{
  "vercy": "1.0-draft",
  "publication": {
    "status": "research-draft",
    "adjudicationStatus": "unreviewed",
    "publishableCanonical": false,
    "generatedAt": "2026-09-13T23:07:57Z",
    "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": 4,
    "engine": "claude",
    "enrichment": {
      "pass": 3,
      "engine": "claude",
      "producedAt": "2026-10-06T12:00:00Z",
      "ingestedAt": "2026-10-06T07:41:10+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-Q40754",
    "registryId": "vr.tr.subtraction",
    "name": "subtraction",
    "version": "0.2.0-wave.4",
    "entryKind": "thing",
    "family": "Thing Registry",
    "domain": [
      "XCT.QLT"
    ],
    "status": "research-draft"
  },
  "canonicalUrl": "https://ver.cy/models/thing/q40754/",
  "model": {
    "registry_id": "vr.tr.subtraction",
    "name": "subtraction",
    "purpose": "Let an agent explain subtraction, relay properties, algorithms, teaching methods and extensions from mathematics and education sources, describe vector subtraction, and distinguish subtraction from negation, set difference, division and absolute difference.",
    "definition": "The arithmetic operation of taking one quantity away from another, written a minus b, giving the difference, with a the minuend and b the subtrahend, the inverse of addition, not commutative or associative, extended from natural numbers to integers, rationals, real and complex numbers and to vector subtraction, which subtracts corresponding components or adds the negative vector; methods include borrowing or regrouping, complements used in computers, where two s complement makes subtraction a form of addition, and mental strategies such as counting up.",
    "what_it_is_for": "Finding differences and removing quantities.",
    "affordances": [
      "explain properties and terms",
      "relay algorithms and teaching methods",
      "describe vector subtraction",
      "distinguish related operations"
    ],
    "distinguishing_features": [
      "Inverse of addition",
      "Not commutative",
      "Can yield negatives",
      "Extends to vectors"
    ],
    "appearance": "Not a physical object; written with the minus sign.",
    "visual_identification": [
      "Arithmetic operation of taking away",
      "Vector subtraction, difference, minus",
      "Negation reverses sign; set difference removes elements; division splits into parts; absolute difference ignores order"
    ],
    "physical_properties": [
      {
        "quantity": "terms",
        "typical_range": "minuend, subtrahend, difference",
        "unit": "list",
        "note": ""
      },
      {
        "quantity": "minus sign in print",
        "typical_range": "1489",
        "unit": "year",
        "note": "Widmann, as commonly cited"
      },
      {
        "quantity": "two s complement",
        "typical_range": "standard in computers",
        "unit": "note",
        "note": ""
      }
    ],
    "families_and_kinds": [
      "whole number subtraction",
      "integer and real subtraction",
      "vector and matrix subtraction",
      "modular subtraction",
      "binary subtraction"
    ],
    "related_models": [
      {
        "relation": "is a kind of",
        "target": "binary operation",
        "why": "in registry terms"
      },
      {
        "relation": "is the inverse of",
        "target": "addition",
        "why": ""
      },
      {
        "relation": "includes",
        "target": "vector subtraction",
        "why": ""
      },
      {
        "relation": "is contrasted with",
        "target": "set difference",
        "why": ""
      }
    ],
    "identifiers": [],
    "standards_and_regulation": [
      "ISO 80000-2 notation",
      "National mathematics curricula"
    ],
    "failure_modes_and_hazards": [
      "Assuming commutativity",
      "Sign errors with negatives",
      "Floating-point cancellation errors"
    ],
    "in_scope": [],
    "out_of_scope": [],
    "characteristics": [],
    "agent_conduct": {
      "may": [
        "Perform and explain subtraction, including with negative numbers.",
        "Check results and point out sign errors and cancellation errors in calculations."
      ],
      "must_not": [
        "Treat subtraction as commutative or associative.",
        "Hide precision lost by subtracting nearly equal floating-point numbers in critical results.",
        "Present a difference as exact when its inputs were rounded or uncertain."
      ],
      "requires_human": [
        "Correcting subtraction errors in financial or dosing records that others rely on."
      ]
    },
    "ethics": {
      "considerations": [
        "Small arithmetic errors in money or medicine can harm people downstream.",
        "Teaching arithmetic patiently matters to people who struggle with it."
      ],
      "affected_parties": [
        "Learners",
        "People relying on calculations"
      ]
    },
    "owners": {
      "steward": "Nobody owns it; it is part of mathematics held in common.",
      "master_systems": []
    }
  },
  "sources": [
    {
      "id": "wikidata",
      "title": "Wikidata item Q40754: subtraction",
      "url": "https://www.wikidata.org/wiki/Q40754",
      "url_status": "live",
      "what_it_supports": "identity and sense of the item",
      "checked_by": "wikidata-api"
    },
    {
      "id": "wikipedia-en",
      "title": "Wikipedia: Subtraction",
      "url": "https://en.wikipedia.org/wiki/Subtraction",
      "url_status": "live",
      "what_it_supports": "general description of the item",
      "checked_by": "wikidata-api sitelink"
    }
  ],
  "structure": {
    "bundles": [
      {
        "id": "understand",
        "name": "Understand",
        "description": "What subtraction is.",
        "rationale": "Definition.",
        "layers": [
          {
            "id": "definition",
            "name": "Definition",
            "description": "Definition.",
            "findings": [
              {
                "id": "definition-finding",
                "name": "Definition",
                "description": "Definition.",
                "questions": [
                  {
                    "text": "What is subtraction, and how does it differ from negation, set difference, division and absolute difference?",
                    "kind": "definition"
                  },
                  {
                    "text": "Is the question about arithmetic, teaching, vectors or computing?",
                    "kind": "boundary"
                  }
                ]
              }
            ]
          },
          {
            "id": "vectors",
            "name": "Vectors",
            "description": "Vector subtraction.",
            "findings": [
              {
                "id": "vectors-finding",
                "name": "Vectors",
                "description": "Vectors.",
                "questions": [
                  {
                    "text": "How is vector subtraction done geometrically and by components?",
                    "kind": "definition"
                  },
                  {
                    "text": "Which entry fits Euclidean vector?",
                    "kind": "action"
                  }
                ]
              }
            ]
          }
        ]
      },
      {
        "id": "methods",
        "name": "Methods",
        "description": "Methods.",
        "rationale": "Sources.",
        "layers": [
          {
            "id": "algorithms",
            "name": "Algorithms",
            "description": "Written algorithms.",
            "findings": [
              {
                "id": "algorithms-finding",
                "name": "Algorithms",
                "description": "Algorithms.",
                "questions": [
                  {
                    "text": "How do borrowing and equal additions methods work?",
                    "kind": "provenance"
                  },
                  {
                    "text": "Which references are standard?",
                    "kind": "provenance"
                  }
                ]
              }
            ]
          },
          {
            "id": "teaching",
            "name": "Teaching",
            "description": "Teaching strategies.",
            "findings": [
              {
                "id": "teaching-finding",
                "name": "Teaching",
                "description": "Teaching.",
                "questions": [
                  {
                    "text": "How do teachers use counting up and number lines for subtraction?",
                    "kind": "provenance"
                  },
                  {
                    "text": "Which sources are cited?",
                    "kind": "provenance"
                  }
                ]
              }
            ]
          }
        ]
      },
      {
        "id": "computing",
        "name": "Computing",
        "description": "Computing.",
        "rationale": "Science.",
        "layers": [
          {
            "id": "complement",
            "name": "Complements",
            "description": "Two s complement.",
            "findings": [
              {
                "id": "complement-finding",
                "name": "Complements",
                "description": "Complements.",
                "questions": [
                  {
                    "text": "How does two s complement turn subtraction into addition?",
                    "kind": "provenance"
                  },
                  {
                    "text": "Which entry fits two s complement?",
                    "kind": "action"
                  }
                ]
              }
            ]
          },
          {
            "id": "float",
            "name": "Floating point",
            "description": "Cancellation.",
            "findings": [
              {
                "id": "float-finding",
                "name": "Floating point",
                "description": "Floating point.",
                "questions": [
                  {
                    "text": "What is catastrophic cancellation in floating-point subtraction?",
                    "kind": "provenance"
                  },
                  {
                    "text": "Which entry fits floating-point arithmetic?",
                    "kind": "action"
                  }
                ]
              }
            ]
          }
        ]
      },
      {
        "id": "context",
        "name": "Context",
        "description": "History.",
        "rationale": "Context.",
        "layers": [
          {
            "id": "negatives",
            "name": "Negative numbers",
            "description": "Negative numbers.",
            "findings": [
              {
                "id": "negatives-finding",
                "name": "Negative numbers",
                "description": "Negative numbers.",
                "questions": [
                  {
                    "text": "How did subtraction lead to acceptance of negative numbers?",
                    "kind": "provenance"
                  },
                  {
                    "text": "Which entry fits negative number?",
                    "kind": "action"
                  }
                ]
              }
            ]
          },
          {
            "id": "sign",
            "name": "Minus sign",
            "description": "Minus sign history.",
            "findings": [
              {
                "id": "sign-finding",
                "name": "Minus sign",
                "description": "Minus sign.",
                "questions": [
                  {
                    "text": "When did the minus sign appear in print?",
                    "kind": "provenance"
                  },
                  {
                    "text": "Which entry fits plus and minus signs?",
                    "kind": "action"
                  }
                ]
              }
            ]
          }
        ]
      }
    ]
  },
  "openQuestions": [
    "Should vector subtraction be a separate entry?",
    "How should mathematics education sources be linked?",
    "Should binary subtraction be linked?"
  ],
  "statistics": {
    "bundles": 4,
    "layers": 8,
    "findings": 8,
    "questions": 16
  }
}