What was already known
Kazhdan proved the amenable direction. Burger, Ozawa and Thom asked about the converse and established it for groups containing nonabelian free subgroups; other partial classes were known.
AI involvement
OpenAI credits an internal model with the manuscript. The amenable direction and earlier nonamenable-group cases are human results.
OpenAI authorship and release provenance attribute the mathematical manuscript to internal-model work, without evidence of autonomous session conditions.
- Supporting source (github.com) — Production and verification account
Importance
The converse answers the question for all countable discrete groups.
Limitations
No completed check of the strong Ulam proof is documented. Finite-dimensional stability is a different property, and the companion Dixmier formalization does not verify this theorem.
Technical verification
No completed human or machine check of the strong Ulam theorem is documented. The Lean scope for the companion Dixmier result cannot be transferred to it. Reported is the evidence default.
Human understanding
No named human explanation of the new flag, circuit and quadratic-form obstruction is documented. Few is the evidence default.
Correction and publication history
If correct, the converse answers the question for all countable discrete groups.
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