What was already known
An elementary two-forest example already defeated the unrestricted wording. The cycle-containing bipartite case remained open.
AI involvement
OpenAI credits Astra with the Chapter 10 family and proof. Humans selected the problem and prepared the manuscript; Xu supplied the later statement bridge.
OpenAI is credited as author and attributes Chapter 10 results to its internal model; the later bridge/formalization is not assigned to that model.
- Supporting source (raw.githubusercontent.com) — Statements and proof entrypoints; source credit
Importance
Gives a polynomial separation for the corrected compactness question.
Limitations
The elementary forest example is prior work. Linmiao Xu later formalized a bridge to the related Erdős #575 formulation; that bridge is Xu’s work. One Chapter 10 optimization remains compressed in the exposition.
Technical verification
The cited Xu project reports complete Lean and NanoDa checks of the cyclic family and #575 bridge. Chapter 10 human reviewers also checked the family’s construction and bound structure, but did not report a complete independent proof reconstruction.
Independent checking
chapter-specific mathematical review of the published argument, with the limited coverage summarized in the audit. Table 1; Chapter 10 discussion
- Checker
- Chapter 10 human reviewers in the Sienicki et al. review corpus
- Scope
- quantitative compactness counterexample and related Chapter 10 steps
- Basis
- Reported by the linked checker
Formal checking
complete formal proof, Comparator and axiom audit. status, main_results and review
- Checker
- Lean and NanoDa kernels via Xu’s pinned project
- Scope
- quantitative connected all-bipartite cyclic family and its #575 bridge
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
Chapter 10 explains the quotient-template family, path-count upper bound and generalized-quadrangle witnesses; Xu explains the #180-to-#575 bridge.
Correction and publication history
Gives a polynomial separation for the corrected compactness question.
Read this published revision