{
  "vercy": "1.0-draft",
  "publication": {
    "status": "research-draft",
    "adjudicationStatus": "unreviewed",
    "publishableCanonical": false,
    "generatedAt": "2026-09-13T01:57:22Z",
    "providers": [
      "Claude"
    ],
    "breadth": "written by Claude from model knowledge without web access - no source was read, every claim is a lead to verify",
    "pass": 2,
    "wave": 3,
    "engine": "claude",
    "enrichment": {
      "pass": 3,
      "engine": "claude",
      "producedAt": "2026-10-06T10:00:00Z",
      "ingestedAt": "2026-10-06T07:06:04+00:00",
      "fields": [
        "agent_conduct",
        "ethics",
        "owners"
      ]
    },
    "gate": {
      "passed": true,
      "version": "1.0",
      "at": "2026-10-06T19:52:03+00:00",
      "evidence": [
        "completeness 1.00",
        "sense: Wikidata description",
        "2 live sources",
        "review by codex: pass"
      ]
    }
  },
  "metaModel": {
    "id": "THING-Q965294",
    "registryId": "vr.tr.thabit-number",
    "name": "Thabit number",
    "version": "0.2.0-wave.3",
    "entryKind": "thing",
    "family": "Thing Registry",
    "domain": [
      "XCT.QTY"
    ],
    "status": "research-draft"
  },
  "canonicalUrl": "https://ver.cy/models/thing/q965294/",
  "model": {
    "registry_id": "vr.tr.thabit-number",
    "name": "Thabit number",
    "purpose": "Let an agent define Thabit numbers and Thabit primes, relay their role in Thabit rule for amicable numbers, relay known results and searches, and distinguish them from related forms such as Proth and Mersenne numbers.",
    "definition": "An integer of the form 3 times 2 to the n minus 1 for a non-negative integer n, the sequence beginning 2, 5, 11, 23, 47, 95, 191, named after the ninth-century mathematician Thabit ibn Qurra, who used them in his rule for generating amicable numbers; Thabit primes are those that are prime, such as 2, 5, 11, 23, 47, 191, 383 and 6143, and are searched for in distributed computing projects.",
    "what_it_is_for": "Not applicable; a class of integers.",
    "affordances": [
      "define and list",
      "explain the amicable number rule",
      "relay primes and searches",
      "distinguish related forms"
    ],
    "distinguishing_features": [
      "Simple closed form",
      "Amicable number link",
      "Ninth-century origin",
      "Search target"
    ],
    "appearance": "The sequence 2, 5, 11, 23, 47, 95, 191, 383, ...",
    "visual_identification": [
      "Numbers 3 times 2^n minus 1",
      "Sequence OEIS A055010, Thabit primes A007505",
      "Mersenne numbers are 2^n minus 1; Proth numbers are k times 2^n plus 1"
    ],
    "physical_properties": [
      {
        "quantity": "first Thabit prime",
        "typical_range": "2",
        "unit": "number",
        "note": "n equals 0"
      },
      {
        "quantity": "known Thabit primes",
        "typical_range": "over 60",
        "unit": "count",
        "note": "as of recent searches"
      }
    ],
    "families_and_kinds": [
      "Thabit numbers in general",
      "Thabit primes",
      "Thabit numbers of the second kind, 3 times 2^n plus 1",
      "generalised Thabit numbers in other bases"
    ],
    "related_models": [
      {
        "relation": "is a kind of",
        "target": "non-negative integer",
        "why": "in registry terms"
      },
      {
        "relation": "is named after",
        "target": "Thabit ibn Qurra",
        "why": "the mathematician"
      },
      {
        "relation": "is used in",
        "target": "Thabit rule for amicable numbers",
        "why": "the classical construction"
      },
      {
        "relation": "is listed in",
        "target": "OEIS",
        "why": "as A055010"
      }
    ],
    "identifiers": [
      {
        "scheme": "OEIS",
        "value_or_pattern": "A055010",
        "note": "Thabit numbers"
      },
      {
        "scheme": "OEIS",
        "value_or_pattern": "A007505",
        "note": "Thabit primes"
      }
    ],
    "standards_and_regulation": [
      "No regulation; mathematical conventions"
    ],
    "failure_modes_and_hazards": [
      "Confusing with Mersenne or Proth numbers",
      "Stale lists of known primes",
      "Computation errors"
    ],
    "in_scope": [],
    "out_of_scope": [],
    "characteristics": [],
    "agent_conduct": {
      "may": [
        "Generate and test Thabit numbers and report which are prime, with the method used.",
        "Explain their use by Thabit ibn Qurra for amicable numbers."
      ],
      "must_not": [
        "Claim a large Thabit number is prime without a proof or a stated probable-prime test.",
        "Credit the work of Thabit ibn Qurra to later mathematicians alone.",
        "Confuse Thabit numbers with similar forms such as Proth or Mersenne numbers."
      ],
      "requires_human": [
        "Announcing a new Thabit prime as a record."
      ]
    },
    "ethics": {
      "considerations": [
        "Fair credit to medieval Islamic mathematics is part of an honest history of science.",
        "Unverified record claims mislead the mathematical community."
      ],
      "affected_parties": [
        "Mathematicians",
        "Students",
        "Historians of science"
      ]
    },
    "owners": {
      "steward": "The public: held in common as mathematical knowledge.",
      "master_systems": []
    }
  },
  "sources": [
    {
      "id": "wikidata",
      "title": "Wikidata item Q965294: Thabit number",
      "url": "https://www.wikidata.org/wiki/Q965294",
      "url_status": "live",
      "what_it_supports": "identity and sense of the item",
      "checked_by": "wikidata-api"
    },
    {
      "id": "wikipedia-en",
      "title": "Wikipedia: Thabit number",
      "url": "https://en.wikipedia.org/wiki/Thabit_number",
      "url_status": "live",
      "what_it_supports": "general description of the item",
      "checked_by": "wikidata-api sitelink"
    }
  ],
  "structure": {
    "bundles": [
      {
        "id": "define",
        "name": "Define",
        "description": "Definition.",
        "rationale": "Mathematics.",
        "layers": [
          {
            "id": "definition",
            "name": "Definition",
            "description": "Definition.",
            "findings": [
              {
                "id": "definition-finding",
                "name": "Definition",
                "description": "Definition.",
                "questions": [
                  {
                    "text": "What is a Thabit number, and how does it relate to Mersenne and Proth numbers?",
                    "kind": "definition"
                  },
                  {
                    "text": "Is the question about Thabit, Mersenne or Proth numbers?",
                    "kind": "boundary"
                  }
                ]
              }
            ]
          },
          {
            "id": "sequence",
            "name": "Sequence",
            "description": "Sequence.",
            "findings": [
              {
                "id": "sequence-finding",
                "name": "Sequence",
                "description": "Sequence.",
                "questions": [
                  {
                    "text": "What are the first Thabit numbers and primes, and where are they catalogued?",
                    "kind": "measurement"
                  },
                  {
                    "text": "Which entry fits Proth number?",
                    "kind": "action"
                  }
                ]
              }
            ]
          }
        ]
      },
      {
        "id": "amicable",
        "name": "Amicable",
        "description": "Amicable numbers.",
        "rationale": "Mathematics.",
        "layers": [
          {
            "id": "rule",
            "name": "Rule",
            "description": "Thabit rule.",
            "findings": [
              {
                "id": "rule-finding",
                "name": "Rule",
                "description": "Rule.",
                "questions": [
                  {
                    "text": "How does Thabit rule use these numbers to generate amicable pairs?",
                    "kind": "provenance"
                  },
                  {
                    "text": "Which entry fits amicable number?",
                    "kind": "action"
                  }
                ]
              }
            ]
          },
          {
            "id": "history",
            "name": "History",
            "description": "History.",
            "findings": [
              {
                "id": "history-finding",
                "name": "History",
                "description": "History.",
                "questions": [
                  {
                    "text": "How did Thabit ibn Qurra, Fermat, Descartes and Euler develop the rule?",
                    "kind": "provenance"
                  },
                  {
                    "text": "Which sources are cited?",
                    "kind": "provenance"
                  }
                ]
              }
            ]
          }
        ]
      },
      {
        "id": "primes",
        "name": "Primes",
        "description": "Thabit primes.",
        "rationale": "Mathematics.",
        "layers": [
          {
            "id": "results",
            "name": "Results",
            "description": "Known results.",
            "findings": [
              {
                "id": "results-finding",
                "name": "Results",
                "description": "Results.",
                "questions": [
                  {
                    "text": "What is known about Thabit primes, including divisibility results?",
                    "kind": "provenance"
                  },
                  {
                    "text": "Which references are standard?",
                    "kind": "provenance"
                  }
                ]
              }
            ]
          },
          {
            "id": "searches",
            "name": "Searches",
            "description": "Searches.",
            "findings": [
              {
                "id": "searches-finding",
                "name": "Searches",
                "description": "Searches.",
                "questions": [
                  {
                    "text": "How are Thabit primes searched for in distributed projects, and what is the largest known?",
                    "kind": "provenance"
                  },
                  {
                    "text": "Is the information current?",
                    "kind": "boundary"
                  }
                ]
              }
            ]
          }
        ]
      },
      {
        "id": "context",
        "name": "Context",
        "description": "Generalisations and use.",
        "rationale": "Context.",
        "layers": [
          {
            "id": "generalised",
            "name": "Generalised",
            "description": "Generalisations.",
            "findings": [
              {
                "id": "generalised-finding",
                "name": "Generalised",
                "description": "Generalised.",
                "questions": [
                  {
                    "text": "What are Thabit numbers of the second kind and generalised forms?",
                    "kind": "provenance"
                  },
                  {
                    "text": "Which entry fits generalised Thabit number?",
                    "kind": "action"
                  }
                ]
              }
            ]
          },
          {
            "id": "education",
            "name": "Education",
            "description": "Teaching.",
            "findings": [
              {
                "id": "education-finding",
                "name": "Education",
                "description": "Education.",
                "questions": [
                  {
                    "text": "How can Thabit numbers be used to teach number theory and its history?",
                    "kind": "provenance"
                  },
                  {
                    "text": "Which entry fits the history of mathematics in the Islamic world?",
                    "kind": "action"
                  }
                ]
              }
            ]
          }
        ]
      }
    ]
  },
  "openQuestions": [
    "Are there infinitely many Thabit primes?",
    "How should OEIS and search projects be linked?",
    "How should the amicable number rule be recorded?"
  ],
  "statistics": {
    "bundles": 4,
    "layers": 8,
    "findings": 8,
    "questions": 16
  }
}