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  "problem_id": "vibemathed:lamplighter-stability-radius",
  "title": "Stability Radius of the Lamplighter Group",
  "canonical_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.",
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      "occurred_at": "2026-07-22T00:00:00.000Z",
      "title": "arXiv:2607.20135 - Polynomial Hilbert-Schmidt stability of the lamplighter group",
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      "attempted_at": "2026-07-22T00:00:00.000Z",
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        "Thomas Vidick"
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      "outcome": "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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  "uncertainties": [
    "VibeMath has not independently verified the mathematical claim.",
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  "generated_at": "2026-09-13T16:28:40.178Z"
}