Conjecture that all gapped ground states satisfy approximate Haag duality

The conjecture proposes that every gapped ground state has approximate Haag duality. No proposer or date is identified in the retrieved sources, and no universal proof was found.

September 1, 2026 claimed counterexample

The preprint A nonabelian anyon violates Haag duality claims a sector-theoretic counterexample, realizes it in Levin–Wen models, and asserts that the failure persists throughout the phase. If correct, this refutes the universal conjecture rather than merely proving a special-case limitation.

Current status (as of September 2026): The conjecture is claimed false by an unrefereed preprint, but that counterexample remains unverified; no general proof or independent confirmation was found.