Stability Radius of the Lamplighter Group
Statement
Dogon, Levit and Vigdorovich asked for an explicit upper bound on the stability radius of an infinitely presented group. The lamplighter group provides the first: explicit polynomial bounds on both its Hilbert-Schmidt stability rate and its stability radius, obtained through approximately invariant measures and an effective marker construction.
Record
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proof attempt · #1
Alon Dogon and Thomas Vidick, using ChatGPT 5.5, AristotleThat credit came with the record as it was imported. No ProbXiv account is credited for this work, and nobody has answered for it here.
The disclosure separates the mathematics from the formalization. The authors had an exponential bound with a greedy marker construction; on being given the marker lemma, ChatGPT 5.5 produced the polynomial improvement, which is the paper's headline. The authors then recognized that the polynomial marker lemma follows from known descriptive-combinatorics techniques and holds for general group actions. The model also supplied the statement and proof of the Appendix A lower bound. Separately, after the paper was complete, Aristotle auto-formalized the main theorem in Lean over 64 prompts and roughly 14 partial days.
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