{
  "vercy": "1.0-draft",
  "publication": {
    "status": "research-draft",
    "adjudicationStatus": "unreviewed",
    "publishableCanonical": false,
    "generatedAt": "2026-09-12T23:20:25Z",
    "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": "2026-10-06T07:02:03+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-Q40276",
    "registryId": "vr.tr.multiplication",
    "name": "multiplication",
    "version": "0.2.0-wave.3",
    "entryKind": "thing",
    "family": "Thing Registry",
    "domain": [
      "XCT.QLT"
    ],
    "status": "research-draft"
  },
  "canonicalUrl": "https://ver.cy/models/thing/q40276/",
  "model": {
    "registry_id": "vr.tr.multiplication",
    "name": "multiplication",
    "purpose": "Let an agent explain multiplication and its properties across number systems, describe generalisations such as scalar, matrix and Hadamard products, relay algorithms and teaching approaches, and help compute or check products.",
    "definition": "A binary arithmetic operation that combines two numbers to give their product, defined for natural numbers as repeated addition and extended to integers, rationals, reals and complex numbers, and generalised to scalar multiplication of vectors, matrix multiplication, the element-wise Hadamard product and multiplication in rings and groups; multiplication is commutative and associative for numbers, distributes over addition, and is a foundation of arithmetic and algebra.",
    "what_it_is_for": "Combining quantities by scaling.",
    "affordances": [
      "explain the operation and properties",
      "describe generalisations",
      "relay algorithms and teaching",
      "compute or check products"
    ],
    "distinguishing_features": [
      "Commutative and associative for numbers",
      "Distributive over addition",
      "Identity one and inverses for nonzero numbers",
      "Non-commutative generalisations"
    ],
    "appearance": "Not a visible object; expressions with times signs, dots or juxtaposition.",
    "visual_identification": [
      "Binary operation giving a product",
      "Numbers, vectors, matrices and abstract structures",
      "Addition combines by summing; exponentiation is repeated multiplication"
    ],
    "physical_properties": [],
    "families_and_kinds": [
      "multiplication of natural numbers, integers, rationals, reals and complex numbers",
      "scalar multiplication of vectors",
      "matrix multiplication",
      "Hadamard element-wise product",
      "multiplication in rings, fields and groups",
      "doubling as a special case"
    ],
    "related_models": [
      {
        "relation": "is a kind of",
        "target": "binary operation",
        "why": "in registry terms"
      },
      {
        "relation": "is inverse to",
        "target": "division",
        "why": "for nonzero divisors"
      },
      {
        "relation": "generalises to",
        "target": "matrix multiplication",
        "why": "in linear algebra"
      },
      {
        "relation": "distributes over",
        "target": "addition",
        "why": "the distributive law"
      }
    ],
    "identifiers": [
      {
        "scheme": "symbols",
        "value_or_pattern": "times sign, middle dot, asterisk",
        "note": "notation"
      }
    ],
    "standards_and_regulation": [
      "ISO 80000-2 notation for multiplication",
      "Curriculum standards for arithmetic"
    ],
    "failure_modes_and_hazards": [
      "Assuming commutativity in matrix multiplication",
      "Overflow in computer arithmetic",
      "Confusing element-wise and matrix products"
    ],
    "in_scope": [],
    "out_of_scope": [],
    "characteristics": [],
    "agent_conduct": {
      "may": [
        "Compute products and explain multiplication from arithmetic to matrices.",
        "Check results and state the number system or algebra used."
      ],
      "must_not": [
        "Present a result computed with rounding or overflow as exact.",
        "Confuse matrix and element-wise multiplication in calculations.",
        "Give multiplication results for money or doses without showing the inputs."
      ],
      "requires_human": [
        "Relying on a computed product for doses, money or engineering loads."
      ]
    },
    "ethics": {
      "considerations": [
        "Calculation errors in doses or money cause real harm.",
        "Maths education shapes opportunity; teaching must be patient with learners."
      ],
      "affected_parties": [
        "Learners",
        "Users of calculations",
        "Patients and clients"
      ]
    },
    "owners": {
      "steward": "Nobody owns an operation; it is held in common.",
      "master_systems": []
    }
  },
  "sources": [
    {
      "id": "wikidata",
      "title": "Wikidata item Q40276: multiplication",
      "url": "https://www.wikidata.org/wiki/Q40276",
      "url_status": "live",
      "what_it_supports": "identity and sense of the item",
      "checked_by": "wikidata-api"
    },
    {
      "id": "wikipedia-en",
      "title": "Wikipedia: Multiplication",
      "url": "https://en.wikipedia.org/wiki/Multiplication",
      "url_status": "live",
      "what_it_supports": "general description of the item",
      "checked_by": "wikidata-api sitelink"
    }
  ],
  "structure": {
    "bundles": [
      {
        "id": "define",
        "name": "Define",
        "description": "What multiplication is.",
        "rationale": "Definition.",
        "layers": [
          {
            "id": "definition",
            "name": "Definition",
            "description": "Definition and properties.",
            "findings": [
              {
                "id": "definition-finding",
                "name": "Definition",
                "description": "Definition.",
                "questions": [
                  {
                    "text": "What is multiplication, and what properties does it have across number systems?",
                    "kind": "definition"
                  },
                  {
                    "text": "Is the question about number multiplication or a generalisation?",
                    "kind": "boundary"
                  }
                ]
              }
            ]
          },
          {
            "id": "generalisations",
            "name": "Generalisations",
            "description": "Generalisations.",
            "findings": [
              {
                "id": "generalisations-finding",
                "name": "Generalisations",
                "description": "Generalisations.",
                "questions": [
                  {
                    "text": "How do scalar, matrix, Hadamard and abstract multiplications differ?",
                    "kind": "definition"
                  },
                  {
                    "text": "Which entry fits the specific generalisation?",
                    "kind": "action"
                  }
                ]
              }
            ]
          }
        ]
      },
      {
        "id": "compute",
        "name": "Compute",
        "description": "Computation.",
        "rationale": "Computation.",
        "layers": [
          {
            "id": "algorithms",
            "name": "Algorithms",
            "description": "Algorithms.",
            "findings": [
              {
                "id": "algorithms-finding",
                "name": "Algorithms",
                "description": "Algorithms.",
                "questions": [
                  {
                    "text": "How are products computed by hand and by algorithms such as long multiplication and Karatsuba?",
                    "kind": "action"
                  },
                  {
                    "text": "What is the result for the values in question?",
                    "kind": "measurement"
                  }
                ]
              }
            ]
          },
          {
            "id": "computers",
            "name": "Computers",
            "description": "Computer arithmetic.",
            "findings": [
              {
                "id": "computers-finding",
                "name": "Computers",
                "description": "Computers.",
                "questions": [
                  {
                    "text": "How do computers multiply integers and floating-point numbers, and where do errors arise?",
                    "kind": "provenance"
                  },
                  {
                    "text": "Which entry fits computer arithmetic?",
                    "kind": "action"
                  }
                ]
              }
            ]
          }
        ]
      },
      {
        "id": "theory",
        "name": "Theory",
        "description": "Algebraic structure.",
        "rationale": "Theory.",
        "layers": [
          {
            "id": "structure",
            "name": "Structure",
            "description": "Rings and groups.",
            "findings": [
              {
                "id": "structure-finding",
                "name": "Structure",
                "description": "Structure.",
                "questions": [
                  {
                    "text": "How is multiplication axiomatised in rings, fields and groups?",
                    "kind": "provenance"
                  },
                  {
                    "text": "Which references are standard?",
                    "kind": "provenance"
                  }
                ]
              }
            ]
          },
          {
            "id": "matrices",
            "name": "Matrices",
            "description": "Matrix multiplication.",
            "findings": [
              {
                "id": "matrices-finding",
                "name": "Matrices",
                "description": "Matrices.",
                "questions": [
                  {
                    "text": "Why is matrix multiplication non-commutative, and how does it represent composition?",
                    "kind": "provenance"
                  },
                  {
                    "text": "Which entry fits linear algebra?",
                    "kind": "action"
                  }
                ]
              }
            ]
          }
        ]
      },
      {
        "id": "context",
        "name": "Context",
        "description": "History and teaching.",
        "rationale": "Context.",
        "layers": [
          {
            "id": "history",
            "name": "History",
            "description": "History.",
            "findings": [
              {
                "id": "history-finding",
                "name": "History",
                "description": "History.",
                "questions": [
                  {
                    "text": "How did multiplication methods develop, from Egyptian doubling to modern algorithms?",
                    "kind": "provenance"
                  },
                  {
                    "text": "Which entry fits the history of arithmetic?",
                    "kind": "action"
                  }
                ]
              }
            ]
          },
          {
            "id": "teach",
            "name": "Teach",
            "description": "Teaching.",
            "findings": [
              {
                "id": "teach-finding",
                "name": "Teach",
                "description": "Teaching.",
                "questions": [
                  {
                    "text": "How is multiplication taught, and which misconceptions arise?",
                    "kind": "provenance"
                  },
                  {
                    "text": "Which sources are cited?",
                    "kind": "provenance"
                  }
                ]
              }
            ]
          }
        ]
      }
    ]
  },
  "openQuestions": [
    "Should matrix multiplication be a separate primary entry?",
    "How should notation standards be linked?",
    "The registry entry has merged aliases naming generalisations; should they be split off?"
  ],
  "statistics": {
    "bundles": 4,
    "layers": 8,
    "findings": 8,
    "questions": 16
  }
}