{
  "vercy": "1.0-draft",
  "publication": {
    "status": "research-draft",
    "adjudicationStatus": "unreviewed",
    "publishableCanonical": false,
    "generatedAt": "2026-09-11T12:56:33Z",
    "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": 1,
    "engine": "claude",
    "enrichment": {
      "pass": 3,
      "engine": "claude",
      "producedAt": "2026-10-05T18:00:00Z",
      "ingestedAt": "2026-10-05T13:27:07+00:00",
      "fields": [
        "agent_conduct",
        "ethics",
        "owners"
      ]
    },
    "gate": {
      "passed": true,
      "version": "1.0",
      "at": "2026-10-06T19:52:01+00:00",
      "evidence": [
        "completeness 1.00",
        "sense: Wikidata description",
        "2 live sources",
        "review by codex: pass"
      ]
    }
  },
  "metaModel": {
    "id": "THING-Q65943",
    "registryId": "vr.tr.theorem",
    "name": "theorem",
    "version": "0.2.0-wave.1",
    "entryKind": "thing",
    "family": "Thing Registry",
    "domain": [
      "INF.KNW"
    ],
    "status": "research-draft"
  },
  "canonicalUrl": "https://ver.cy/models/thing/q65943/",
  "model": {
    "registry_id": "vr.tr.theorem",
    "name": "theorem",
    "purpose": "Let an agent explain theorems by statement, proof, history and use, distinguish related terms, and point to formal verification resources.",
    "definition": "A mathematical statement proved true by logical deduction from axioms and previously established results, such as the Pythagorean theorem or the fundamental theorem of arithmetic; related terms include lemma, corollary and proposition.",
    "what_it_is_for": "Building mathematical knowledge.",
    "affordances": [
      "state and explain a theorem",
      "outline or check a proof",
      "distinguish lemma, corollary and conjecture",
      "find formalised proofs"
    ],
    "distinguishing_features": [
      "Proved statement",
      "Depends on axioms",
      "Builds on earlier results",
      "Can be formally verified"
    ],
    "appearance": "Not physical; statements and proofs in texts and formal libraries.",
    "visual_identification": [
      "Named results with proofs",
      "Lemmas and corollaries",
      "Conjectures are unproved"
    ],
    "physical_properties": [],
    "families_and_kinds": [
      "major named theorems",
      "lemmas",
      "corollaries",
      "existence and classification theorems",
      "formally verified theorems"
    ],
    "related_models": [
      {
        "relation": "is a kind of",
        "target": "proposition",
        "why": "category"
      },
      {
        "relation": "is established by",
        "target": "mathematical proof",
        "why": "method"
      },
      {
        "relation": "is contrasted with",
        "target": "conjecture",
        "why": "unproved statement"
      },
      {
        "relation": "is related to",
        "target": "axiom",
        "why": "foundation"
      }
    ],
    "identifiers": [],
    "standards_and_regulation": [
      "No specific regulation"
    ],
    "failure_modes_and_hazards": [
      "Misstating hypotheses",
      "Misattributing theorems",
      "Treating conjectures as proved"
    ],
    "in_scope": [],
    "out_of_scope": [],
    "characteristics": [],
    "agent_conduct": {
      "may": [
        "State a theorem with its hypotheses and cite where it is proved.",
        "Check or help write proofs at the request of the person doing the work."
      ],
      "must_not": [
        "Present a conjecture or unproved claim as a theorem.",
        "Drop hypotheses of a theorem so that it appears to apply where it does not.",
        "Attribute a theorem or proof to the wrong person.",
        "Pass off machine-generated proofs as a student's own work in assessed settings."
      ],
      "requires_human": [
        "Accepting a machine-checked proof as the basis for a safety-critical system."
      ]
    },
    "ethics": {
      "considerations": [
        "Credit for results matters to mathematicians' careers and has often been denied to some groups.",
        "Misapplied theorems can make flawed engineering or statistics look rigorous."
      ],
      "affected_parties": [
        "Mathematicians and students",
        "Users of results in science and engineering"
      ]
    },
    "owners": {
      "steward": "Nobody owns a theorem; it belongs to mathematics, and its discoverers are credited.",
      "master_systems": []
    }
  },
  "sources": [
    {
      "id": "wikidata",
      "title": "Wikidata item Q65943: theorem",
      "url": "https://www.wikidata.org/wiki/Q65943",
      "url_status": "live",
      "what_it_supports": "identity and sense of the item",
      "checked_by": "wikidata-api"
    },
    {
      "id": "wikipedia-en",
      "title": "Wikipedia: Theorem",
      "url": "https://en.wikipedia.org/wiki/Theorem",
      "url_status": "live",
      "what_it_supports": "general description of the item",
      "checked_by": "wikidata-api sitelink"
    }
  ],
  "structure": {
    "bundles": [
      {
        "id": "statement",
        "name": "Statement",
        "description": "What it says.",
        "rationale": "Hypotheses matter.",
        "layers": [
          {
            "id": "state",
            "name": "State",
            "description": "Precise statement.",
            "findings": [
              {
                "id": "state-finding",
                "name": "State",
                "description": "Statement.",
                "questions": [
                  {
                    "text": "What exactly does the theorem state, including all hypotheses?",
                    "kind": "definition"
                  },
                  {
                    "text": "What happens if a hypothesis is dropped?",
                    "kind": "boundary"
                  }
                ]
              }
            ]
          },
          {
            "id": "meaning",
            "name": "Meaning",
            "description": "Intuition.",
            "findings": [
              {
                "id": "meaning-finding",
                "name": "Meaning",
                "description": "Intuition.",
                "questions": [
                  {
                    "text": "How can the theorem be explained intuitively?",
                    "kind": "action"
                  },
                  {
                    "text": "Which example illustrates it?",
                    "kind": "action"
                  }
                ]
              }
            ]
          }
        ]
      },
      {
        "id": "proof",
        "name": "Proof",
        "description": "Why it is true.",
        "rationale": "Proofs justify.",
        "layers": [
          {
            "id": "outline",
            "name": "Outline",
            "description": "Proof sketch.",
            "findings": [
              {
                "id": "outline-finding",
                "name": "Outline",
                "description": "Proof outline.",
                "questions": [
                  {
                    "text": "What are the main steps of a standard proof?",
                    "kind": "definition"
                  },
                  {
                    "text": "Which earlier results does it use?",
                    "kind": "provenance"
                  }
                ]
              }
            ]
          },
          {
            "id": "check",
            "name": "Check",
            "description": "Verifying.",
            "findings": [
              {
                "id": "check-finding",
                "name": "Check",
                "description": "Checking proofs.",
                "questions": [
                  {
                    "text": "Is this proposed proof correct, and where might it fail?",
                    "kind": "boundary"
                  },
                  {
                    "text": "Is there a formalised proof in a proof assistant?",
                    "kind": "provenance"
                  }
                ]
              }
            ]
          }
        ]
      },
      {
        "id": "terms",
        "name": "Terms",
        "description": "Related terms.",
        "rationale": "Terminology differs.",
        "layers": [
          {
            "id": "lemma",
            "name": "Lemma",
            "description": "Lemmas and corollaries.",
            "findings": [
              {
                "id": "lemma-finding",
                "name": "Lemma",
                "description": "Lemmas and corollaries.",
                "questions": [
                  {
                    "text": "Is this result a lemma, corollary or main theorem?",
                    "kind": "definition"
                  },
                  {
                    "text": "Why is it labelled that way?",
                    "kind": "definition"
                  }
                ]
              }
            ]
          },
          {
            "id": "conjecture",
            "name": "Conjecture",
            "description": "Unproved statements.",
            "findings": [
              {
                "id": "conjecture-finding",
                "name": "Conjecture",
                "description": "Conjectures.",
                "questions": [
                  {
                    "text": "Has this statement actually been proved, or is it still a conjecture?",
                    "kind": "provenance"
                  },
                  {
                    "text": "Which source confirms its status?",
                    "kind": "provenance"
                  }
                ]
              }
            ]
          }
        ]
      },
      {
        "id": "history",
        "name": "History",
        "description": "Origins.",
        "rationale": "Attribution matters.",
        "layers": [
          {
            "id": "who",
            "name": "Who",
            "description": "Discoverers.",
            "findings": [
              {
                "id": "who-finding",
                "name": "Who",
                "description": "Attribution.",
                "questions": [
                  {
                    "text": "Who first proved the theorem, according to historians of mathematics?",
                    "kind": "provenance"
                  },
                  {
                    "text": "Is the naming historically accurate?",
                    "kind": "boundary"
                  }
                ]
              }
            ]
          },
          {
            "id": "uses",
            "name": "Uses",
            "description": "Applications.",
            "findings": [
              {
                "id": "uses-finding",
                "name": "Uses",
                "description": "Applications.",
                "questions": [
                  {
                    "text": "Where is the theorem used in mathematics or applications?",
                    "kind": "provenance"
                  },
                  {
                    "text": "Which fields depend on it?",
                    "kind": "provenance"
                  }
                ]
              }
            ]
          }
        ]
      }
    ]
  },
  "openQuestions": [
    "Should each theorem be a separate entry?",
    "How should formal libraries be linked?",
    "How should naming disputes be recorded?"
  ],
  "statistics": {
    "bundles": 4,
    "layers": 8,
    "findings": 8,
    "questions": 16
  }
}