{
  "vercy": "1.0-draft",
  "publication": {
    "status": "research-draft",
    "adjudicationStatus": "unreviewed",
    "publishableCanonical": false,
    "generatedAt": "2026-09-14T03:47:14Z",
    "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": "2026-10-06T07:44:39+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-Q245595",
    "registryId": "vr.tr.cycle",
    "name": "cycle",
    "version": "0.2.0-wave.4",
    "entryKind": "thing",
    "family": "Thing Registry",
    "domain": [
      "XCT.TME"
    ],
    "status": "research-draft"
  },
  "canonicalUrl": "https://ver.cy/models/thing/q245595/",
  "model": {
    "registry_id": "vr.tr.cycle",
    "name": "cycle",
    "purpose": "Let an agent explain the graph-theory cycle, relay its definition, kinds and role from mathematics sources, describe the related notions its aliases name, and distinguish it from a path and from everyday senses of cycle.",
    "definition": "In graph theory, a cycle is a closed path in a graph that starts and ends at the same vertex, following edges without repeating a vertex in between; the registry aliases name related notions such as an induced cycle and a self-avoiding polygon. Cycles are a basic structure in the study of graphs and networks, and a graph with no cycles is acyclic. This is the mathematical sense, distinct from everyday cycles such as a repeating process.",
    "what_it_is_for": "Describing a closed path in a graph.",
    "affordances": [
      "explain the definition",
      "relay kinds and role",
      "describe related notions",
      "distinguish it from a path"
    ],
    "distinguishing_features": [
      "Closed path",
      "Returns to start",
      "No repeated inner vertex",
      "Basic graph structure"
    ],
    "appearance": "Not a physical object; drawn as a loop of vertices joined by edges returning to the start.",
    "visual_identification": [
      "A closed path returning to its start in a graph",
      "Induced cycle, self-avoiding polygon",
      "A path does not return to its start; an everyday cycle is a repeating process"
    ],
    "physical_properties": [
      {
        "quantity": "field",
        "typical_range": "graph theory",
        "unit": "note",
        "note": ""
      },
      {
        "quantity": "property",
        "typical_range": "closed, non-repeating path",
        "unit": "note",
        "note": ""
      },
      {
        "quantity": "registry parent",
        "typical_range": "circuit",
        "unit": "note",
        "note": ""
      }
    ],
    "families_and_kinds": [
      "simple cycle",
      "induced cycle",
      "Hamiltonian cycle"
    ],
    "related_models": [
      {
        "relation": "is a kind of",
        "target": "path",
        "why": "related"
      },
      {
        "relation": "is a kind of",
        "target": "circuit",
        "why": "in registry terms"
      },
      {
        "relation": "is contrasted with",
        "target": "acyclic graph",
        "why": ""
      },
      {
        "relation": "is contrasted with",
        "target": "everyday cycle",
        "why": ""
      }
    ],
    "identifiers": [],
    "standards_and_regulation": [
      "Mathematical definition"
    ],
    "failure_modes_and_hazards": [
      "Confusing with an open path",
      "Mixing the math and everyday senses",
      "Conflating cycle kinds"
    ],
    "in_scope": [],
    "out_of_scope": [],
    "characteristics": [],
    "agent_conduct": {
      "may": [
        "Detect and report cycles in graphs, such as dependency graphs, that it is authorized to analyse.",
        "Explain the graph-theory definition and how a cycle differs from an open path or a walk."
      ],
      "must_not": [
        "Report a graph as acyclic without checking it completely.",
        "Silently break cycles in someone else's dependency or workflow data by deleting edges.",
        "Mix the graph-theory sense with everyday senses of cycle in technical explanations.",
        "Present a closed walk that repeats vertices as a simple cycle."
      ],
      "requires_human": [
        "Changing a shared dependency structure to remove a cycle that others rely on."
      ]
    },
    "ethics": {
      "considerations": [
        "Undetected cycles can cause deadlocks and endless loops in systems people depend on.",
        "Precise definitions matter for students and for correctness proofs."
      ],
      "affected_parties": [
        "Students and researchers",
        "Users of affected systems",
        "Software maintainers"
      ]
    },
    "owners": {
      "steward": "Nobody: a mathematical concept held in common.",
      "master_systems": []
    }
  },
  "sources": [
    {
      "id": "wikidata",
      "title": "Wikidata item Q245595: cycle",
      "url": "https://www.wikidata.org/wiki/Q245595",
      "url_status": "live",
      "what_it_supports": "identity and sense of the item",
      "checked_by": "wikidata-api"
    },
    {
      "id": "wikipedia-en",
      "title": "Wikipedia: Cycle (graph theory)",
      "url": "https://en.wikipedia.org/wiki/Cycle_%28graph_theory%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 graph cycle is.",
        "rationale": "Definition.",
        "layers": [
          {
            "id": "definition",
            "name": "Definition",
            "description": "Definition.",
            "findings": [
              {
                "id": "definition-finding",
                "name": "Definition",
                "description": "Definition.",
                "questions": [
                  {
                    "text": "What is a cycle in graph theory, and how does it differ from a path and from an everyday cycle?",
                    "kind": "definition"
                  },
                  {
                    "text": "Is the mathematical sense meant?",
                    "kind": "boundary"
                  }
                ]
              }
            ]
          },
          {
            "id": "kinds",
            "name": "Kinds",
            "description": "Kinds.",
            "findings": [
              {
                "id": "kinds-finding",
                "name": "Kinds",
                "description": "Kinds.",
                "questions": [
                  {
                    "text": "What are simple, induced and Hamiltonian cycles?",
                    "kind": "definition"
                  },
                  {
                    "text": "Which entry fits the specific kind?",
                    "kind": "action"
                  }
                ]
              }
            ]
          }
        ]
      },
      {
        "id": "theory",
        "name": "Theory",
        "description": "Theory.",
        "rationale": "Sources.",
        "layers": [
          {
            "id": "role",
            "name": "Role",
            "description": "Role.",
            "findings": [
              {
                "id": "role-finding",
                "name": "Role",
                "description": "Role.",
                "questions": [
                  {
                    "text": "Why are cycles important in the study of graphs?",
                    "kind": "provenance"
                  },
                  {
                    "text": "Which references are standard?",
                    "kind": "provenance"
                  }
                ]
              }
            ]
          },
          {
            "id": "acyclic",
            "name": "Acyclic",
            "description": "Acyclic graphs.",
            "findings": [
              {
                "id": "acyclic-finding",
                "name": "Acyclic",
                "description": "Acyclic.",
                "questions": [
                  {
                    "text": "What does it mean for a graph to be acyclic?",
                    "kind": "provenance"
                  },
                  {
                    "text": "Which entry fits acyclic graph?",
                    "kind": "action"
                  }
                ]
              }
            ]
          }
        ]
      },
      {
        "id": "applications",
        "name": "Applications",
        "description": "Applications.",
        "rationale": "Sources.",
        "layers": [
          {
            "id": "networks",
            "name": "Networks",
            "description": "Networks.",
            "findings": [
              {
                "id": "networks-finding",
                "name": "Networks",
                "description": "Networks.",
                "questions": [
                  {
                    "text": "How do cycles matter in networks and algorithms?",
                    "kind": "provenance"
                  },
                  {
                    "text": "Which sources are cited?",
                    "kind": "provenance"
                  }
                ]
              }
            ]
          },
          {
            "id": "detection",
            "name": "Detection",
            "description": "Cycle detection.",
            "findings": [
              {
                "id": "detection-finding",
                "name": "Detection",
                "description": "Detection.",
                "questions": [
                  {
                    "text": "How are cycles detected in a graph?",
                    "kind": "provenance"
                  },
                  {
                    "text": "Which sources are cited?",
                    "kind": "provenance"
                  }
                ]
              }
            ]
          }
        ]
      },
      {
        "id": "context",
        "name": "Context",
        "description": "Context.",
        "rationale": "Context.",
        "layers": [
          {
            "id": "graph",
            "name": "Graph",
            "description": "Graphs.",
            "findings": [
              {
                "id": "graph-finding",
                "name": "Graph",
                "description": "Graph.",
                "questions": [
                  {
                    "text": "How does a cycle fit the broader idea of a graph?",
                    "kind": "provenance"
                  },
                  {
                    "text": "Which entry fits graph?",
                    "kind": "action"
                  }
                ]
              }
            ]
          },
          {
            "id": "senses",
            "name": "Senses",
            "description": "Other senses.",
            "findings": [
              {
                "id": "senses-finding",
                "name": "Senses",
                "description": "Senses.",
                "questions": [
                  {
                    "text": "How does the graph cycle differ from cycle as a repeating process?",
                    "kind": "provenance"
                  },
                  {
                    "text": "Is the sense correctly identified?",
                    "kind": "boundary"
                  }
                ]
              }
            ]
          }
        ]
      }
    ]
  },
  "openQuestions": [
    "Should cycle kinds be separate entries?",
    "How should the everyday sense be signposted?",
    "How should acyclic graphs be linked?"
  ],
  "statistics": {
    "bundles": 4,
    "layers": 8,
    "findings": 8,
    "questions": 16
  }
}