{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R1638",
  "content_hash": null,
  "slug": "mandelbrot-area-computable-status-packet-quality-20260801",
  "type": "claim",
  "title": "Dated status and exact unresolved remainder",
  "summary": "Unresolved in this packet after the dated source check. Strongest checked result: 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. Exact unresolved remainder: 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.",
  "relevance": "For Computability of the area of the Mandelbrot set, this successor gives readable dated status prose and the exact remaining research boundary.",
  "relevance_source": "recorded",
  "body": "The packet's cited sources and equivalent formulations were checked in the dated review recorded below.\n\nStrongest checked result: 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.\n\nExact unresolved remainder: 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://doi.org/10.1002/malq.200310124",
      "locator": "main computable-analysis results and conditional criteria for the Mandelbrot set as a compact plane subset"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://doi.org/10.1002/malq.200310124",
    "locator": "main computable-analysis results and conditional criteria for the Mandelbrot set as a compact plane subset"
  },
  "models": [],
  "continuation": null,
  "relations": [
    {
      "slug": "R1342",
      "title": "Current checked status and unresolved remainder",
      "object_type": "claim",
      "relation": "supersedes",
      "direction": "outgoing",
      "metadata": {
        "reason": "Replaces unreadable status prose with the dated review from 2026-08-01."
      }
    },
    {
      "slug": "mandelbrot-area-computable",
      "title": "mandelbrot area computable",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}