{
  "vercy": "1.0-draft",
  "publication": {
    "status": "research-draft",
    "adjudicationStatus": "unreviewed",
    "publishableCanonical": false,
    "generatedAt": "2026-09-12T21:03:38Z",
    "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": 3,
    "engine": "claude",
    "enrichment": {
      "pass": 3,
      "engine": "claude",
      "producedAt": "2026-10-06T10:00:00Z",
      "ingestedAt": "2026-10-06T06:57:30+00:00",
      "fields": [
        "agent_conduct",
        "ethics",
        "owners"
      ]
    },
    "gate": {
      "passed": true,
      "version": "1.0",
      "at": "2026-10-06T19:52:01+00:00",
      "evidence": [
        "completeness 1.00",
        "sense: Wikidata description",
        "2 live sources",
        "review by codex: pass"
      ]
    }
  },
  "metaModel": {
    "id": "THING-Q60679",
    "registryId": "vr.tr.harmonic-divisor-number",
    "name": "harmonic divisor number",
    "version": "0.2.0-wave.3",
    "entryKind": "thing",
    "family": "Thing Registry",
    "domain": [
      "XCT.QTY"
    ],
    "status": "research-draft"
  },
  "canonicalUrl": "https://ver.cy/models/thing/q60679/",
  "model": {
    "registry_id": "vr.tr.harmonic-divisor-number",
    "name": "harmonic divisor number",
    "purpose": "Let an agent define harmonic divisor numbers precisely, test a given integer, relate them to perfect numbers and open conjectures, and point to sequence references.",
    "definition": "A positive integer whose divisors have an integer harmonic mean, also called an Ore number after Oystein Ore who introduced them in 1948; the first are 1, 6, 28, 140, 270 and 496, every perfect number is a harmonic divisor number, and it is conjectured that no odd harmonic divisor number greater than 1 exists.",
    "what_it_is_for": "Not for anything; a curiosity in number theory.",
    "affordances": [
      "test whether an integer is a harmonic divisor number",
      "list small examples",
      "explain the link to perfect numbers",
      "state open problems"
    ],
    "distinguishing_features": [
      "Defined by the harmonic mean of divisors",
      "Contains all perfect numbers",
      "Conjectured to have no odd members beyond 1",
      "Named after Ore"
    ],
    "appearance": "Not visible; a property of integers.",
    "visual_identification": [
      "Divisors have integer harmonic mean",
      "Examples 1, 6, 28, 140, 270, 496",
      "Perfect numbers are a subset; abundant numbers are a different notion"
    ],
    "physical_properties": [
      {
        "quantity": "first terms",
        "typical_range": "1, 6, 28, 140, 270, 496, 672",
        "unit": "integers",
        "note": ""
      }
    ],
    "families_and_kinds": [
      "harmonic divisor numbers",
      "perfect numbers as a subset",
      "related notions such as refactorable and arithmetic numbers"
    ],
    "related_models": [
      {
        "relation": "is a kind of",
        "target": "positive integer",
        "why": "a property of integers"
      },
      {
        "relation": "includes",
        "target": "perfect number",
        "why": "every perfect number qualifies"
      },
      {
        "relation": "is listed in",
        "target": "On-Line Encyclopedia of Integer Sequences",
        "why": "sequence A001599"
      },
      {
        "relation": "is related to",
        "target": "harmonic mean",
        "why": "the defining average"
      }
    ],
    "identifiers": [
      {
        "scheme": "OEIS",
        "value_or_pattern": "A001599",
        "note": "harmonic or Ore numbers"
      }
    ],
    "standards_and_regulation": [
      "No regulation; definitions follow the literature and the OEIS"
    ],
    "failure_modes_and_hazards": [
      "Confusing with arithmetic or refactorable numbers",
      "Presenting the odd conjecture as proven",
      "Errors in computing the harmonic mean"
    ],
    "in_scope": [],
    "out_of_scope": [],
    "characteristics": [],
    "agent_conduct": {
      "may": [
        "Define harmonic divisor numbers and test whether a given integer is one.",
        "Relate them to perfect numbers and cite sequence references.",
        "Explain the conjecture about odd harmonic divisor numbers as still open."
      ],
      "must_not": [
        "Present the conjecture that no odd harmonic divisor number exceeds 1 as proven.",
        "Report a number as a harmonic divisor number without checking its harmonic mean exactly.",
        "Confuse harmonic divisor numbers with arithmetic or refactorable numbers.",
        "Attribute results to Oystein Ore or other mathematicians that they did not publish."
      ],
      "requires_human": [
        "Announcing a claimed proof or counterexample as a new result."
      ]
    },
    "ethics": {
      "considerations": [
        "Accurate attribution respects the mathematicians who did the work.",
        "Overstated claims in number theory mislead students and waste other people's checking time."
      ],
      "affected_parties": [
        "Students and learners",
        "Mathematicians",
        "Readers of references"
      ]
    },
    "owners": {
      "steward": "Nobody owns the concept; the mathematical community and sequence databases maintain the record.",
      "master_systems": []
    }
  },
  "sources": [
    {
      "id": "wikidata",
      "title": "Wikidata item Q60679: harmonic divisor number",
      "url": "https://www.wikidata.org/wiki/Q60679",
      "url_status": "live",
      "what_it_supports": "identity and sense of the item",
      "checked_by": "wikidata-api"
    },
    {
      "id": "wikipedia-en",
      "title": "Wikipedia: Harmonic divisor number",
      "url": "https://en.wikipedia.org/wiki/Harmonic_divisor_number",
      "url_status": "live",
      "what_it_supports": "general description of the item",
      "checked_by": "wikidata-api sitelink"
    }
  ],
  "structure": {
    "bundles": [
      {
        "id": "define",
        "name": "Define",
        "description": "The definition.",
        "rationale": "Precision.",
        "layers": [
          {
            "id": "definition",
            "name": "Definition",
            "description": "Definition.",
            "findings": [
              {
                "id": "definition-finding",
                "name": "Definition",
                "description": "Definition.",
                "questions": [
                  {
                    "text": "What is the harmonic mean of the divisors, and when is it an integer?",
                    "kind": "definition"
                  },
                  {
                    "text": "Is the question about harmonic divisor numbers or a related class?",
                    "kind": "boundary"
                  }
                ]
              }
            ]
          },
          {
            "id": "examples",
            "name": "Examples",
            "description": "Examples.",
            "findings": [
              {
                "id": "examples-finding",
                "name": "Examples",
                "description": "Examples.",
                "questions": [
                  {
                    "text": "What are the harmonic divisor numbers below a given bound?",
                    "kind": "measurement"
                  },
                  {
                    "text": "Which entry fits integer sequences?",
                    "kind": "action"
                  }
                ]
              }
            ]
          }
        ]
      },
      {
        "id": "theory",
        "name": "Theory",
        "description": "Properties.",
        "rationale": "Theory.",
        "layers": [
          {
            "id": "perfect",
            "name": "Perfect",
            "description": "Perfect numbers.",
            "findings": [
              {
                "id": "perfect-finding",
                "name": "Perfect",
                "description": "Perfect.",
                "questions": [
                  {
                    "text": "Why is every perfect number a harmonic divisor number?",
                    "kind": "provenance"
                  },
                  {
                    "text": "Which entry fits perfect numbers?",
                    "kind": "action"
                  }
                ]
              }
            ]
          },
          {
            "id": "conjectures",
            "name": "Conjectures",
            "description": "Open problems.",
            "findings": [
              {
                "id": "conjectures-finding",
                "name": "Conjectures",
                "description": "Conjectures.",
                "questions": [
                  {
                    "text": "What is known and conjectured about odd harmonic divisor numbers and their density?",
                    "kind": "provenance"
                  },
                  {
                    "text": "What is proven versus conjectured?",
                    "kind": "boundary"
                  }
                ]
              }
            ]
          }
        ]
      },
      {
        "id": "compute",
        "name": "Compute",
        "description": "Computation.",
        "rationale": "Computation.",
        "layers": [
          {
            "id": "test",
            "name": "Test",
            "description": "Testing.",
            "findings": [
              {
                "id": "test-finding",
                "name": "Test",
                "description": "Test.",
                "questions": [
                  {
                    "text": "How is an integer tested using the number and sum of divisors?",
                    "kind": "action"
                  },
                  {
                    "text": "What is the result for the number in question?",
                    "kind": "measurement"
                  }
                ]
              }
            ]
          },
          {
            "id": "search",
            "name": "Search",
            "description": "Searches.",
            "findings": [
              {
                "id": "search-finding",
                "name": "Search",
                "description": "Search.",
                "questions": [
                  {
                    "text": "How far have harmonic divisor numbers been enumerated, with attribution?",
                    "kind": "provenance"
                  },
                  {
                    "text": "Which references are standard?",
                    "kind": "provenance"
                  }
                ]
              }
            ]
          }
        ]
      },
      {
        "id": "context",
        "name": "Context",
        "description": "History and teaching.",
        "rationale": "Context.",
        "layers": [
          {
            "id": "history",
            "name": "History",
            "description": "Ore.",
            "findings": [
              {
                "id": "history-finding",
                "name": "History",
                "description": "History.",
                "questions": [
                  {
                    "text": "How did Ore introduce these numbers, and how did later work develop them?",
                    "kind": "provenance"
                  },
                  {
                    "text": "Which entry fits Oystein Ore?",
                    "kind": "action"
                  }
                ]
              }
            ]
          },
          {
            "id": "teach",
            "name": "Teach",
            "description": "Teaching.",
            "findings": [
              {
                "id": "teach-finding",
                "name": "Teach",
                "description": "Teaching.",
                "questions": [
                  {
                    "text": "How are harmonic divisor numbers used in teaching?",
                    "kind": "action"
                  },
                  {
                    "text": "Which misconceptions arise?",
                    "kind": "provenance"
                  }
                ]
              }
            ]
          }
        ]
      }
    ]
  },
  "openQuestions": [
    "Should perfect numbers be linked as the primary related entry?",
    "How should OEIS entries be linked?",
    "How should the odd conjecture be recorded?"
  ],
  "statistics": {
    "bundles": 4,
    "layers": 8,
    "findings": 8,
    "questions": 16
  }
}