom check","Have a faculty member review the statement file against the paper"]},"delivery":{"work":"Use the artifact as a reference design for AI-assisted formal research workflows.","dependencies":["Research computing capacity","Faculty reviewer"],"ownership":"Research computing director with CS faculty.","skillsAdoption":"Workshop on formal verification limits.","governanceCheckpoints":["Faculty sign-off on statement-review checklist"],"acceptanceCriteria":["Proposal: replay documented","Proposal: checklist adopted"],"risks":["Result later fails expert review","Over-generalizing from one claim"]}},"retrievedAt":"2026-11-02T14:36:45Z","enrichedAt":"2026-11-02T14:44:10Z","enrichmentBasis":"retrieved source","accessibilityWorkforceImplications":"Limited direct effect; relevant to teaching about formal verification.","procurementImplications":"Discovery claims should not drive research-AI purchasing without independent evidence.","operatingModelImplications":"Research offices may need a stance on AI-credited authorship.","sourceVerification":{"openedUrl":"https://raw.githubusercontent.com/anthropics/formal-math/main/eth/README.md","referenceExcerpt":"Lean checks the proofs, but no machine checks that this file says what the paper says","promptVersion":"sled-research-v4.0","model":null,"basis":"agent-reported inspection"}}}]}