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A Sidorenko counterexample

Sidorenko’s conjecture predicts the lower bound for every bipartite pattern.

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Understanding the problem

Read the background

Sidorenko’s conjecture predicts the lower bound for every bipartite pattern. One rigorously established counterexample would refute that universal statement despite many known positive classes.

Homomorphisms include noninjective maps. The statement is about the specified bipartite pattern and existence of a host, not failure for every bipartite graph.

Why it matters

If correct, refutes the universal Sidorenko assertion with an explicitly specified finite pattern.

What counts as progress

A sourced resolution or substantial advance on the precise target, with hypotheses, prior context, and verification evidence stated separately.

What to watch for

  • Assess the precise statement and assumptions before comparing results.
  • Homomorphisms include noninjective maps. The statement is about the specified bipartite pattern and existence of a host, not failure for every bipartite graph.
  • Track independent assessments, dependencies, corrections, and withdrawals separately from importance.

Background review: 2026-10-11. Selected sources:

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