{
  "vercy": "1.0-draft",
  "publication": {
    "status": "research-draft",
    "adjudicationStatus": "unreviewed",
    "publishableCanonical": false,
    "generatedAt": "2026-09-13T19:07:11Z",
    "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": "2026-10-06T11:00:00Z",
      "ingestedAt": "2026-10-06T07:39:38+00:00",
      "fields": [
        "agent_conduct",
        "ethics",
        "owners"
      ]
    },
    "revisions": [
      {
        "at": "2026-10-06T22:33:31+00:00",
        "engine": "codex",
        "fields": [
          "agent_conduct",
          "failure_modes_and_hazards",
          "purpose"
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        "answering_review": "83648fc4164c572dc3dde96c1248b60c6a769533ce7a41225ab3987decfb5e70"
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    "gate": {
      "passed": true,
      "version": "1.0",
      "at": "2026-10-07T10:10:26+00:00",
      "evidence": [
        "completeness 1.00",
        "sense: Wikidata description",
        "2 live sources",
        "review by codex: pass"
      ]
    }
  },
  "metaModel": {
    "id": "THING-Q1364910",
    "registryId": "vr.tr.intersection-geometry",
    "name": "intersection (geometry)",
    "version": "0.2.0-wave.4",
    "entryKind": "thing",
    "family": "Thing Registry",
    "domain": [
      "XCT.QLT"
    ],
    "status": "research-draft"
  },
  "canonicalUrl": "https://ver.cy/models/thing/q1364910/",
  "model": {
    "registry_id": "vr.tr.intersection-geometry",
    "name": "intersection (geometry)",
    "purpose": "Let an agent explain geometric intersections, relay methods and formulas from geometry and computational geometry sources, describe the cases the registry aliases name, distinguish geometric intersection from set intersection generally and from the metacentre as a naval concept, and explain tangency as an intersection at a shared point of contact.",
    "definition": "In geometry, the set of points common to two or more figures, such as the point where two lines meet, the line where two planes meet, the intersection curve of two surfaces, line-plane, line-sphere and line segment intersections and the intersection of a polyhedron with a line; the registry aliases also include the metacentre, a point in naval architecture defined by intersecting lines of buoyancy, which is a specific application.",
    "what_it_is_for": "Not applicable; a geometric concept.",
    "affordances": [
      "explain the concept",
      "relay methods",
      "describe named cases",
      "distinguish related concepts"
    ],
    "distinguishing_features": [
      "Common points",
      "Dimension-dependent results",
      "Computational algorithms",
      "Applications in graphics"
    ],
    "appearance": "Not a visible object; points or curves where figures meet.",
    "visual_identification": [
      "Common points of geometric figures",
      "Intersection curve, line-plane, line-sphere, line segment and polyhedron-line intersections; metacentre",
      "Set intersection is general; tangency is touching without crossing; the metacentre is a ship stability point"
    ],
    "physical_properties": [
      {
        "quantity": "two lines in a plane",
        "typical_range": "one point, none or infinitely many",
        "unit": "note",
        "note": ""
      },
      {
        "quantity": "line-sphere",
        "typical_range": "solve a quadratic",
        "unit": "note",
        "note": ""
      },
      {
        "quantity": "Bentley-Ottmann algorithm",
        "typical_range": "1979",
        "unit": "year",
        "note": "segment intersections"
      }
    ],
    "families_and_kinds": [
      "line-line and line-plane intersections",
      "line-sphere and ray-surface intersections",
      "intersection curves of surfaces",
      "segment intersection problems",
      "polyhedron-line intersections",
      "applied cases such as the metacentre"
    ],
    "related_models": [
      {
        "relation": "is a kind of",
        "target": "intersection",
        "why": "in registry terms"
      },
      {
        "relation": "is a kind of",
        "target": "locus",
        "why": "in registry terms"
      },
      {
        "relation": "is used in",
        "target": "ray tracing",
        "why": ""
      },
      {
        "relation": "is related to",
        "target": "metacentric height",
        "why": "in naval architecture"
      }
    ],
    "identifiers": [],
    "standards_and_regulation": [
      "No regulation"
    ],
    "failure_modes_and_hazards": [
      "Numerical instability can affect computed intersections.",
      "Treating tangency as separate from intersection can omit shared points.",
      "The registry alias metacentre names a distinct applied concept."
    ],
    "in_scope": [],
    "out_of_scope": [],
    "characteristics": [],
    "agent_conduct": {
      "may": [
        "Compute intersections of lines, planes, surfaces and solids with stated tolerances.",
        "Identify tangential intersections and distinguish them from crossings in results."
      ],
      "must_not": [
        "Report numerically unstable intersections as exact.",
        "Exclude a shared point from an intersection merely because it is a point of tangency.",
        "File the metacentre in the registry aliases as a general geometric intersection.",
        "Use unchecked intersection results in safety-critical design."
      ],
      "requires_human": [
        "Human review is required when using computed intersections in structural or ship stability design."
      ]
    },
    "ethics": {
      "considerations": [
        "Errors in geometry can propagate into unsafe designs.",
        "Ship stability depends on the metacentre, which is safety-critical."
      ],
      "affected_parties": [
        "Engineers and designers",
        "Students",
        "Users of designed objects"
      ]
    },
    "owners": {
      "steward": "Nobody owns the concept; it belongs to mathematics.",
      "master_systems": []
    }
  },
  "sources": [
    {
      "id": "wikidata",
      "title": "Wikidata item Q1364910: intersection (geometry)",
      "url": "https://www.wikidata.org/wiki/Q1364910",
      "url_status": "live",
      "what_it_supports": "identity and sense of the item",
      "checked_by": "wikidata-api"
    },
    {
      "id": "wikipedia-en",
      "title": "Wikipedia: Intersection (geometry)",
      "url": "https://en.wikipedia.org/wiki/Intersection_%28geometry%29",
      "url_status": "live",
      "what_it_supports": "general description of the item",
      "checked_by": "wikidata-api sitelink"
    }
  ],
  "structure": {
    "bundles": [
      {
        "id": "understand",
        "name": "Understand",
        "description": "What a geometric intersection is.",
        "rationale": "Science.",
        "layers": [
          {
            "id": "definition",
            "name": "Definition",
            "description": "Definition.",
            "findings": [
              {
                "id": "definition-finding",
                "name": "Definition",
                "description": "Definition.",
                "questions": [
                  {
                    "text": "What is an intersection in geometry, and how does it differ from set intersection, tangency and the metacentre?",
                    "kind": "definition"
                  },
                  {
                    "text": "Is the question about theory, a formula, computation or naval architecture?",
                    "kind": "boundary"
                  }
                ]
              }
            ]
          },
          {
            "id": "cases",
            "name": "Cases",
            "description": "Named cases.",
            "findings": [
              {
                "id": "cases-finding",
                "name": "Cases",
                "description": "Cases.",
                "questions": [
                  {
                    "text": "What are line-plane, line-sphere, line segment and polyhedron-line intersections and intersection curves?",
                    "kind": "definition"
                  },
                  {
                    "text": "Which entry fits the specific case?",
                    "kind": "action"
                  }
                ]
              }
            ]
          }
        ]
      },
      {
        "id": "methods",
        "name": "Methods",
        "description": "Methods.",
        "rationale": "Science.",
        "layers": [
          {
            "id": "analytic",
            "name": "Analytic",
            "description": "Analytic methods.",
            "findings": [
              {
                "id": "analytic-finding",
                "name": "Analytic",
                "description": "Analytic.",
                "questions": [
                  {
                    "text": "How are intersections found with equations and vectors?",
                    "kind": "provenance"
                  },
                  {
                    "text": "Which references are standard?",
                    "kind": "provenance"
                  }
                ]
              }
            ]
          },
          {
            "id": "computational",
            "name": "Computational",
            "description": "Computational geometry.",
            "findings": [
              {
                "id": "computational-finding",
                "name": "Computational",
                "description": "Computational.",
                "questions": [
                  {
                    "text": "How do algorithms such as Bentley-Ottmann find intersections efficiently?",
                    "kind": "provenance"
                  },
                  {
                    "text": "Which sources are cited?",
                    "kind": "provenance"
                  }
                ]
              }
            ]
          }
        ]
      },
      {
        "id": "applications",
        "name": "Applications",
        "description": "Applications.",
        "rationale": "Application.",
        "layers": [
          {
            "id": "graphics",
            "name": "Graphics",
            "description": "Graphics and CAD.",
            "findings": [
              {
                "id": "graphics-finding",
                "name": "Graphics",
                "description": "Graphics.",
                "questions": [
                  {
                    "text": "How are intersections used in ray tracing, collision detection and CAD?",
                    "kind": "provenance"
                  },
                  {
                    "text": "Which entry fits collision detection?",
                    "kind": "action"
                  }
                ]
              }
            ]
          },
          {
            "id": "naval",
            "name": "Naval",
            "description": "Metacentre.",
            "findings": [
              {
                "id": "naval-finding",
                "name": "Naval",
                "description": "Naval.",
                "questions": [
                  {
                    "text": "What is the metacentre, and why does it matter for ship stability?",
                    "kind": "provenance"
                  },
                  {
                    "text": "Which entry fits metacentric height?",
                    "kind": "action"
                  }
                ]
              }
            ]
          }
        ]
      },
      {
        "id": "context",
        "name": "Context",
        "description": "Algebraic geometry and history.",
        "rationale": "Context.",
        "layers": [
          {
            "id": "algebraic",
            "name": "Algebraic",
            "description": "Intersection theory.",
            "findings": [
              {
                "id": "algebraic-finding",
                "name": "Algebraic",
                "description": "Algebraic.",
                "questions": [
                  {
                    "text": "What is intersection theory in algebraic geometry, such as Bezout s theorem?",
                    "kind": "provenance"
                  },
                  {
                    "text": "Which entry fits Bezout s theorem?",
                    "kind": "action"
                  }
                ]
              }
            ]
          },
          {
            "id": "history",
            "name": "History",
            "description": "History.",
            "findings": [
              {
                "id": "history-finding",
                "name": "History",
                "description": "History.",
                "questions": [
                  {
                    "text": "How did Descartes coordinate geometry make intersections computable?",
                    "kind": "provenance"
                  },
                  {
                    "text": "Which entry fits analytic geometry?",
                    "kind": "action"
                  }
                ]
              }
            ]
          }
        ]
      }
    ]
  },
  "openQuestions": [
    "Should the metacentre be linked as a separate entry?",
    "How should geometry sources be linked?",
    "The registry entry has merged aliases naming specific cases; should they be grouped?"
  ],
  "statistics": {
    "bundles": 4,
    "layers": 8,
    "findings": 8,
    "questions": 16
  }
}