What was already known
Ji, Li and Wang conjectured this strict chip-count band. It was known for trees, cycles, complete graphs and complete bipartite graphs, but not every connected graph.
AI involvement
Wang and Lannan credit GPT-5.6-Sol with the Section 3 proof. They verified the argument and wrote the exposition; Ji and Li assisted with review.
The authors attribute the proof of the general middle-stair theorem to GPT-5.6-Sol; session independence is not established.
Importance
Proves the conjecture for all finite connected simple graphs.
Limitations
Wang and Lannan report verifying the model-found proof, but do not describe their checking protocol.
Technical verification
The authors expressly say they verified the resulting Section 3 argument for Theorem 1.2; this is a source-reported completed human proof check.
Formal checking
The authors expressly say they verified the resulting Section 3 argument for Theorem 1.2; this is a source-reported completed human proof check.
- Checker
- Daniel Wang and Nathan Lannan
- Scope
- Theorem 1.2: period two in the strict middle chip-count band on every connected simple graph
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
The human-authored proof explains prefix heights, waiting rounds, edge charges and complement configurations, then derives period two from alternating firing sequences.
Correction and publication history
Proves the conjecture for all finite connected simple graphs.
Read this published revision