{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R770",
  "content_hash": null,
  "slug": "tc114-claim-partial-parameter-search-1e19",
  "type": "claim",
  "title": "A later partial search reached |z|=10^19",
  "summary": "The 2020 Charity Engine run searched the stated (d,z) rectangle for 114 and reported no solution.",
  "relevance": "For A bounded three-cubes search for 114, record tc114-claim-partial-parameter-search-1e19 (“A later partial search reached |z|=10^19”) records a bound, answer, status fact, or structural consequence. The record states: The 2020 Charity Engine run searched the stated (d,z) rectangle for 114 and reported no solution.",
  "relevance_source": "recorded",
  "body": "During 2020, Charity Engine searched the eight targets left after the first run, including 114, with\n\\[\nz_{\\max}=10^{19},\\qquad d_{\\max}=z_{\\max}/54.\n\\]\nSince \\(d\\) is integral, its largest allowed value is\n\\[\n\\left\\lfloor\\frac{10^{19}}{54}\\right\\rfloor\n=185185185185185185.\n\\]\nThe run produced a representation of 579 in January 2021 and reported none for 114.\n\nThis rectangle is much deeper in \\(|z|\\) than the complete \\(10^{17}\\) run, yet its \\(d\\)-bound is too small to cover every solution with \\(|z|\\leq10^{19}\\). Full coverage at that \\(z\\)-bound would require \\(d_{\\max}=(\\sqrt[3]{2}-1)10^{19}\\). The computation therefore supplies substantial evidence inside a named parameter rectangle. It does not exclude the rest of the height-\\(10^{20}\\) box. Remark 5.1 gives the same possible-error caveat for the crowd-sourced computation.",
  "status": "supported",
  "evidence_grade": "computational",
  "scope": {
    "kind": "bounded",
    "statement": "canonical search pairs for k=114 with abs(z) at most 10^19 and d=abs(x+y) at most floor(10^19/54)",
    "bounds": {
      "canonical_abs_z": {
        "min": 0,
        "max": 10000000000000000000
      },
      "d": {
        "min": 0,
        "max": 185185185185185180
      }
    },
    "exhaustive": true
  },
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "claim",
    "citation": {
      "url": "https://doi.org/10.1073/pnas.2022377118",
      "locator": "Booker and Sutherland, Section 5.B and Remark 5.1, page 11"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://doi.org/10.1073/pnas.2022377118",
    "locator": "Booker and Sutherland, Section 5.B and Remark 5.1, page 11"
  },
  "relations": [
    {
      "slug": "R767",
      "title": "The height-10^20 question remains open",
      "object_type": "claim",
      "relation": "supports",
      "direction": "outgoing"
    },
    {
      "slug": "three-cubes-114-height-1e20",
      "title": "three cubes 114 height 1e20",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}