What was already known
Many lattice and growth-restricted cases were studied. The target here is bond percolation on arbitrary quasi-transitive graphs with critical probability below one. Anthropic’s earlier 28 August 2026 artifact reports the remaining integer-lattice cases; its narrower lattice scope is distinct from this general quasi-transitive-graph claim.
What changed and why it matters
Advances the stated target relative to the recorded baseline.
The AI contribution
OpenAI attributes the manuscript to its internal model; individual human contributions remain unspecified.
Limitations
Bond percolation is distinct from site percolation. Infinite, connected, locally finite, quasi-transitive graphs and p_c<1 are required. Earlier lattice-only claims are not counted as the same general result. Preprint. AIProofWatch read the source statement and context; it has not refereed the proof, compiled a formal development, or established community acceptance. The earlier Claude lattice result is separately credited and linked as related progress; this record does not assign priority for that narrower target to OpenAI.
Verification evidence
Evidence labels show what supports the claim. Importance rates its impact if correct.
Author claim
The original source reports this scoped result; AIProofWatch reviewed its statement, not the full proof.
Accessible artifact / proof
A research manuscript or proof artifact is publicly accessible; availability is not independent checking.
Correction and publication history
News-led source-context amendment, preserving the existing claim, rating, AI attribution and checking limits. No subscriber alerts.
Read this published revisionFull source review, 11 October 2026. Historical addition; subscriber alerts disabled.
Read this published revision