cert-machine · the monthly ledger

Decided, November 2026: the monthly register

Every published claim this machine decided in November 2026, read from the register: what held, what did not, and what went wrong, in one closed vocabulary. The page is a dated diff of the records — nothing on it is typed.

The month is still running: this is November 2026 as of 2026-11-08 (git 4a3e7b88), and the page is rebuilt with every site build until the month closes. A row belongs to the month in which its deciding record first held it (the first commit, by git's pickaxe on the record). 134 claims were decided before November 2026 (and 1 recorded then is still queued) and are on the claims desk, not here.

tl;dr
  • The finding. 10 published claims decided in November 2026: 7 CERTIFIED, 2 REFUTED, 1 MIXED. 4 of them name something that went wrong — 1 wrong quantity, 1 float printed as exact, 1 tolerance witness, 1 checker wider than definition; the other 6 hold as printed. 1 row is one audit of many items (a dataset's keys, a benchmark's counts); the row counts once and names its most frequent defect.
  • The mechanism. Each row is derived from the record that decided it; a claim with no record gets no row. CERTIFIED and REFUTED are theorems; PARTIAL, MIXED, REPAIRED and NEEDS DATA are compositions of the three verdicts, named on the claims desk.
  • Check it. node tools/run-claims-ledger.js && node tools/build-report-monthly.js — the register is certs/claims-ledger.json.
decided this month
10
7 CERTIFIED, 2 REFUTED, 1 MIXED.
held as printed
6
The row names nothing that went wrong. Most published claims hold, and the ledger says so first.
something went wrong
4
1 wrong quantity, 1 float printed as exact, 1 tolerance witness, 1 checker wider than definition.
decided before
134
Carried on the claims desk; the register holds 145 rows in all.
§1 · the rows

What was decided, in the order it was decided

recordedclaimclaimantverdictwhat went wrongwhere
2026‑11‑03a Lean bridge from OpenAI's claimed refutation of ETH to Anthropic's, the light theorem: OAI.Bridges.AnthropicETH.not_positiveRateETH_implies_ethIsFalse : ¬ OAI.ParityWL.Complexity.PositiveRateETH → MainResults.ETHIsFalse (OpenAI ParityLifts' ETH predicate, negated, implies Anthropic's ETHIsFalse)Dan With Glasses (Daniel Hawkley, formalize.now, per his message and his page)CERTIFIED—the record
2026‑11‑03the heavy link of the same bridge: OAI.Bridges.ETH.not_positiveRateETH : ¬ OAI.ParityWL.Complexity.PositiveRateETH, proved from OpenAI's original_sat_main (so OpenAI's accepted theorem reaches Anthropic's ETHIsFalse inside OpenAI's Lean)Dan With Glasses (Daniel Hawkley, formalize.now, per his message and his page)CERTIFIED—the record
2026‑11‑03Weight-Space Programming: an edit of 131,072 weights (0.016% of the model), written with no training, lifts Qwen3.5-0.8B's MATH-500 accuracy from 7.9% to 48.1% (6×)Takehi, Teoh, Zhang, Khattab, MIT CSAIL (the post of 2026-11-02)MIXEDwrong quantitythe record
2026‑11‑04ETH (complexitylib's, on cslib's deterministic multitape Turing machine with encCNF) is false, from Anthropic's own proof through C2, every step elaborated and checked in one Lean (v4.36.0-rc2): no step from Anthropic's proof to the standard machine crosses a version seam (EthBridge.AnthropicChain.not_eth)Anthropic's proof (anthropics/formal-math eth/ @ 16a5ce41), ported and joined in claimbox: the statement by hand; the port and the corollary by an AI agent (Claude), in claimboxCERTIFIED—the record
2026‑11‑04the Exponential Time Hypothesis is false, natively in Lean on cslib's multitape Turing machine: cslib-community/complexitylib's native ETH refutation (PR #1338) and its word-RAM simulation (PR #2027), the headline theorem ComplexityAbstracts.SubexponentialSATAbstract.not_eth (leanprover/lean4:v4.36.0-rc2)cslib-community/complexitylib — AI agents (Codex and Claude Code workers) with an AI reviewer, per the PR bodiesCERTIFIED—the record
2026‑11‑05ETH (complexitylib's, on cslib's deterministic multitape Turing machine with encCNF) is false, from OpenAI's own proof through Hawkley's two links and C2, every step elaborated and checked in one Lean (v4.36.0-rc2): no step from OpenAI's proof to the standard machine crosses a version seam (EthBridge.OpenAIChain.not_eth)OpenAI's proof and Hawkley's bridges (openai/math @ 7ef5c0cc (OpenAI's family-378 proof and ParityLifts, 3,183 files) and thinkthoughts/math @ d6b79b7d (Hawkley's OAI.Bridges, 27 files), the closure of the two bridge files, pinned at d6b79b7d), ported and joined in claimbox: the statement by hand; the port and the corollary by an AI agent (Claude), in claimboxCERTIFIED—the record
2026‑11‑0726 circles in the unit square, no overlaps, sum of radii = 2.63586276 (the AlphaEvolve construction as stored under key "AlphaEvolve")ThetaEvolve, entry "AlphaEvolve"; submitted by maximusrufusCERTIFIED—the record
2026‑11‑07Second autocorrelation inequality: the step function stored under key "8B-w_RL@65" (3072 cells) gives C2 >= 0.9469ThetaEvolve, entry "8B-w_RL@65"; submitted by maximusrufusREFUTEDfloat printed as exactthe record
2026‑11‑0726 circles in the unit square, no overlaps up to tolerance 1e-6 as stated in the source, sum of radii = 2.6359857 (key "8B-w_RL@65")ThetaEvolve, entry "8B-w_RL@65"; submitted by maximusrufusCERTIFIEDtolerance witnessthe record
2026‑11‑07EinsteinArena solution 2506 (agent "CodexProLong", created 2026-08-15) to the problem "The Prime Number Theorem": the submitted construction satisfies the problem's stated constraint and attains the score printed for it, 0.9976572852677297EinsteinArena solution 2506; submitted by maximusrufusREFUTEDchecker wider than definitionthe record
§2 · the vocabulary

What went wrong, in words

The vocabulary is closed: 14 kinds, defined once in tools/run-claims-ledger.js. A defect that fits none of them refuses the register until the vocabulary is decided on, never "other".

§3 · not here

What this page does not count

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