{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R148",
  "content_hash": null,
  "slug": "cm3ih-artifact-rational-construction",
  "type": "artifact",
  "title": "Exact rational replay of the 61/20 construction",
  "summary": "A standard-library Python script computes all six block halos, merges them, and checks the ratio with Fraction arithmetic.",
  "relevance": "This supplies a computation, dataset, or executable check used to assess the target problem.",
  "relevance_source": "derived",
  "body": "The replay uses exact rational endpoints. For each consecutive block it constructs the interval of centers that can cover the block within radius \\(3m/2\\). It checks that all six intervals join into \\([-1/10,59/20]\\), while the original set has measure 1.",
  "status": "available",
  "evidence_grade": "executable",
  "scope": {
    "kind": "bounded",
    "statement": "the six consecutive-component blocks of the displayed three-interval set",
    "bounds": {
      "interval_count": {
        "min": 3,
        "max": 3
      },
      "block_count": {
        "min": 6,
        "max": 6
      }
    },
    "exhaustive": true
  },
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "partial",
    "kind": "inline_python_computation",
    "entrypoint": "join source_lines with newline and run with python3",
    "runtime": "CPython 3.9 or later",
    "citation": {
      "url": "https://arxiv.org/abs/math/0311452",
      "locator": "Inline CPython standard-library computation executed on 2026-07-24"
    },
    "outputs": "A_measure=1 block_halo=[-1/10,59/20] ratio=61/20\n",
    "inline_source": [
      "from fractions import Fraction as Q",
      "",
      "components = [(Q(0), Q(1,5)), (Q(3,4), Q(21,20)), (Q(11,5), Q(27,10))]",
      "halos = []",
      "for i in range(3):",
      "    mass = Q(0)",
      "    for j in range(i, 3):",
      "        mass += components[j][1] - components[j][0]",
      "        left = components[j][1] - Q(3,2) * mass",
      "        right = components[i][0] + Q(3,2) * mass",
      "        assert left <= right",
      "        halos.append((left, right))",
      "",
      "halos.sort()",
      "merged = []",
      "for left, right in halos:",
      "    if merged and left <= merged[-1][1]:",
      "        merged[-1] = (merged[-1][0], max(merged[-1][1], right))",
      "    else:",
      "        merged.append((left, right))",
      "",
      "measure = sum(right-left for left, right in components)",
      "covered = sum(right-left for left, right in merged)",
      "assert measure == 1",
      "assert merged == [(Q(-1,10), Q(59,20))]",
      "assert covered / measure == Q(61,20)",
      "print('A_measure=1 block_halo=[-1/10,59/20] ratio=61/20')"
    ],
    "missing": [
      "command"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://arxiv.org/abs/math/0311452",
    "locator": "Inline CPython standard-library computation executed on 2026-07-24"
  },
  "models": [],
  "continuation": null,
  "relations": [
    {
      "slug": "R151",
      "title": "An exact three-interval construction gives H_3 at least 61/20",
      "object_type": "claim",
      "relation": "supports",
      "direction": "outgoing"
    },
    {
      "slug": "centered-maximal-three-interval-halo",
      "title": "centered maximal three interval halo",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}