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The Burger-Ozawa-Thom question: does strong Ulam stability characterize amenability?

Theorem 1.1: a countable discrete group is strongly Ulam stable if and only if it is amenable. For every nonamenable countable $G$ and $\delta>0$ there is a separable $H$ and a normalized $\mu:G\to U(H)$ with defect below $\delta$ that stays at uniform distance more than $1/10$ from every unitary representation on $H$ . Not shown: anything about finite-dimensional (ordinary) Ulam stability, or uncountable groups.

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Occurred: Oct 5, 2026

Delta type: SOURCE CLAIM

Assumptions: VibeMathed verification: unreviewed. Publication: announcement. AI contribution: ai-discovered. VibeMathed editorial classifications, scores, notes, relations, and dataset structure are CC BY 4.0. Source statements and linked content retain their own rights.

Canonical aliases: The Burger-Ozawa-Thom question: does strong Ulam stability characterize amenability? · Strong Ulam stability and amenability

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VibeMathed record: The Burger-Ozawa-Thom question: does strong Ulam stability characterize amenability?

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No independent mathematician has checked this yet. Checked here: Theorem 1.1 of 'Strong Ulam Stability Characterizes Amenability' was read against the question as quoted from Burger-Ozawa-Thom (p. 111). The proof (flags from a strongly proximal boundary action, layered unitary circuits, and an anticommuting-involution quadratic-form obstruction) was not refereed. No Lean formalization. Scope the paper itself states: infinite-dimensional Hilbert spaces are essential; the result says nothing about finite-dimensional Ulam stability, which some nonamenable groups have.