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The Target-Free Clique Conjecture for Threshold-Linear Networks

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.

Exact FrontierDelta

Prior state unknowndisproved

Scope and record

Occurred: Jul 23, 2026

Delta type: SOURCE CLAIM

Assumptions: VibeMathed verification: site-confirmed. Publication: preprint. AI contribution: ai-assisted. Imported under CC BY 4.0.

Canonical aliases: The Target-Free Clique Conjecture for Threshold-Linear Networks · Target-free clique

Confidence: Not scored

Registry verification: site confirmed · preprint · resolved

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Attribution

VibeMathed
registry · event recorded by

Jesse Geneson
human · human collaborator

Codex (GPT-5.6)
model · ai model contributor · OpenAI / Anthropic

Claude Code (Opus 4.8, Fable 5)
model · ai model contributor · OpenAI / Anthropic

Lineage and corrections

This event attributed to Jesse Geneson

This event attributed to Claude Code (Opus 4.8, Fable 5)

This event attributed to Codex (GPT-5.6)

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The Target-Free Clique Conjecture for Threshold-Linear Networks — Mathematical Frontier Network