What was already known
Procaccia and Tucker-Foltz posed square maximality. Zhang had proved a rectangular balancing theorem; a grid-graph estimate by Tapp is another input.
AI involvement
Jiechen Zhang directed the proof and supplied earlier results. GPT-5.6 Sol contributed the rectangular area penalty and normalized-hull lemmas; Sloan Nietert helped design the breakthrough prompt. Zhang reports checking the mathematics and formal-statement alignment.
The model supplied the retained area-penalty and hull lemmas central to the proof, while Zhang led and checked the overall result.
Importance
Resolves the square-grid spanning-tree conjecture with its equality case.
Limitations
The reported formal check covers the inequality and equality characterization. The argument uses earlier human results. The broader arbitrary-spanning-subgraph strengthening is a separate formal statement.
Technical verification
The cited record reports sorry-free Lean proofs with standard axioms and Comparator/NanoDa checking of both headline statements. Zhang explicitly checked the mathematical argument and performed a detailed source-to-Lean specification audit. These are distinct machine and human methods, reported by the source rather than reproduced here.
Independent checking
Sorry-free kernel proof, standard-axiom audit and independent statement/proof replay
- Checker
- Lean kernel, Comparator and NanoDa in Zhang's pinned repository
- Scope
- SquareMaximalityPalomar.squareMaximality and equality_iff_latticeSquare
- Basis
- Reported by the linked checker
Independent checking
Checked definitions, hypotheses, intermediate arguments, cited results and conclusions; completed specification audit on 22 August 2026
- Checker
- Jiechen Zhang
- Scope
- Square-maximality inequality, equality case and paper-to-Lean correspondence
- Basis
- Reported by the linked checker
Human understanding
Default for missing evidence of human explanation: Zhang checked the argument and source alignment, but this documented check does not itself establish that a person can explain the model-supplied area-penalty and normalized-hull mechanism.
Correction and publication history
Resolves the square-grid spanning-tree conjecture with its equality case.
Read this published revision