What was already known
The paper’s base embedding bound has O(h²) loss. The AI-origin terminal-set peeling argument improves that dependence to O(log h). The paper’s repairs to earlier separator results are separate human contributions.
AI involvement
The authors explicitly credit GPT-5.6 Sol with devising the initial improvement in Appendix B. They substantially simplified its presentation; the underlying human baseline and repairs remain separately credited.
Importance
Improves a parameter dependence in graph separators and metric embeddings; the retained contribution is Appendix B, not the whole paper.
Limitations
The existential statements are formally checked; the paper’s polynomial-time construction claims are outside the selected formal checking scope. The repository README omits an h factor in one separator summary: the exact Lean bound contains √(|V(H)|+|E(H)|) and agrees with O(h log h √m) for the paper’s forbidden subdivision.
Technical verification
The authors report Lean verification of the existential statements, with independently separated and human-checked definitions/statements. The pinned exact improved theorem retains the graph-size/edge factor. The exact check execution date is not supplied; the paper date is retained separately.
Formal checking
The authors report Lean verification of the existential statements, with independently separated and human-checked definitions/statements. The pinned exact improved theorem retains the graph-size/edge factor.
- Checker
- Authors’ Lean 4 formalization
- Scope
- Existential non-expansive embeddings and balanced separator bounds, with exact forbidden-induced-minor and vertex-weighted metric definitions; not polynomial running time.
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
Davies, Rzążewski, Spalding-Jamieson and Walczak explain the central terminal-set peeling argument and its separator consequence in Appendix B, after simplifying the AI-origin improvement.
Correction and publication history
Added this sourced contribution with its stated scope, AI attribution, checking evidence and research limits.
Read this published revision