{
  "vercy": "1.0-draft",
  "publication": {
    "status": "research-draft",
    "adjudicationStatus": "unreviewed",
    "publishableCanonical": false,
    "generatedAt": "2026-09-11T15:11:43Z",
    "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": "2026-10-05T17:00:00Z",
      "ingestedAt": "2026-10-05T13:31:16+00:00",
      "fields": [
        "agent_conduct",
        "ethics",
        "owners"
      ]
    },
    "gate": {
      "passed": true,
      "version": "1.0",
      "at": "2026-10-06T19:51:54+00:00",
      "evidence": [
        "completeness 1.00",
        "sense: Wikidata description",
        "2 live sources",
        "review by codex: pass"
      ]
    }
  },
  "metaModel": {
    "id": "THING-Q1371213",
    "registryId": "vr.tr.affine-connection",
    "name": "affine connection",
    "version": "0.2.0-wave.1",
    "entryKind": "thing",
    "family": "Thing Registry",
    "domain": [
      "XCT.REL"
    ],
    "status": "research-draft"
  },
  "canonicalUrl": "https://ver.cy/models/thing/q1371213/",
  "model": {
    "registry_id": "vr.tr.affine-connection",
    "name": "affine connection",
    "purpose": "Let an agent explain affine connections by definition, Christoffel symbols, parallel transport, curvature and applications, for students and researchers.",
    "definition": "In differential geometry, a structure on a smooth manifold that specifies how to differentiate vector fields along curves and to parallel transport vectors, defining geodesics and curvature; the Levi-Civita connection is the unique torsion-free connection compatible with a Riemannian metric and underlies general relativity.",
    "what_it_is_for": "Differential geometry, physics and geometric modelling.",
    "affordances": [
      "explain the definition and axioms",
      "compute Christoffel symbols for a metric",
      "describe parallel transport and geodesics",
      "relate connections to curvature and relativity"
    ],
    "distinguishing_features": [
      "Defines covariant differentiation",
      "Gives parallel transport",
      "May have torsion and curvature",
      "Levi-Civita is metric-compatible and torsion-free"
    ],
    "appearance": "Not physical; formulas with Christoffel symbols and diagrams of parallel transport.",
    "visual_identification": [
      "Covariant derivative notation",
      "Christoffel symbols",
      "A metric alone is a different structure"
    ],
    "physical_properties": [],
    "families_and_kinds": [
      "Levi-Civita connection",
      "connections with torsion",
      "flat connections",
      "projective and conformal connections",
      "connections on vector bundles (generalisation)"
    ],
    "related_models": [
      {
        "relation": "is a kind of",
        "target": "connection (mathematics)",
        "why": "category"
      },
      {
        "relation": "defines",
        "target": "geodesic",
        "why": "curve"
      },
      {
        "relation": "is related to",
        "target": "continuous function",
        "why": "smooth maps"
      },
      {
        "relation": "is used in",
        "target": "general relativity",
        "why": "application"
      }
    ],
    "identifiers": [],
    "standards_and_regulation": [
      "No specific regulation"
    ],
    "failure_modes_and_hazards": [
      "Index and sign convention errors",
      "Confusing connection and metric"
    ],
    "in_scope": [],
    "out_of_scope": [],
    "characteristics": [],
    "agent_conduct": {
      "may": [
        "State definitions and standard results about affine connections, citing the literature.",
        "Compute connection coefficients for given metrics."
      ],
      "must_not": [
        "Present unproven claims as theorems.",
        "Misattribute results to mathematicians or physicists without a source."
      ],
      "requires_human": [
        "Publishing a claimed new result in a reference work."
      ]
    },
    "ethics": {
      "considerations": [
        "Correct attribution matters to scholarship.",
        "Errors in teaching material mislead learners."
      ],
      "affected_parties": [
        "Students and researchers"
      ]
    },
    "owners": {
      "steward": "Nobody: a mathematical concept held in common.",
      "master_systems": []
    }
  },
  "sources": [
    {
      "id": "wikidata",
      "title": "Wikidata item Q1371213: affine connection",
      "url": "https://www.wikidata.org/wiki/Q1371213",
      "url_status": "live",
      "what_it_supports": "identity and sense of the item",
      "checked_by": "wikidata-api"
    },
    {
      "id": "wikipedia-en",
      "title": "Wikipedia: Affine connection",
      "url": "https://en.wikipedia.org/wiki/Affine_connection",
      "url_status": "live",
      "what_it_supports": "general description of the item",
      "checked_by": "wikidata-api sitelink"
    }
  ],
  "structure": {
    "bundles": [
      {
        "id": "definition",
        "name": "Definition",
        "description": "What it is.",
        "rationale": "Axioms define connections.",
        "layers": [
          {
            "id": "axioms",
            "name": "Axioms",
            "description": "Defining properties.",
            "findings": [
              {
                "id": "axioms-finding",
                "name": "Axioms",
                "description": "Axioms.",
                "questions": [
                  {
                    "text": "What properties define an affine connection?",
                    "kind": "definition"
                  },
                  {
                    "text": "How does it differ from a metric?",
                    "kind": "boundary"
                  }
                ]
              }
            ]
          },
          {
            "id": "christoffel",
            "name": "Christoffel",
            "description": "Coordinates.",
            "findings": [
              {
                "id": "christoffel-finding",
                "name": "Christoffel",
                "description": "Christoffel symbols.",
                "questions": [
                  {
                    "text": "What are the Christoffel symbols for this metric?",
                    "kind": "measurement"
                  },
                  {
                    "text": "Which sign and index conventions are used?",
                    "kind": "boundary"
                  }
                ]
              }
            ]
          }
        ]
      },
      {
        "id": "geometry",
        "name": "Geometry",
        "description": "Transport and curvature.",
        "rationale": "Connections shape geometry.",
        "layers": [
          {
            "id": "transport",
            "name": "Transport",
            "description": "Parallel transport.",
            "findings": [
              {
                "id": "transport-finding",
                "name": "Transport",
                "description": "Parallel transport.",
                "questions": [
                  {
                    "text": "How does parallel transport work along this curve?",
                    "kind": "definition"
                  },
                  {
                    "text": "What are the geodesics?",
                    "kind": "definition"
                  }
                ]
              }
            ]
          },
          {
            "id": "curvature",
            "name": "Curvature",
            "description": "Riemann tensor.",
            "findings": [
              {
                "id": "curvature-finding",
                "name": "Curvature",
                "description": "Curvature.",
                "questions": [
                  {
                    "text": "How is curvature computed from the connection?",
                    "kind": "definition"
                  },
                  {
                    "text": "What does torsion measure?",
                    "kind": "definition"
                  }
                ]
              }
            ]
          }
        ]
      },
      {
        "id": "physics",
        "name": "Physics",
        "description": "Relativity.",
        "rationale": "Gravity is geometry.",
        "layers": [
          {
            "id": "relativity",
            "name": "Relativity",
            "description": "General relativity.",
            "findings": [
              {
                "id": "relativity-finding",
                "name": "Relativity",
                "description": "General relativity.",
                "questions": [
                  {
                    "text": "How does the Levi-Civita connection describe free fall in general relativity?",
                    "kind": "definition"
                  },
                  {
                    "text": "Which equations use it?",
                    "kind": "definition"
                  }
                ]
              }
            ]
          },
          {
            "id": "gauge",
            "name": "Gauge",
            "description": "Gauge theories.",
            "findings": [
              {
                "id": "gauge-finding",
                "name": "Gauge",
                "description": "Gauge theories.",
                "questions": [
                  {
                    "text": "How do connections on bundles appear in gauge theories?",
                    "kind": "definition"
                  },
                  {
                    "text": "Which references explain it?",
                    "kind": "provenance"
                  }
                ]
              }
            ]
          }
        ]
      },
      {
        "id": "learning",
        "name": "Learning",
        "description": "Study.",
        "rationale": "Prerequisites matter.",
        "layers": [
          {
            "id": "references",
            "name": "References",
            "description": "Textbooks.",
            "findings": [
              {
                "id": "references-finding",
                "name": "References",
                "description": "Textbooks.",
                "questions": [
                  {
                    "text": "Which textbooks introduce affine connections?",
                    "kind": "provenance"
                  },
                  {
                    "text": "What prerequisites are needed?",
                    "kind": "definition"
                  }
                ]
              }
            ]
          },
          {
            "id": "tools",
            "name": "Tools",
            "description": "Computation.",
            "findings": [
              {
                "id": "tools-finding",
                "name": "Tools",
                "description": "Computation.",
                "questions": [
                  {
                    "text": "Which software computes Christoffel symbols and curvature?",
                    "kind": "provenance"
                  },
                  {
                    "text": "How can results be checked?",
                    "kind": "action"
                  }
                ]
              }
            ]
          }
        ]
      }
    ]
  },
  "openQuestions": [
    "Should the Levi-Civita connection be a separate entry?",
    "How should textbooks be linked?",
    "How should computational tools be linked?"
  ],
  "statistics": {
    "bundles": 4,
    "layers": 8,
    "findings": 8,
    "questions": 16
  }
}