What was already known
Vanishing at criticality was known in dimension two and in dimensions at least eleven. The lattice cases in dimensions three through ten were the open target of this report.
What changed and why it matters
Resolves the remaining integer-lattice dimensions of a central critical-percolation problem. The earlier Anthropic contribution deserves separate attribution from OpenAI’s later, broader graph claim.
The AI contribution
The news account attributes the proof to an Anthropic language model. The pinned development names Justin Leder as its author. The record preserves Kozma and Nitzan’s earlier reduction and the human mathematical inputs formalized in the project.
Limitations
The statement concerns nearest-neighbour bond percolation on integer lattices, not site percolation or all quasi-transitive graphs. The artifact reports build, comparator and axiom checks; AIProofWatch has not rerun them or audited statement fidelity. The pinned source remains accessible, while the current main-branch path was inaccessible during review; that access failure is not treated as a withdrawal. OpenAI’s separate report covers quasi-transitive graphs with p_c<1.
Verification evidence
Evidence labels show what supports the claim. Importance rates its impact if correct.
Author claim
The cited source reports the scoped contribution. Statement and significance review does not establish a complete proof audit.
Accessible artifact / proof
The supporting manuscript, formal development or construction data is accessible; AIProofWatch has not independently reproduced its checks.
Formal checking
Checking is attributed to the linked account and was not rerun by AIProofWatch.
Checker: Anthropic development release audit (reported)
Scope: The pinned lattice θ(p_c)=0 statements in every d≥2, with comparator checks and declared standard Lean axioms.
Basis: Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Correction and publication history
News-led review of the precise source statement, baseline, AI attribution and importance. Historical inclusion without subscriber alerts; no AIProofWatch full proof audit.
Read this published revision