Connes's 1976 rigidity question predicted that property-TD/icc groups acting constructibly are uniquely determined by their von Neumann algebras; its embedding form (CEP) asserts every II₁ factor embeds in an ultrapower of the hyperfinite factor — a statement equivalent to many reformulations across quantum information (Tsirelson's problem) and model theory.
A foundational fixture of von Neumann algebra theory for half a century. The embedding form was refuted in 2020 by Ji, Natarajan, Vidick, Wright and Yuen via quantum complexity (MIP* = RE) — a landmark of indirect proof. The stronger rigidity expectation for specific group constructions lingered.
Disproof announced by OpenAI's Astra model, 1 August 2026, in the ten-results batch, with Lean-checked formalisation and external mathematicians preparing the manuscripts. Whatever the final peer verdict settles to, the episode already demonstrates AI operating at the frontier of functional analysis — a field long considered out of reach for language models.
Context: the embedding form (CEP) was already refuted in 2020 by Ji, Natarajan, Vidick, Wright and Yuen (MIP*=RE), building on the Junge–et al. equivalence with Tsirelson's problem in quantum information — so the landscape this claim enters is one where the headline implication is known and the interest lies in the rigidity formulation and the methods. Confirmation here means the announced manuscripts surviving peer review and the Lean certificates checking independently; until then the honest status is claimed-disproof under review, as recorded.
Verified by curator — see the API for full claim provenance.
