What was already known
The authors had asked whether a uniform rectangle-to-triangle bound held for every finite planar lattice set, including a weaker formulation.
AI involvement
The authors credit ChatGPT 5.5 Pro with finding the finite lattice-set construction after a simple prompt. They proofread and rewrote it, quantified the bound and developed the separate analytic consequences.
ChatGPT 5.5 Pro supplied the retained finite lattice-set construction; the authors completed and quantified the final theorem and developed distinct analytic applications.
Importance
Gives a constructive negative answer to both uniform-bound questions.
Limitations
The quantitative amplification and separate Schrödinger-wave consequences include later human work. The model transcript is summarized by the authors. Their check and rewritten proof are source reported.
Technical verification
The authors expressly report fully proofreading the correct-in-principle model construction and give a complete rewritten proof in Section 2; this is a source-reported human check of the assessed construction.
Formal checking
full proofreading, clarification and rewriting of the model-found construction; source-reported.
- Checker
- Jonathan Bennett, Vjekoslav Kovač, Shohei Nakamura and Itamar Oliveira
- Scope
- Finite lattice sets with an unbounded rectangle-to-isosceles-triangle ratio, the construction behind Theorem 1.2
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
The authors explain the finite-field circle construction, product amplification and lattice lifting that yield the ratio bounds.
Correction and publication history
Gives a constructive negative answer to both uniform-bound questions.
Read this published revision