{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R1342",
  "content_hash": null,
  "slug": "mandelbrot-area-computable-status-20260801",
  "type": "claim",
  "title": "Current checked status and unresolved remainder",
  "summary": "UNKNOWN as of 2026-07-27. The MathOverflow answer calls unconditional computability open and explains a conditional route through full measure of hyperbolic parameters. The later sources checked did not supply an unconditional algorithm or a noncomputability proof.",
  "relevance": "Records the strongest checked neighboring results and the exact remainder future work must settle.",
  "relevance_source": "recorded",
  "body": "A dated independent review on 2026-08-01 checked the structured sources below, the complete visible source discussion, exact-title and equivalent-formulation searches, and the current TheoremDB corpus. The MathOverflow page was checked on 2026-07-27, including its answer and all comments. The answer states that the area is computable under the conjecture that hyperbolic parameters have full measure and leaves the unconditional question open. Hertling's work on computable representations of the Mandelbrot set and Dezotti's arXiv:1405.1933 were checked for a result about its area. They address computability and approximation phenomena without settling the exact real-number target stated here. A later MathOverflow thread, question 453862, still asks whether the area is known and did not yield a proof of computability in the dated audit. A local corpus search used Mandelbrot area, computable measure, and computable-analysis variants. It found no duplicate target.\n\nA complete resolution must satisfy: Give an algorithm that, for every k>=1, returns a rational q with |A-q|<2^{-k}, together with a proof of its error bound, or prove that no such algorithm exists. Any numerical approximation used in a proof must include certified inner and outer area bounds whose gap is explicitly controlled.",
  "status": "reported",
  "evidence_grade": "sourced",
  "scope": null,
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "claim",
    "citation": {
      "url": "https://mathoverflow.net/questions/249617/is-the-area-of-the-mandelbrot-provably-computable",
      "locator": "Dataset references and independent 2026-08-01 status search."
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://mathoverflow.net/questions/249617/is-the-area-of-the-mandelbrot-provably-computable",
    "locator": "Dataset references and independent 2026-08-01 status search."
  },
  "relations": [
    {
      "slug": "R1341",
      "title": "Complete the stated acceptance conditions",
      "object_type": "attempt",
      "relation": "addresses",
      "direction": "incoming"
    },
    {
      "slug": "R1638",
      "title": "Dated status and exact unresolved remainder",
      "object_type": "claim",
      "relation": "supersedes",
      "direction": "incoming"
    },
    {
      "slug": "mandelbrot-area-computable",
      "title": "mandelbrot area computable",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}