{
  "vercy": "1.0-draft",
  "publication": {
    "status": "research-draft",
    "adjudicationStatus": "unreviewed",
    "publishableCanonical": false,
    "generatedAt": "2026-09-13T01:44:01Z",
    "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": "2026-10-06T07:04:11+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-Q951293",
    "registryId": "vr.tr.woodall-number",
    "name": "Woodall number",
    "version": "0.2.0-wave.3",
    "entryKind": "thing",
    "family": "Thing Registry",
    "domain": [
      "XCT.QTY"
    ],
    "status": "research-draft"
  },
  "canonicalUrl": "https://ver.cy/models/thing/q951293/",
  "model": {
    "registry_id": "vr.tr.woodall-number",
    "name": "Woodall number",
    "purpose": "Let an agent define Woodall numbers and Woodall primes, relay known results and searches from number theory references, and distinguish them from Cullen numbers and other special forms.",
    "definition": "A natural number of the form n times 2 to the n minus 1 for a positive integer n, the sequence beginning 1, 7, 23, 63, 159, 383, named after H. R. Woodall who studied their primality with Cunningham in 1917; Woodall primes are Woodall numbers that are prime, such as 7, 23, 383 and 5119, are conjectured to be infinitely many, and are the counterpart of Cullen numbers of the form n times 2 to the n plus 1.",
    "what_it_is_for": "Not applicable; a class of integers.",
    "affordances": [
      "define and list",
      "relay primes and results",
      "relay computational searches",
      "distinguish from Cullen numbers"
    ],
    "distinguishing_features": [
      "Simple closed form",
      "Rare primes",
      "Counterpart of Cullen numbers",
      "Distributed search targets"
    ],
    "appearance": "The sequence 1, 7, 23, 63, 159, 383, 895, ...",
    "visual_identification": [
      "Numbers n times 2^n minus 1",
      "Sequence OEIS A003261, Woodall primes A050918",
      "Cullen numbers add one instead; Mersenne numbers are 2^n minus 1"
    ],
    "physical_properties": [
      {
        "quantity": "first Woodall prime",
        "typical_range": "7",
        "unit": "number",
        "note": "n equals 2"
      },
      {
        "quantity": "known Woodall primes",
        "typical_range": "about 30",
        "unit": "count",
        "note": "as of recent searches"
      }
    ],
    "families_and_kinds": [
      "Woodall numbers in general",
      "Woodall primes",
      "generalised Woodall numbers in other bases",
      "Cullen numbers as the related class"
    ],
    "related_models": [
      {
        "relation": "is a kind of",
        "target": "positive integer",
        "why": "in registry terms"
      },
      {
        "relation": "is contrasted with",
        "target": "Cullen number",
        "why": "the plus-one counterpart"
      },
      {
        "relation": "is named after",
        "target": "H. R. Woodall",
        "why": "the mathematician"
      },
      {
        "relation": "is listed in",
        "target": "OEIS",
        "why": "as A003261"
      }
    ],
    "identifiers": [
      {
        "scheme": "OEIS",
        "value_or_pattern": "A003261",
        "note": "Woodall numbers"
      },
      {
        "scheme": "OEIS",
        "value_or_pattern": "A050918",
        "note": "Woodall primes"
      }
    ],
    "standards_and_regulation": [
      "No regulation; mathematical conventions"
    ],
    "failure_modes_and_hazards": [
      "Confusing with Cullen or Mersenne numbers",
      "Stale lists of known primes",
      "Computation errors"
    ],
    "in_scope": [],
    "out_of_scope": [],
    "characteristics": [],
    "agent_conduct": {
      "may": [
        "Compute and verify Woodall numbers and test candidates for primality.",
        "Explain their relation to Cullen numbers and known Woodall primes."
      ],
      "must_not": [
        "Announce a new Woodall prime without independent verification.",
        "Claim credit for a distributed computing project's result.",
        "Present a probable prime as proven prime."
      ],
      "requires_human": [
        "Publishing a claimed record prime discovery."
      ]
    },
    "ethics": {
      "considerations": [
        "Record claims in computational number theory rest on verification by others.",
        "Volunteers in distributed searches deserve credit for their contributions."
      ],
      "affected_parties": [
        "Mathematicians",
        "Volunteer computing participants",
        "Students"
      ]
    },
    "owners": {
      "steward": "Nobody owns a number sequence; search projects record their own discoveries.",
      "master_systems": [
        "Integer sequence databases",
        "Prime number record lists"
      ]
    }
  },
  "sources": [
    {
      "id": "wikidata",
      "title": "Wikidata item Q951293: Woodall number",
      "url": "https://www.wikidata.org/wiki/Q951293",
      "url_status": "live",
      "what_it_supports": "identity and sense of the item",
      "checked_by": "wikidata-api"
    },
    {
      "id": "wikipedia-en",
      "title": "Wikipedia: Woodall number",
      "url": "https://en.wikipedia.org/wiki/Woodall_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 Woodall number, and how does it relate to Cullen numbers?",
                    "kind": "definition"
                  },
                  {
                    "text": "Is the question about Woodall, Cullen or Mersenne numbers?",
                    "kind": "boundary"
                  }
                ]
              }
            ]
          },
          {
            "id": "sequence",
            "name": "Sequence",
            "description": "Sequence.",
            "findings": [
              {
                "id": "sequence-finding",
                "name": "Sequence",
                "description": "Sequence.",
                "questions": [
                  {
                    "text": "What are the first Woodall numbers and primes, and where are they catalogued?",
                    "kind": "measurement"
                  },
                  {
                    "text": "Which entry fits Cullen number?",
                    "kind": "action"
                  }
                ]
              }
            ]
          }
        ]
      },
      {
        "id": "results",
        "name": "Results",
        "description": "Results.",
        "rationale": "Mathematics.",
        "layers": [
          {
            "id": "primality",
            "name": "Primality",
            "description": "Primality results.",
            "findings": [
              {
                "id": "primality-finding",
                "name": "Primality",
                "description": "Primality.",
                "questions": [
                  {
                    "text": "What is known about Woodall primes, including divisibility results and density?",
                    "kind": "provenance"
                  },
                  {
                    "text": "Which references are standard?",
                    "kind": "provenance"
                  }
                ]
              }
            ]
          },
          {
            "id": "searches",
            "name": "Searches",
            "description": "Computational searches.",
            "findings": [
              {
                "id": "searches-finding",
                "name": "Searches",
                "description": "Searches.",
                "questions": [
                  {
                    "text": "How are Woodall primes searched for in distributed computing projects, and what is the largest known?",
                    "kind": "provenance"
                  },
                  {
                    "text": "Is the information current?",
                    "kind": "boundary"
                  }
                ]
              }
            ]
          }
        ]
      },
      {
        "id": "context",
        "name": "Context",
        "description": "History and generalisations.",
        "rationale": "Context.",
        "layers": [
          {
            "id": "history",
            "name": "History",
            "description": "History.",
            "findings": [
              {
                "id": "history-finding",
                "name": "History",
                "description": "History.",
                "questions": [
                  {
                    "text": "How did Woodall and Cunningham study these numbers in 1917?",
                    "kind": "provenance"
                  },
                  {
                    "text": "Which sources are cited?",
                    "kind": "provenance"
                  }
                ]
              }
            ]
          },
          {
            "id": "generalised",
            "name": "Generalised",
            "description": "Generalisations.",
            "findings": [
              {
                "id": "generalised-finding",
                "name": "Generalised",
                "description": "Generalised.",
                "questions": [
                  {
                    "text": "What are generalised Woodall numbers in other bases?",
                    "kind": "provenance"
                  },
                  {
                    "text": "Which entry fits generalised Woodall number?",
                    "kind": "action"
                  }
                ]
              }
            ]
          }
        ]
      },
      {
        "id": "use",
        "name": "Use",
        "description": "Recreational and educational.",
        "rationale": "Practice.",
        "layers": [
          {
            "id": "recreational",
            "name": "Recreational",
            "description": "Recreational mathematics.",
            "findings": [
              {
                "id": "recreational-finding",
                "name": "Recreational",
                "description": "Recreational.",
                "questions": [
                  {
                    "text": "How do Woodall numbers appear in recreational mathematics and prime hunting?",
                    "kind": "provenance"
                  },
                  {
                    "text": "Which entry fits prime number search?",
                    "kind": "action"
                  }
                ]
              }
            ]
          },
          {
            "id": "education",
            "name": "Education",
            "description": "Teaching.",
            "findings": [
              {
                "id": "education-finding",
                "name": "Education",
                "description": "Education.",
                "questions": [
                  {
                    "text": "How can Woodall numbers be used to teach exponent forms and primality?",
                    "kind": "provenance"
                  },
                  {
                    "text": "Which entry fits mathematics education?",
                    "kind": "action"
                  }
                ]
              }
            ]
          }
        ]
      }
    ]
  },
  "openQuestions": [
    "Are there infinitely many Woodall primes?",
    "How should OEIS and search projects be linked?",
    "How should generalised Woodall numbers be recorded?"
  ],
  "statistics": {
    "bundles": 4,
    "layers": 8,
    "findings": 8,
    "questions": 16
  }
}