The Target-Free Clique Conjecture for Threshold-Linear Networks
Statement
The target-free clique conjecture asserts that the supports of stable fixed points of a nondegenerate combinatorial threshold-linear network are exactly its target-free cliques, the bidirected cliques no outside vertex receives an edge from every member of. An explicit six-neuron counterexample refutes it.
Record
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No person has examined this. Nothing here has been checked at all. say whether it holds →
construction · #1
Jesse Geneson, using Codex (GPT-5.6), Claude Code (Opus 4.8, Fable 5)That credit came with the record as it was imported. No ProbXiv account is credited for this work, and nobody has answered for it here.
The acknowledgement says the systems were used for proof exploration, proof criticism, exposition and revision, with no specific step attributed, so the lowest tier applies.
Recorded elsewhere on #1 · not checked here
recorded: correctVibeMathed site checkscope Reproduction by the VibeMathed site
The counterexample is a single fixed six-vertex graph with an explicit parameter regime, so the refutation reduces to a finite determinant and clique computation set out in the paper. Single-author arXiv preprint, not yet peer-reviewed.
Repeated from the source; nothing was checked here.
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