{
  "vercy": "1.0-draft",
  "publication": {
    "status": "research-draft",
    "adjudicationStatus": "unreviewed",
    "publishableCanonical": false,
    "generatedAt": "2026-09-12T04:28:23Z",
    "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": "2026-10-05T23:55:00Z",
      "ingestedAt": "2026-10-05T20:51:37+00:00",
      "fields": [
        "agent_conduct",
        "ethics",
        "owners"
      ]
    },
    "gate": {
      "passed": true,
      "version": "1.0",
      "at": "2026-10-06T19:51:56+00:00",
      "evidence": [
        "completeness 1.00",
        "sense: Wikidata description",
        "2 live sources",
        "review by codex: pass"
      ]
    }
  },
  "metaModel": {
    "id": "THING-Q205",
    "registryId": "vr.tr.infinity",
    "name": "infinity",
    "version": "0.2.0-wave.2",
    "entryKind": "thing",
    "family": "Thing Registry",
    "domain": [
      "XCT.QLT"
    ],
    "status": "research-draft"
  },
  "canonicalUrl": "https://ver.cy/models/thing/q205/",
  "model": {
    "registry_id": "vr.tr.infinity",
    "name": "infinity",
    "purpose": "Let an agent explain infinity in mathematics and its formalisations, present philosophical and theological views with attribution, describe infinity in physics and cosmology, and address common paradoxes and misconceptions.",
    "definition": "The concept of something without bound or end, in mathematics formalised as infinite cardinalities and ordinals, limits and infinite sets, with distinctions between potential infinity as endless process and actual infinity as completed totality and the absolute infinite of Cantor, and in philosophy, theology and physics discussed as boundlessness of the universe, the divine or time; infinity is represented by the lemniscate symbol and underlies calculus, set theory and cosmology.",
    "what_it_is_for": "Boundlessness in mathematics and thought.",
    "affordances": [
      "explain mathematical infinity",
      "present philosophical views",
      "describe physical uses",
      "address paradoxes"
    ],
    "distinguishing_features": [
      "Potential versus actual",
      "Different sizes of infinity",
      "Limits",
      "Paradoxes"
    ],
    "appearance": "Not physical; a concept and symbol.",
    "visual_identification": [
      "Without bound or end",
      "Cardinal, ordinal, limit and potential forms",
      "Very large finite numbers are not infinite; the symbol is not a number in ordinary arithmetic"
    ],
    "physical_properties": [],
    "families_and_kinds": [
      "infinite cardinals",
      "infinite ordinals",
      "infinity in limits and calculus",
      "potential and actual infinity in philosophy",
      "infinity in physics and cosmology"
    ],
    "related_models": [
      {
        "relation": "is a kind of",
        "target": "cardinality",
        "why": "category"
      },
      {
        "relation": "is related to",
        "target": "ordinal number",
        "why": "transfinite ordinals"
      },
      {
        "relation": "is related to",
        "target": "real",
        "why": "the continuum"
      },
      {
        "relation": "is related to",
        "target": "God",
        "why": "theological infinity"
      }
    ],
    "identifiers": [],
    "standards_and_regulation": [
      "Mathematical conventions",
      "No regulation"
    ],
    "failure_modes_and_hazards": [
      "Treating infinity as an ordinary number",
      "Conflating mathematical and physical infinity",
      "Presenting contested philosophical views as settled"
    ],
    "in_scope": [],
    "out_of_scope": [],
    "characteristics": [],
    "agent_conduct": {
      "may": [
        "Explain potential and actual infinity, cardinalities and limits with correct mathematical definitions.",
        "Check calculations for steps that treat infinity as an ordinary number."
      ],
      "must_not": [
        "Present an argument that divides by infinity or manipulates divergent series naively as a valid proof.",
        "Claim a physical quantity is infinite when the evidence shows only that it is very large or unmeasured.",
        "Misstate unresolved questions, such as the continuum hypothesis, as settled."
      ],
      "requires_human": [
        "Publishing claims of a new result about infinite sets as established mathematics."
      ]
    },
    "ethics": {
      "considerations": [
        "Infinity is often invoked to lend false authority to religious, financial or scientific claims.",
        "Clear teaching of the concept prevents confusion that discourages learners."
      ],
      "affected_parties": [
        "Students and learners",
        "Readers of popular science"
      ]
    },
    "owners": {
      "steward": "Nobody: a concept held in common by mathematics and philosophy.",
      "master_systems": []
    }
  },
  "sources": [
    {
      "id": "wikidata",
      "title": "Wikidata item Q205: infinity",
      "url": "https://www.wikidata.org/wiki/Q205",
      "url_status": "live",
      "what_it_supports": "identity and sense of the item",
      "checked_by": "wikidata-api"
    },
    {
      "id": "wikipedia-en",
      "title": "Wikipedia: Infinity",
      "url": "https://en.wikipedia.org/wiki/Infinity",
      "url_status": "live",
      "what_it_supports": "general description of the item",
      "checked_by": "wikidata-api sitelink"
    }
  ],
  "structure": {
    "bundles": [
      {
        "id": "understand",
        "name": "Understand",
        "description": "What infinity is.",
        "rationale": "Mathematics.",
        "layers": [
          {
            "id": "concept",
            "name": "Concept",
            "description": "Concept and distinctions.",
            "findings": [
              {
                "id": "concept-finding",
                "name": "Concept",
                "description": "Concept.",
                "questions": [
                  {
                    "text": "What is infinity, and how do potential, actual and absolute infinity differ?",
                    "kind": "definition"
                  },
                  {
                    "text": "Is the mathematical, philosophical or physical sense meant?",
                    "kind": "boundary"
                  }
                ]
              }
            ]
          },
          {
            "id": "sizes",
            "name": "Sizes",
            "description": "Sizes of infinity.",
            "findings": [
              {
                "id": "sizes-finding",
                "name": "Sizes",
                "description": "Sizes.",
                "questions": [
                  {
                    "text": "How did Cantor show that infinite sets have different sizes, and what are countable and uncountable infinities?",
                    "kind": "definition"
                  },
                  {
                    "text": "Which entry fits set theory?",
                    "kind": "action"
                  }
                ]
              }
            ]
          }
        ]
      },
      {
        "id": "use",
        "name": "Use",
        "description": "Infinity in mathematics.",
        "rationale": "Practice.",
        "layers": [
          {
            "id": "limits",
            "name": "Limits",
            "description": "Limits and calculus.",
            "findings": [
              {
                "id": "limits-finding",
                "name": "Limits",
                "description": "Limits.",
                "questions": [
                  {
                    "text": "How is infinity used in limits, series and calculus, and how are infinite processes handled rigorously?",
                    "kind": "definition"
                  },
                  {
                    "text": "Which entry fits limits?",
                    "kind": "action"
                  }
                ]
              }
            ]
          },
          {
            "id": "paradoxes",
            "name": "Paradoxes",
            "description": "Paradoxes.",
            "findings": [
              {
                "id": "paradoxes-finding",
                "name": "Paradoxes",
                "description": "Paradoxes.",
                "questions": [
                  {
                    "text": "What do paradoxes such as Hilbert hotel and Zeno show, and how are they resolved?",
                    "kind": "definition"
                  },
                  {
                    "text": "Which entry fits Zeno paradoxes?",
                    "kind": "action"
                  }
                ]
              }
            ]
          }
        ]
      },
      {
        "id": "beyond",
        "name": "Beyond",
        "description": "Philosophy and physics.",
        "rationale": "Attribution.",
        "layers": [
          {
            "id": "philosophy",
            "name": "Philosophy",
            "description": "Philosophy and theology.",
            "findings": [
              {
                "id": "philosophy-finding",
                "name": "Philosophy",
                "description": "Philosophy.",
                "questions": [
                  {
                    "text": "How have philosophers and theologians treated infinity, from Aristotle to modern debates, with positions attributed?",
                    "kind": "provenance"
                  },
                  {
                    "text": "Is the presentation attributed?",
                    "kind": "boundary"
                  }
                ]
              }
            ]
          },
          {
            "id": "physics",
            "name": "Physics",
            "description": "Physics and cosmology.",
            "findings": [
              {
                "id": "physics-finding",
                "name": "Physics",
                "description": "Physics.",
                "questions": [
                  {
                    "text": "Is the universe infinite, and how do physicists handle infinities in theories, with findings and uncertainties attributed?",
                    "kind": "provenance"
                  },
                  {
                    "text": "Which entry fits cosmology?",
                    "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 the concept of infinity develop from Greek mathematics through Cantor to modern set theory?",
                    "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 infinity be taught with countability and paradoxes?",
                    "kind": "action"
                  },
                  {
                    "text": "Which misconceptions arise?",
                    "kind": "provenance"
                  }
                ]
              }
            ]
          }
        ]
      }
    ]
  },
  "openQuestions": [
    "Should cardinal numbers be a separate entry?",
    "How should set theory resources be linked?",
    "How should cosmology resources be linked?"
  ],
  "statistics": {
    "bundles": 4,
    "layers": 8,
    "findings": 8,
    "questions": 16
  }
}