{
  "vercy": "1.0-draft",
  "publication": {
    "status": "research-draft",
    "adjudicationStatus": "unreviewed",
    "publishableCanonical": false,
    "generatedAt": "2026-09-11T21:25:36Z",
    "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": "2026-10-05T20:46:32+00:00",
      "fields": [
        "agent_conduct",
        "ethics",
        "owners"
      ]
    },
    "gate": {
      "passed": true,
      "version": "1.0",
      "at": "2026-10-06T19:51:57+00:00",
      "evidence": [
        "completeness 1.00",
        "sense: Wikidata description",
        "2 live sources",
        "review by codex: pass"
      ]
    }
  },
  "metaModel": {
    "id": "THING-Q2532492",
    "registryId": "vr.tr.bridge-q2532492",
    "name": "bridge",
    "version": "0.2.0-wave.2",
    "entryKind": "thing",
    "family": "Thing Registry",
    "domain": [
      "XCT.REL"
    ],
    "status": "research-draft"
  },
  "canonicalUrl": "https://ver.cy/models/thing/q2532492/",
  "model": {
    "registry_id": "vr.tr.bridge-q2532492",
    "name": "bridge",
    "purpose": "Let an agent define bridges in graphs, explain algorithms to find them, relate them to connectivity and network reliability, and separate other senses of bridge.",
    "definition": "In graph theory, an edge whose removal increases the number of connected components of a graph, so that it is the only path between the two parts it joins, also called a cut-edge or isthmus; bridges are found by depth-first search algorithms and matter for network reliability, since a bridge is a single point of failure between two regions of a network.",
    "what_it_is_for": "Identifying critical edges in graphs and networks.",
    "affordances": [
      "define bridges and related concepts",
      "explain bridge-finding algorithms",
      "apply to network reliability",
      "separate other senses"
    ],
    "distinguishing_features": [
      "Cut-edge",
      "Not on a cycle",
      "Connectivity-critical",
      "Algorithmically detectable"
    ],
    "appearance": "Not physical; an edge in a graph diagram whose removal disconnects parts.",
    "visual_identification": [
      "Edge whose removal disconnects the graph",
      "Not part of any cycle",
      "A cut vertex is the vertex analogue"
    ],
    "physical_properties": [],
    "families_and_kinds": [
      "bridges in undirected graphs",
      "bridges in trees, where every edge is a bridge",
      "bridge-related concepts such as 2-edge-connected components",
      "strong bridges in directed graphs"
    ],
    "related_models": [
      {
        "relation": "is a kind of",
        "target": "edge",
        "why": "category"
      },
      {
        "relation": "is related to",
        "target": "graph theory",
        "why": "field"
      },
      {
        "relation": "is related to",
        "target": "connectivity",
        "why": "the property affected"
      },
      {
        "relation": "is related to",
        "target": "ordered pair",
        "why": "edges as pairs"
      }
    ],
    "identifiers": [],
    "standards_and_regulation": [
      "Mathematical terminology conventions"
    ],
    "failure_modes_and_hazards": [
      "Confusing with physical bridges or the card game",
      "Inefficient detection in large graphs",
      "Ignoring bridges in network design"
    ],
    "in_scope": [],
    "out_of_scope": [],
    "characteristics": [],
    "agent_conduct": {
      "may": [
        "Find bridges in a graph using standard algorithms and report them.",
        "Flag bridges in networks it is authorized to analyse as single points of failure."
      ],
      "must_not": [
        "Confuse the graph-theory sense with a physical bridge or the card game.",
        "Publish the bridges of a real infrastructure or communication network in a way that helps someone attack it.",
        "Report a graph as free of bridges without having checked it completely."
      ],
      "requires_human": [
        "Using bridge analysis to decide which links of a real network to cut, remove or protect."
      ]
    },
    "ethics": {
      "considerations": [
        "Bridges in real networks show where one failure cuts off whole communities.",
        "The same analysis can protect a network or target it."
      ],
      "affected_parties": [
        "Users of networks",
        "Network operators",
        "Communities served by a single link"
      ]
    },
    "owners": {
      "steward": "Nobody: a mathematical concept; the operator of a network answers for its use there.",
      "master_systems": []
    }
  },
  "sources": [
    {
      "id": "wikidata",
      "title": "Wikidata item Q2532492: bridge",
      "url": "https://www.wikidata.org/wiki/Q2532492",
      "url_status": "live",
      "what_it_supports": "identity and sense of the item",
      "checked_by": "wikidata-api"
    },
    {
      "id": "wikipedia-en",
      "title": "Wikipedia: Bridge (graph theory)",
      "url": "https://en.wikipedia.org/wiki/Bridge_%28graph_theory%29",
      "url_status": "live",
      "what_it_supports": "general description of the item",
      "checked_by": "wikidata-api sitelink"
    }
  ],
  "structure": {
    "bundles": [
      {
        "id": "define",
        "name": "Define",
        "description": "What a bridge is.",
        "rationale": "Definitions.",
        "layers": [
          {
            "id": "definition",
            "name": "Definition",
            "description": "Definition.",
            "findings": [
              {
                "id": "definition-finding",
                "name": "Definition",
                "description": "Definition.",
                "questions": [
                  {
                    "text": "What is a bridge in a graph, and why is an edge a bridge exactly when it lies on no cycle?",
                    "kind": "definition"
                  },
                  {
                    "text": "How does a bridge differ from a cut vertex?",
                    "kind": "definition"
                  }
                ]
              }
            ]
          },
          {
            "id": "senses",
            "name": "Senses",
            "description": "Other senses.",
            "findings": [
              {
                "id": "senses-finding",
                "name": "Senses",
                "description": "Other senses.",
                "questions": [
                  {
                    "text": "Is a physical bridge, a network bridge device, the card game or the graph concept meant?",
                    "kind": "boundary"
                  },
                  {
                    "text": "Which entry fits?",
                    "kind": "action"
                  }
                ]
              }
            ]
          }
        ]
      },
      {
        "id": "find",
        "name": "Find",
        "description": "Finding bridges.",
        "rationale": "Algorithms.",
        "layers": [
          {
            "id": "algorithm",
            "name": "Algorithm",
            "description": "Bridge-finding algorithms.",
            "findings": [
              {
                "id": "algorithm-finding",
                "name": "Algorithm",
                "description": "Algorithms.",
                "questions": [
                  {
                    "text": "How does the depth-first search algorithm with low-link values find all bridges in linear time?",
                    "kind": "definition"
                  },
                  {
                    "text": "How can it be implemented for this graph?",
                    "kind": "action"
                  }
                ]
              }
            ]
          },
          {
            "id": "components",
            "name": "Components",
            "description": "2-edge-connected components.",
            "findings": [
              {
                "id": "components-finding",
                "name": "Components",
                "description": "Components.",
                "questions": [
                  {
                    "text": "How are 2-edge-connected components computed from bridges?",
                    "kind": "definition"
                  },
                  {
                    "text": "What is the bridge tree of a graph?",
                    "kind": "definition"
                  }
                ]
              }
            ]
          }
        ]
      },
      {
        "id": "apply",
        "name": "Apply",
        "description": "Applications.",
        "rationale": "Networks.",
        "layers": [
          {
            "id": "reliability",
            "name": "Reliability",
            "description": "Network reliability.",
            "findings": [
              {
                "id": "reliability-finding",
                "name": "Reliability",
                "description": "Reliability.",
                "questions": [
                  {
                    "text": "Which links in this network are bridges and therefore single points of failure?",
                    "kind": "action"
                  },
                  {
                    "text": "How can redundancy remove them?",
                    "kind": "action"
                  }
                ]
              }
            ]
          },
          {
            "id": "other",
            "name": "Other",
            "description": "Other applications.",
            "findings": [
              {
                "id": "other-finding",
                "name": "Other",
                "description": "Other applications.",
                "questions": [
                  {
                    "text": "How are bridges used in analysing social, transport and biological networks?",
                    "kind": "provenance"
                  },
                  {
                    "text": "How do directed graphs change the concept?",
                    "kind": "definition"
                  }
                ]
              }
            ]
          }
        ]
      },
      {
        "id": "learn",
        "name": "Learn",
        "description": "Teaching.",
        "rationale": "Education.",
        "layers": [
          {
            "id": "teach",
            "name": "Teach",
            "description": "Teaching bridges.",
            "findings": [
              {
                "id": "teach-finding",
                "name": "Teach",
                "description": "Teaching.",
                "questions": [
                  {
                    "text": "How can bridges and connectivity be taught with small examples?",
                    "kind": "action"
                  },
                  {
                    "text": "Which misconceptions arise?",
                    "kind": "provenance"
                  }
                ]
              }
            ]
          },
          {
            "id": "history",
            "name": "History",
            "description": "History.",
            "findings": [
              {
                "id": "history-finding",
                "name": "History",
                "description": "History.",
                "questions": [
                  {
                    "text": "Who introduced bridge-finding algorithms, and how have they evolved?",
                    "kind": "provenance"
                  },
                  {
                    "text": "Which references are standard?",
                    "kind": "provenance"
                  }
                ]
              }
            ]
          }
        ]
      }
    ]
  },
  "openQuestions": [
    "Should cut vertices be a separate entry?",
    "How should algorithm references be linked?",
    "How should other senses be split?"
  ],
  "statistics": {
    "bundles": 4,
    "layers": 8,
    "findings": 8,
    "questions": 16
  }
}