{
  "vercy": "1.0-draft",
  "publication": {
    "status": "research-draft",
    "adjudicationStatus": "unreviewed",
    "publishableCanonical": false,
    "generatedAt": "2026-09-12T06:00:47Z",
    "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": 2,
    "engine": "claude",
    "enrichment": {
      "pass": 3,
      "engine": "claude",
      "producedAt": "2026-10-05T23:50:00Z",
      "ingestedAt": "2026-10-05T20:56:29+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",
        "sense: Wikidata description",
        "2 live sources",
        "review by codex: pass"
      ]
    }
  },
  "metaModel": {
    "id": "THING-Q12507",
    "registryId": "vr.tr.sphere",
    "name": "sphere",
    "version": "0.2.0-wave.2",
    "entryKind": "thing",
    "family": "Thing Registry",
    "domain": [
      "XCT.QLT"
    ],
    "status": "research-draft"
  },
  "canonicalUrl": "https://ver.cy/models/thing/q12507/",
  "model": {
    "registry_id": "vr.tr.sphere",
    "name": "sphere",
    "purpose": "Let an agent explain the sphere and its geometry, support calculations of area, volume and related quantities, describe generalisations and applications in science and engineering, and support learning.",
    "definition": "In geometry, the set of all points in three-dimensional space at a fixed distance, the radius, from a given centre, forming a perfectly round surface enclosing a ball, with area and volume given by classical formulas, generalised to unit spheres, higher-dimensional spheres and related notions such as circumscribed spheres and midspheres of polyhedra; spheres are geometric primitives in mathematics, model planets, bubbles and balls in science, and shape objects such as domes and radomes.",
    "what_it_is_for": "Round surface at fixed distance from a centre.",
    "affordances": [
      "explain geometry",
      "support calculations",
      "describe generalisations and applications",
      "support learning"
    ],
    "distinguishing_features": [
      "Constant radius",
      "Maximal symmetry",
      "Minimal surface for volume",
      "Generalisable"
    ],
    "appearance": "Perfectly round surface.",
    "visual_identification": [
      "All points at distance r from a centre",
      "Surface enclosing a ball",
      "A ball includes the interior; a spheroid is stretched; a circle is the two-dimensional analogue"
    ],
    "physical_properties": [],
    "families_and_kinds": [
      "the unit sphere",
      "spheres in higher dimensions",
      "circumscribed, inscribed and midspheres",
      "spherical geometry and great circles",
      "physical spheres such as balls, bubbles and planets"
    ],
    "related_models": [
      {
        "relation": "is a kind of",
        "target": "geometric primitive",
        "why": "category"
      },
      {
        "relation": "is a kind of",
        "target": "spheroid",
        "why": "category"
      },
      {
        "relation": "is related to",
        "target": "triangle",
        "why": "triangles on spherical surfaces"
      },
      {
        "relation": "is related to",
        "target": "point",
        "why": "points defining a sphere"
      }
    ],
    "identifiers": [],
    "standards_and_regulation": [
      "Mathematical notation conventions",
      "Curriculum standards for geometry",
      "No regulation of the concept"
    ],
    "failure_modes_and_hazards": [
      "Confusing sphere with ball",
      "Formula errors",
      "Assuming physical objects are perfect spheres"
    ],
    "in_scope": [],
    "out_of_scope": [],
    "characteristics": [],
    "agent_conduct": {
      "may": [
        "Explain the sphere, its surface area and volume.",
        "Support calculations, stating units and the radius used.",
        "Distinguish a sphere from a ball and describe generalisations."
      ],
      "must_not": [
        "Treat physical objects such as the Earth as perfect spheres when accuracy matters.",
        "Confuse sphere and ball in calculations.",
        "Present formula results without checking units.",
        "Present homework answers as the student's own work when that would be dishonest."
      ],
      "requires_human": [
        "Relying on spherical calculations in safety-critical design such as pressure vessels."
      ]
    },
    "ethics": {
      "considerations": [
        "Errors in geometry carry into engineering and navigation.",
        "Help with learning should build understanding, not replace it."
      ],
      "affected_parties": [
        "Students",
        "Engineers",
        "Navigators"
      ]
    },
    "owners": {
      "steward": "Nobody: a mathematical object held in common.",
      "master_systems": []
    }
  },
  "sources": [
    {
      "id": "wikidata",
      "title": "Wikidata item Q12507: sphere",
      "url": "https://www.wikidata.org/wiki/Q12507",
      "url_status": "live",
      "what_it_supports": "identity and sense of the item",
      "checked_by": "wikidata-api"
    },
    {
      "id": "wikipedia-en",
      "title": "Wikipedia: Sphere",
      "url": "https://en.wikipedia.org/wiki/Sphere",
      "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 sphere is.",
        "rationale": "Mathematics.",
        "layers": [
          {
            "id": "definition",
            "name": "Definition",
            "description": "Definition and properties.",
            "findings": [
              {
                "id": "definition-finding",
                "name": "Definition",
                "description": "Definition.",
                "questions": [
                  {
                    "text": "What is a sphere, and what properties of symmetry, area and volume does it have?",
                    "kind": "definition"
                  },
                  {
                    "text": "Is the surface or the solid ball meant?",
                    "kind": "boundary"
                  }
                ]
              }
            ]
          },
          {
            "id": "geometry",
            "name": "Geometry",
            "description": "Spherical geometry.",
            "findings": [
              {
                "id": "geometry-finding",
                "name": "Geometry",
                "description": "Geometry.",
                "questions": [
                  {
                    "text": "How do great circles, spherical triangles and geodesics work on a sphere?",
                    "kind": "definition"
                  },
                  {
                    "text": "Which entry fits spherical geometry?",
                    "kind": "action"
                  }
                ]
              }
            ]
          }
        ]
      },
      {
        "id": "calculate",
        "name": "Calculate",
        "description": "Calculations.",
        "rationale": "Practice.",
        "layers": [
          {
            "id": "formulas",
            "name": "Formulas",
            "description": "Area and volume.",
            "findings": [
              {
                "id": "formulas-finding",
                "name": "Formulas",
                "description": "Formulas.",
                "questions": [
                  {
                    "text": "How are the surface area and volume of this sphere calculated, and how do they scale with radius?",
                    "kind": "action"
                  },
                  {
                    "text": "Which units apply?",
                    "kind": "measurement"
                  }
                ]
              }
            ]
          },
          {
            "id": "related",
            "name": "Related",
            "description": "Related spheres.",
            "findings": [
              {
                "id": "related-finding",
                "name": "Related",
                "description": "Related.",
                "questions": [
                  {
                    "text": "How are circumscribed spheres, inscribed spheres and midspheres of polyhedra found?",
                    "kind": "action"
                  },
                  {
                    "text": "Which entry fits polyhedra?",
                    "kind": "action"
                  }
                ]
              }
            ]
          }
        ]
      },
      {
        "id": "apply",
        "name": "Apply",
        "description": "Applications and generalisations.",
        "rationale": "Science.",
        "layers": [
          {
            "id": "science",
            "name": "Science",
            "description": "Science and engineering.",
            "findings": [
              {
                "id": "science-finding",
                "name": "Science",
                "description": "Science.",
                "questions": [
                  {
                    "text": "Why do planets, bubbles and drops approximate spheres, and how are spherical shapes used in domes, radomes and tanks?",
                    "kind": "provenance"
                  },
                  {
                    "text": "Which entry fits a specific application?",
                    "kind": "action"
                  }
                ]
              }
            ]
          },
          {
            "id": "higher",
            "name": "Higher",
            "description": "Higher dimensions.",
            "findings": [
              {
                "id": "higher-finding",
                "name": "Higher",
                "description": "Higher.",
                "questions": [
                  {
                    "text": "How are spheres generalised to higher dimensions and abstract spaces?",
                    "kind": "provenance"
                  },
                  {
                    "text": "Which entry fits topology?",
                    "kind": "action"
                  }
                ]
              }
            ]
          }
        ]
      },
      {
        "id": "learn",
        "name": "Learn",
        "description": "History and teaching.",
        "rationale": "Education.",
        "layers": [
          {
            "id": "history",
            "name": "History",
            "description": "History.",
            "findings": [
              {
                "id": "history-finding",
                "name": "History",
                "description": "History.",
                "questions": [
                  {
                    "text": "How did Archimedes and later mathematicians establish the geometry of the sphere?",
                    "kind": "provenance"
                  },
                  {
                    "text": "Which references are standard?",
                    "kind": "provenance"
                  }
                ]
              }
            ]
          },
          {
            "id": "teach",
            "name": "Teach",
            "description": "Teaching.",
            "findings": [
              {
                "id": "teach-finding",
                "name": "Teach",
                "description": "Teaching.",
                "questions": [
                  {
                    "text": "How can the sphere be taught with models?",
                    "kind": "action"
                  },
                  {
                    "text": "Which misconceptions arise?",
                    "kind": "provenance"
                  }
                ]
              }
            ]
          }
        ]
      }
    ]
  },
  "openQuestions": [
    "Should spherical geometry be a separate entry?",
    "How should textbooks be linked?",
    "How should applications be linked?"
  ],
  "statistics": {
    "bundles": 4,
    "layers": 8,
    "findings": 8,
    "questions": 16
  }
}