Garamvölgyi-Jackson-Jordán Conjecture on Cliques in Minimally Globally Rigid Graphs
Statement
Every minimally generically globally rigid graph in containing a subgraph isomorphic to is itself isomorphic to , confirming Conjecture 6.3 of Garamvölgyi, Jackson and Jordán (2025).
Context
A 2025 conjecture by the central figures of graph rigidity theory, posed in an active program but with no accumulated literature yet.
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"The proof is entirely generated by ChatGPT 5.5." The author had an intuition about the natural stress-matrix strategy but deliberately withheld it from the prompt; the model independently identified the same strategy, resolved the algebraic difficulty the author was stuck on, and produced the proof, which the author checked and edited.
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