What was already known
The conjecture predicted edge expansion at least one for every 0/1-polytope; positive results held for special classes, including fixed-margin matrix polytopes.
AI involvement
Yang reports that GPT-5.6 Sol produced the construction and analysis in one response to the problem statement. Yang independently checked, streamlined and wrote up the proof.
The author attributes the complete construction and analysis to a one-shot model response with only the problem prompt; later human verification does not change that origin.
- Supporting source (arxiv.org) — Earlier positive fixed-margin subclass, Theorem 2.2 and Corollary 2.4
Importance
Refutes the general conjecture and its inverse-polynomial weakening.
Limitations
The construction concerns unrestricted 0/1-polytopes. It does not overturn known expansion bounds for special subclasses. Yang’s proof check is source-reported and was not repeated here.
Technical verification
Yang explicitly reports independent verification of the construction and analysis, and the manuscript provides a complete argument for the exponentially small edge-expansion theorem. This is a source-reported completed human proof check, not an AIProofWatch reproduction.
Independent checking
Yang reports independently checking and streamlining the full construction and expansion argument.
- Checker
- Xiongxin Yang
- Scope
- Theorem 1: full-dimensional 0/1-polytopes with exponentially small graph edge expansion
- Basis
- Reported by the linked checker
Human understanding
Yang’s streamlined paper explains the Cayley-sum construction, cross-layer adjacency and cut that yields the expansion estimate.
Correction and publication history
Yang’s construction refutes the conjecture for unrestricted 0/1-polytopes.
Read this published revision