The Target-Free Clique Conjecture for Threshold-Linear Networks
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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.
Context
A named conjecture in the combinatorial threshold-linear network literature, real and cited within mathematical neuroscience.
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machine: correctscope 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 Single-author arXiv preprint, not yet peer-reviewed.
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