combinatorics / Mathematical neuroscience

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.

10Significance / 100
1Frontier events
0Verification tasks
0Recorded attempts

Temporal state

Current frontier

No reconciled state yet.

Append-only history

Frontier timeline

combinatoricsJul 23, 2026Significance 10/100Registry: site confirmed

The Target-Free Clique Conjecture for Threshold-Linear Networks

Prior state unknowndisproved

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.

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

Research memory

Claims and attempts

Scoped claims

Source authenticated

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.

Recorded attempts

Evidence graph

Connected research record

No public relationships recorded yet.