{
  "vercy": "1.0-draft",
  "publication": {
    "status": "research-draft",
    "adjudicationStatus": "unreviewed",
    "publishableCanonical": false,
    "generatedAt": "2026-09-11T06:19:07Z",
    "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": "2026-10-05T13:23:50+00:00",
      "fields": [
        "agent_conduct",
        "ethics",
        "owners"
      ]
    },
    "gate": {
      "passed": true,
      "version": "1.0",
      "at": "2026-10-06T19:51:53+00:00",
      "evidence": [
        "completeness 1.00",
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        "2 live sources",
        "review by codex: pass"
      ]
    }
  },
  "metaModel": {
    "id": "THING-Q11348",
    "registryId": "vr.tr.function",
    "name": "function",
    "version": "0.2.0-wave.1",
    "entryKind": "thing",
    "family": "Thing Registry",
    "domain": [
      "XCT.QLT"
    ],
    "status": "research-draft"
  },
  "canonicalUrl": "https://ver.cy/models/thing/q11348/",
  "model": {
    "registry_id": "vr.tr.function",
    "name": "function",
    "purpose": "Let an agent handle functions by domain, codomain, rule and properties, and distinguish mathematical functions from programming functions and biological functions.",
    "definition": "In mathematics, a relation that assigns to each element of a set (the domain) exactly one element of another set (the codomain).",
    "what_it_is_for": "Describing dependence between quantities in mathematics, science and computing.",
    "affordances": [
      "define it by a rule, table or graph",
      "evaluate it at points",
      "study its properties such as continuity",
      "compose and invert it where possible"
    ],
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      "Each input has exactly one output",
      "Defined with domain and codomain",
      "Partial functions leave some inputs undefined",
      "Properties include injective, surjective, bijective"
    ],
    "appearance": "Formulas such as f(x) = x squared, graphs and tables.",
    "visual_identification": [
      "Notation f: A -> B",
      "Graphs passing the vertical line test",
      "Programming functions are a related but different sense"
    ],
    "physical_properties": [],
    "families_and_kinds": [
      "polynomial, rational, exponential and trigonometric functions",
      "injective, surjective and bijective functions",
      "partial functions",
      "multivariable functions"
    ],
    "related_models": [
      {
        "relation": "is a kind of",
        "target": "binary relation",
        "why": "mathematics"
      },
      {
        "relation": "is studied by",
        "target": "mathematics",
        "why": "analysis"
      },
      {
        "relation": "is confused with",
        "target": "function in programming or biology",
        "why": "other senses"
      },
      {
        "relation": "is represented by",
        "target": "curve",
        "why": "graph"
      }
    ],
    "identifiers": [
      {
        "scheme": "DLMF chapter",
        "value_or_pattern": "NIST DLMF identifiers",
        "note": "special functions"
      }
    ],
    "standards_and_regulation": [
      "ISO 80000-2 notation"
    ],
    "failure_modes_and_hazards": [
      "Evaluating outside the domain",
      "Confusing a function with its formula",
      "Assuming invertibility"
    ],
    "in_scope": [],
    "out_of_scope": [],
    "characteristics": [],
    "agent_conduct": {
      "may": [
        "Define, compute and analyse functions.",
        "Explain function concepts to learners."
      ],
      "must_not": [
        "Misstate a function's domain or properties in a proof or calculation.",
        "Present an unverified proof as correct.",
        "Claim credit for others' mathematical work."
      ],
      "requires_human": [
        "Using mathematical results in safety-critical systems."
      ]
    },
    "ethics": {
      "considerations": [
        "Mathematical errors can propagate into critical systems.",
        "Credit for results matters to mathematicians."
      ],
      "affected_parties": [
        "Students",
        "Users of mathematical results"
      ]
    },
    "owners": {
      "steward": "Nobody owns a mathematical concept; it is held in common.",
      "master_systems": []
    }
  },
  "sources": [
    {
      "id": "wikidata",
      "title": "Wikidata item Q11348: function",
      "url": "https://www.wikidata.org/wiki/Q11348",
      "url_status": "live",
      "what_it_supports": "identity and sense of the item",
      "checked_by": "wikidata-api"
    },
    {
      "id": "wikipedia-en",
      "title": "Wikipedia: Function (mathematics)",
      "url": "https://en.wikipedia.org/wiki/Function_%28mathematics%29",
      "url_status": "live",
      "what_it_supports": "general description of the item",
      "checked_by": "wikidata-api sitelink"
    }
  ],
  "structure": {
    "bundles": [
      {
        "id": "definition",
        "name": "Definition",
        "description": "Domain and rule.",
        "rationale": "Domain and rule define a function.",
        "layers": [
          {
            "id": "domain",
            "name": "Domain and codomain",
            "description": "Sets.",
            "findings": [
              {
                "id": "domain-finding",
                "name": "Domain",
                "description": "Domain and codomain.",
                "questions": [
                  {
                    "text": "What are the domain and codomain?",
                    "kind": "definition"
                  },
                  {
                    "text": "Is it defined for all inputs?",
                    "kind": "boundary"
                  }
                ]
              }
            ]
          },
          {
            "id": "rule",
            "name": "Rule",
            "description": "How outputs are computed.",
            "findings": [
              {
                "id": "rule-finding",
                "name": "Rule",
                "description": "Defining rule.",
                "questions": [
                  {
                    "text": "What rule defines it?",
                    "kind": "definition"
                  },
                  {
                    "text": "Is it given by formula, table or algorithm?",
                    "kind": "definition"
                  }
                ]
              }
            ]
          }
        ]
      },
      {
        "id": "properties",
        "name": "Properties",
        "description": "Behaviour.",
        "rationale": "Properties decide what can be done.",
        "layers": [
          {
            "id": "mapping",
            "name": "Mapping properties",
            "description": "Injective, surjective.",
            "findings": [
              {
                "id": "mapping-finding",
                "name": "Mapping",
                "description": "Mapping properties.",
                "questions": [
                  {
                    "text": "Is it injective, surjective or bijective?",
                    "kind": "measurement"
                  },
                  {
                    "text": "Does it have an inverse?",
                    "kind": "boundary"
                  }
                ]
              }
            ]
          },
          {
            "id": "analysis",
            "name": "Analytic properties",
            "description": "Continuity, differentiability.",
            "findings": [
              {
                "id": "analysis-finding",
                "name": "Analysis",
                "description": "Analytic properties.",
                "questions": [
                  {
                    "text": "Is it continuous and differentiable?",
                    "kind": "measurement"
                  },
                  {
                    "text": "Where not?",
                    "kind": "boundary"
                  }
                ]
              }
            ]
          }
        ]
      },
      {
        "id": "representation",
        "name": "Representation",
        "description": "Graphs and code.",
        "rationale": "Representations help use.",
        "layers": [
          {
            "id": "graph",
            "name": "Graph",
            "description": "Plot.",
            "findings": [
              {
                "id": "graph-finding",
                "name": "Graph",
                "description": "Graph.",
                "questions": [
                  {
                    "text": "What does its graph look like?",
                    "kind": "definition"
                  },
                  {
                    "text": "What are its key features?",
                    "kind": "measurement"
                  }
                ]
              }
            ]
          },
          {
            "id": "computation",
            "name": "Computation",
            "description": "Evaluation.",
            "findings": [
              {
                "id": "computation-finding",
                "name": "Computation",
                "description": "Numerical evaluation.",
                "questions": [
                  {
                    "text": "How can it be evaluated accurately?",
                    "kind": "action"
                  },
                  {
                    "text": "Where is it numerically unstable?",
                    "kind": "boundary"
                  }
                ]
              }
            ]
          }
        ]
      },
      {
        "id": "use",
        "name": "Use",
        "description": "Modelling.",
        "rationale": "Functions model relationships.",
        "layers": [
          {
            "id": "model",
            "name": "Model",
            "description": "Applications.",
            "findings": [
              {
                "id": "model-finding",
                "name": "Model",
                "description": "Modelling use.",
                "questions": [
                  {
                    "text": "What relationship does it model?",
                    "kind": "definition"
                  },
                  {
                    "text": "How well does it fit data?",
                    "kind": "measurement"
                  }
                ]
              }
            ]
          },
          {
            "id": "senses",
            "name": "Other senses",
            "description": "Programming and biology.",
            "findings": [
              {
                "id": "senses-finding",
                "name": "Senses",
                "description": "Disambiguation.",
                "questions": [
                  {
                    "text": "Is the mathematical sense meant?",
                    "kind": "boundary"
                  },
                  {
                    "text": "Which other entry fits better?",
                    "kind": "action"
                  }
                ]
              }
            ]
          }
        ]
      }
    ]
  },
  "openQuestions": [
    "Should classes of functions be separate entries?",
    "How should programming functions be linked?",
    "How should special functions be catalogued?"
  ],
  "statistics": {
    "bundles": 4,
    "layers": 8,
    "findings": 8,
    "questions": 16
  }
}
