What was already known
Garamvölgyi, Jackson and Jordán posed the clique statement as a conjecture. Existing stress-rank and rigidity-matroid tools had not supplied the needed clique-edge cancellation.
AI involvement
Portier credits ChatGPT 5.5 with the proof and independent stress-matrix strategy. He had suspected a similar strategy, then checked and edited the model’s final proof.
The author explicitly attributes the proof and independent rediscovery of its stress-matrix strategy to ChatGPT, while retaining his earlier unprompted intuition and later human checking.
Importance
Resolves a named structural conjecture in generic graph rigidity.
Limitations
Portier reports checking the generated proof. Jordán later gave a distinct shorter proof, which does not independently verify Portier’s original argument.
Technical verification
Portier explicitly reports checking the model-generated proof of the exact clique theorem before publishing the edited final argument. Jordán's distinct proof is not counted as a check of the model argument.
Formal checking
author's check of the complete ChatGPT-generated proof followed by clarity edits
- Checker
- Julien Portier, author
- Scope
- Theorem 1.2 excluding K_{d+2} from edge-minimal generically globally rigid graphs with at least d+3 vertices
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
Portier describes the stress-matrix strategy and its rank-preserving difficulty, and his checked exposition works through the clique cancellation and rigidity-circuit contradiction.
Correction and publication history
Resolves a named structural conjecture in generic graph rigidity.
Read this published revision