{
  "vercy": "1.0-draft",
  "publication": {
    "status": "research-draft",
    "adjudicationStatus": "unreviewed",
    "publishableCanonical": false,
    "generatedAt": "2026-09-11T05:15:23Z",
    "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": "2026-10-05T16:30:00Z",
      "ingestedAt": "2026-10-05T13:23:25+00:00",
      "fields": [
        "agent_conduct",
        "ethics",
        "owners"
      ]
    },
    "gate": {
      "passed": true,
      "version": "1.0",
      "at": "2026-10-06T19:51:59+00:00",
      "evidence": [
        "completeness 1.00",
        "sense: Wikidata description",
        "2 live sources",
        "review by codex: pass"
      ]
    }
  },
  "metaModel": {
    "id": "THING-Q395",
    "registryId": "vr.tr.mathematics",
    "name": "mathematics",
    "version": "0.2.0-wave.1",
    "entryKind": "thing",
    "family": "Thing Registry",
    "domain": [
      "INF.KNW"
    ],
    "status": "research-draft"
  },
  "canonicalUrl": "https://ver.cy/models/thing/q395/",
  "model": {
    "registry_id": "vr.tr.mathematics",
    "name": "mathematics",
    "purpose": "Let an agent treat mathematics as a discipline with fields, proofs and conventions, and state mathematical claims with their assumptions.",
    "definition": "The formal science of quantity, structure, space and change, which proves results from axioms by logical deduction and is used throughout science and engineering.",
    "what_it_is_for": "Reasoning precisely, modelling the world and computing.",
    "affordances": [
      "prove theorems",
      "model and compute",
      "teach and learn it",
      "verify proofs, including by computer"
    ],
    "distinguishing_features": [
      "Truth by proof from axioms",
      "Pure and applied branches",
      "Conventions and notation vary",
      "Results are cumulative and rarely overturned, unlike empirical science"
    ],
    "appearance": "Symbols, equations, proofs, diagrams and code.",
    "visual_identification": [
      "Notation and proofs",
      "Field labels in the Mathematics Subject Classification",
      "Applied fields such as mathematical programming"
    ],
    "physical_properties": [],
    "families_and_kinds": [
      "algebra",
      "analysis",
      "geometry and topology",
      "number theory",
      "probability and statistics",
      "discrete mathematics",
      "applied mathematics and optimisation"
    ],
    "related_models": [
      {
        "relation": "has part",
        "target": "integer, sequence, series",
        "why": "objects of study"
      },
      {
        "relation": "is used in",
        "target": "science and engineering",
        "why": "applications"
      },
      {
        "relation": "is a kind of",
        "target": "formal science",
        "why": "discipline"
      },
      {
        "relation": "is confused with",
        "target": "arithmetic",
        "why": "a small part"
      }
    ],
    "identifiers": [
      {
        "scheme": "MSC 2020 code",
        "value_or_pattern": "two digits, letter, two digits",
        "note": "Mathematics Subject Classification"
      }
    ],
    "standards_and_regulation": [
      "ISO 80000-2 mathematical signs and symbols"
    ],
    "failure_modes_and_hazards": [
      "Unstated assumptions",
      "Errors in unverified proofs",
      "Misapplied models"
    ],
    "in_scope": [],
    "out_of_scope": [],
    "characteristics": [],
    "agent_conduct": {
      "may": [
        "Prove results or cite proofs, stating assumptions.",
        "Check calculations and flag unverified steps."
      ],
      "must_not": [
        "Present an unverified proof as established.",
        "Hide assumptions behind results.",
        "Apply a model outside its valid range without saying so."
      ],
      "requires_human": [
        "Relying on a mathematical model in decisions about people's safety or rights."
      ]
    },
    "ethics": {
      "considerations": [
        "Mathematical models used in decisions can encode bias behind a show of objectivity."
      ],
      "affected_parties": [
        "Users of models",
        "Students"
      ]
    },
    "owners": {
      "steward": "Nobody owns mathematics; it is held in common.",
      "master_systems": []
    }
  },
  "sources": [
    {
      "id": "wikidata",
      "title": "Wikidata item Q395: mathematics",
      "url": "https://www.wikidata.org/wiki/Q395",
      "url_status": "live",
      "what_it_supports": "identity and sense of the item",
      "checked_by": "wikidata-api"
    },
    {
      "id": "wikipedia-en",
      "title": "Wikipedia: Mathematics",
      "url": "https://en.wikipedia.org/wiki/Mathematics",
      "url_status": "live",
      "what_it_supports": "general description of the item",
      "checked_by": "wikidata-api sitelink"
    }
  ],
  "structure": {
    "bundles": [
      {
        "id": "fields",
        "name": "Fields",
        "description": "Branches.",
        "rationale": "The field locates a result.",
        "layers": [
          {
            "id": "branch",
            "name": "Branch",
            "description": "MSC classification.",
            "findings": [
              {
                "id": "branch-finding",
                "name": "Branch",
                "description": "The branch.",
                "questions": [
                  {
                    "text": "Which branch of mathematics is this?",
                    "kind": "definition"
                  },
                  {
                    "text": "Which MSC code applies?",
                    "kind": "provenance"
                  }
                ]
              }
            ]
          },
          {
            "id": "objects",
            "name": "Objects",
            "description": "What is studied.",
            "findings": [
              {
                "id": "objects-finding",
                "name": "Objects",
                "description": "Mathematical objects.",
                "questions": [
                  {
                    "text": "Which objects does it concern?",
                    "kind": "definition"
                  },
                  {
                    "text": "How are they defined?",
                    "kind": "definition"
                  }
                ]
              }
            ]
          }
        ]
      },
      {
        "id": "claims",
        "name": "Claims",
        "description": "Theorems and conjectures.",
        "rationale": "Status of a claim is crucial.",
        "layers": [
          {
            "id": "status",
            "name": "Status",
            "description": "Proven or conjectured.",
            "findings": [
              {
                "id": "status-finding",
                "name": "Status",
                "description": "Proof status.",
                "questions": [
                  {
                    "text": "Is this result proven, and where?",
                    "kind": "provenance"
                  },
                  {
                    "text": "Is it a conjecture?",
                    "kind": "boundary"
                  }
                ]
              }
            ]
          },
          {
            "id": "assumptions",
            "name": "Assumptions",
            "description": "Axioms and hypotheses.",
            "findings": [
              {
                "id": "assumptions-finding",
                "name": "Assumptions",
                "description": "Assumptions required.",
                "questions": [
                  {
                    "text": "Which assumptions does the result need?",
                    "kind": "definition"
                  },
                  {
                    "text": "What fails without them?",
                    "kind": "boundary"
                  }
                ]
              }
            ]
          }
        ]
      },
      {
        "id": "applications",
        "name": "Applications",
        "description": "Using mathematics.",
        "rationale": "Models are only as good as their fit.",
        "layers": [
          {
            "id": "models",
            "name": "Models",
            "description": "Mathematical models.",
            "findings": [
              {
                "id": "models-finding",
                "name": "Model",
                "description": "The model used.",
                "questions": [
                  {
                    "text": "Which mathematical model is used, and why?",
                    "kind": "definition"
                  },
                  {
                    "text": "How well does it fit the data?",
                    "kind": "measurement"
                  }
                ]
              }
            ]
          },
          {
            "id": "computation",
            "name": "Computation",
            "description": "Numerics.",
            "findings": [
              {
                "id": "computation-finding",
                "name": "Computation",
                "description": "Numerical methods.",
                "questions": [
                  {
                    "text": "Which numerical methods are used?",
                    "kind": "definition"
                  },
                  {
                    "text": "What are their error bounds?",
                    "kind": "measurement"
                  }
                ]
              }
            ]
          }
        ]
      },
      {
        "id": "learning",
        "name": "Learning",
        "description": "Teaching mathematics.",
        "rationale": "Learning mathematics needs clear explanation.",
        "layers": [
          {
            "id": "explanation",
            "name": "Explanation",
            "description": "Clear reasoning.",
            "findings": [
              {
                "id": "explanation-finding",
                "name": "Explanation",
                "description": "How to explain.",
                "questions": [
                  {
                    "text": "How can this be explained step by step?",
                    "kind": "action"
                  },
                  {
                    "text": "What misconceptions are common?",
                    "kind": "boundary"
                  }
                ]
              }
            ]
          },
          {
            "id": "verification",
            "name": "Verification",
            "description": "Checking work.",
            "findings": [
              {
                "id": "verification-finding",
                "name": "Verification",
                "description": "How to check.",
                "questions": [
                  {
                    "text": "How can the result be checked?",
                    "kind": "action"
                  },
                  {
                    "text": "Should a proof assistant be used?",
                    "kind": "definition"
                  }
                ]
              }
            ]
          }
        ]
      }
    ]
  },
  "openQuestions": [
    "Should fields be separate entries by MSC?",
    "How should agents distinguish proven results from conjectures?",
    "The registry entry has merged aliases such as ecosystemology; should they be split off?"
  ],
  "statistics": {
    "bundles": 4,
    "layers": 8,
    "findings": 8,
    "questions": 16
  }
}