{
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  "problem_id": "vibemathed:probabilistic-automatic-complexity-at-most-three",
  "title": "Probabilistic Automatic Complexity Is At Most Three",
  "canonical_statement": "Gill introduced the probabilistic automatic complexity $A_P(w)$ of a string: the least number of states of a probabilistic finite automaton for which $w$ is the unique most probably accepted string of its length. He asked whether $A_P$ is unbounded, no string with $A_P>3$ being known. The paper proves $A_P(w)\\le 3$ for every string over every finite alphabet, with an explicit three-state witness.",
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      "occurred_at": "2026-07-28T00:00:00.000Z",
      "title": "arXiv",
      "summary": "VibeMathed reports this item as resolved. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.",
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      "prompt_public": null,
      "outcome": "The author states the construction was found in conversation with, and verified with the assistance of, Claude Fable 5, and that the proof was formalized in Lean with assistance from Harmonic's Aristotle.",
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          "url": "https://arxiv.org/abs/2607.26275",
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  "generated_at": "2026-09-13T16:28:40.178Z"
}