{
  "vercy": "1.0-draft",
  "publication": {
    "status": "research-draft",
    "adjudicationStatus": "unreviewed",
    "publishableCanonical": false,
    "generatedAt": "2026-09-13T01:23:35Z",
    "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": "2026-10-06T06:59:39+00:00",
      "fields": [
        "agent_conduct",
        "ethics",
        "owners"
      ]
    },
    "gate": {
      "passed": true,
      "version": "1.0",
      "at": "2026-10-06T19:51:58+00:00",
      "evidence": [
        "completeness 1.00",
        "sense: Wikidata description",
        "2 live sources",
        "review by codex: pass"
      ]
    }
  },
  "metaModel": {
    "id": "THING-Q3280976",
    "registryId": "vr.tr.superabundant-number",
    "name": "superabundant number",
    "version": "0.2.0-wave.3",
    "entryKind": "thing",
    "family": "Thing Registry",
    "domain": [
      "XCT.QTY"
    ],
    "status": "research-draft"
  },
  "canonicalUrl": "https://ver.cy/models/thing/q3280976/",
  "model": {
    "registry_id": "vr.tr.superabundant-number",
    "name": "superabundant number",
    "purpose": "Let an agent define superabundant numbers, relay their sequence and properties from number theory references, explain their link to the Riemann hypothesis, and distinguish them from highly abundant and colossally abundant numbers.",
    "definition": "A positive integer n for which the ratio of the sum of its divisors to n itself is greater than that ratio for every smaller positive integer, the sequence beginning 1, 2, 4, 6, 12, 24, 36, 48, 60, 120, 180, 240, 360; superabundant numbers were defined by Alaoglu and Erdos in 1944, are all highly abundant, are closely related to colossally abundant numbers, and connect to the Riemann hypothesis through Robin inequality.",
    "what_it_is_for": "Not applicable; a class of integers.",
    "affordances": [
      "define and list",
      "relay properties",
      "explain the Riemann link",
      "distinguish related classes"
    ],
    "distinguishing_features": [
      "Record abundancy ratio",
      "Prime factorisation structure",
      "Robin inequality link",
      "Subset of highly abundant numbers"
    ],
    "appearance": "The sequence 1, 2, 4, 6, 12, 24, 36, 48, 60, 120, ...",
    "visual_identification": [
      "Record values of sigma(n)/n",
      "Sequence OEIS A004394",
      "Highly abundant numbers set records for sigma(n); colossally abundant numbers use a stricter criterion"
    ],
    "physical_properties": [
      {
        "quantity": "smallest",
        "typical_range": "1",
        "unit": "number",
        "note": ""
      }
    ],
    "families_and_kinds": [
      "superabundant numbers in general",
      "colossally abundant numbers as a subsequence",
      "highly abundant numbers as the containing class",
      "highly composite numbers as a related class"
    ],
    "related_models": [
      {
        "relation": "is a kind of",
        "target": "highly abundant number",
        "why": "in registry terms"
      },
      {
        "relation": "is defined by",
        "target": "divisor function",
        "why": "sigma(n)/n"
      },
      {
        "relation": "is related to",
        "target": "Riemann hypothesis",
        "why": "through Robin inequality"
      },
      {
        "relation": "is listed in",
        "target": "OEIS",
        "why": "as A004394"
      }
    ],
    "identifiers": [
      {
        "scheme": "OEIS",
        "value_or_pattern": "A004394",
        "note": ""
      }
    ],
    "standards_and_regulation": [
      "No regulation; mathematical conventions"
    ],
    "failure_modes_and_hazards": [
      "Confusing with highly abundant or highly composite numbers",
      "Overstating the Riemann hypothesis connection",
      "Computation errors"
    ],
    "in_scope": [],
    "out_of_scope": [],
    "characteristics": [],
    "agent_conduct": {
      "may": [
        "Compute, list and verify superabundant numbers.",
        "Explain their relation to highly composite numbers and the Riemann hypothesis."
      ],
      "must_not": [
        "Claim that a computation proves or disproves the Riemann hypothesis without peer review.",
        "Present unverified terms of the sequence as checked.",
        "Attribute results to mathematicians without sources."
      ],
      "requires_human": [
        "Publishing claims of a new mathematical result."
      ]
    },
    "ethics": {
      "considerations": [
        "Bold claims about famous open problems can mislead students and the public.",
        "Mathematicians' credit for results deserves accurate attribution."
      ],
      "affected_parties": [
        "Students",
        "Mathematicians",
        "Readers of popular mathematics"
      ]
    },
    "owners": {
      "steward": "Nobody owns a number sequence; it belongs to shared mathematical knowledge.",
      "master_systems": [
        "Integer sequence databases"
      ]
    }
  },
  "sources": [
    {
      "id": "wikidata",
      "title": "Wikidata item Q3280976: superabundant number",
      "url": "https://www.wikidata.org/wiki/Q3280976",
      "url_status": "live",
      "what_it_supports": "identity and sense of the item",
      "checked_by": "wikidata-api"
    },
    {
      "id": "wikipedia-en",
      "title": "Wikipedia: Superabundant number",
      "url": "https://en.wikipedia.org/wiki/Superabundant_number",
      "url_status": "live",
      "what_it_supports": "general description of the item",
      "checked_by": "wikidata-api sitelink"
    }
  ],
  "structure": {
    "bundles": [
      {
        "id": "define",
        "name": "Define",
        "description": "Definition.",
        "rationale": "Mathematics.",
        "layers": [
          {
            "id": "definition",
            "name": "Definition",
            "description": "Definition.",
            "findings": [
              {
                "id": "definition-finding",
                "name": "Definition",
                "description": "Definition.",
                "questions": [
                  {
                    "text": "What is a superabundant number, and how is it checked?",
                    "kind": "definition"
                  },
                  {
                    "text": "Is the question about superabundant, highly abundant or colossally abundant numbers?",
                    "kind": "boundary"
                  }
                ]
              }
            ]
          },
          {
            "id": "sequence",
            "name": "Sequence",
            "description": "Sequence.",
            "findings": [
              {
                "id": "sequence-finding",
                "name": "Sequence",
                "description": "Sequence.",
                "questions": [
                  {
                    "text": "What are the first superabundant numbers, and where is the sequence catalogued?",
                    "kind": "measurement"
                  },
                  {
                    "text": "Which entry fits divisor function?",
                    "kind": "action"
                  }
                ]
              }
            ]
          }
        ]
      },
      {
        "id": "results",
        "name": "Results",
        "description": "Results.",
        "rationale": "Mathematics.",
        "layers": [
          {
            "id": "structure",
            "name": "Structure",
            "description": "Structure.",
            "findings": [
              {
                "id": "structure-finding",
                "name": "Structure",
                "description": "Structure.",
                "questions": [
                  {
                    "text": "What did Alaoglu and Erdos prove about the prime factorisation of superabundant numbers?",
                    "kind": "provenance"
                  },
                  {
                    "text": "Which references are standard?",
                    "kind": "provenance"
                  }
                ]
              }
            ]
          },
          {
            "id": "riemann",
            "name": "Riemann",
            "description": "Riemann hypothesis link.",
            "findings": [
              {
                "id": "riemann-finding",
                "name": "Riemann",
                "description": "Riemann.",
                "questions": [
                  {
                    "text": "How does Robin inequality connect superabundant and colossally abundant numbers to the Riemann hypothesis?",
                    "kind": "provenance"
                  },
                  {
                    "text": "Which entry fits Robin theorem?",
                    "kind": "action"
                  }
                ]
              }
            ]
          }
        ]
      },
      {
        "id": "compute",
        "name": "Compute",
        "description": "Computation.",
        "rationale": "Practice.",
        "layers": [
          {
            "id": "algorithms",
            "name": "Algorithms",
            "description": "Algorithms.",
            "findings": [
              {
                "id": "algorithms-finding",
                "name": "Algorithms",
                "description": "Algorithms.",
                "questions": [
                  {
                    "text": "How are superabundant numbers computed, and how far have they been enumerated?",
                    "kind": "provenance"
                  },
                  {
                    "text": "Which sources are cited?",
                    "kind": "provenance"
                  }
                ]
              }
            ]
          },
          {
            "id": "related",
            "name": "Related",
            "description": "Related classes.",
            "findings": [
              {
                "id": "related-finding",
                "name": "Related",
                "description": "Related.",
                "questions": [
                  {
                    "text": "How do superabundant numbers relate to highly composite and colossally abundant numbers?",
                    "kind": "provenance"
                  },
                  {
                    "text": "Which entry fits colossally abundant number?",
                    "kind": "action"
                  }
                ]
              }
            ]
          }
        ]
      },
      {
        "id": "context",
        "name": "Context",
        "description": "History.",
        "rationale": "Context.",
        "layers": [
          {
            "id": "history",
            "name": "History",
            "description": "History.",
            "findings": [
              {
                "id": "history-finding",
                "name": "History",
                "description": "History.",
                "questions": [
                  {
                    "text": "How did Ramanujan, Alaoglu and Erdos develop the study of these numbers?",
                    "kind": "provenance"
                  },
                  {
                    "text": "Which entry fits the history of number theory?",
                    "kind": "action"
                  }
                ]
              }
            ]
          },
          {
            "id": "open",
            "name": "Open",
            "description": "Open questions.",
            "findings": [
              {
                "id": "open-finding",
                "name": "Open",
                "description": "Open.",
                "questions": [
                  {
                    "text": "What open problems exist about superabundant numbers?",
                    "kind": "provenance"
                  },
                  {
                    "text": "Which entry fits open problems in number theory?",
                    "kind": "action"
                  }
                ]
              }
            ]
          }
        ]
      }
    ]
  },
  "openQuestions": [
    "Are all superabundant numbers beyond some point colossally abundant or not?",
    "How should OEIS and literature be linked?",
    "How should the Riemann link be presented accurately?"
  ],
  "statistics": {
    "bundles": 4,
    "layers": 8,
    "findings": 8,
    "questions": 16
  }
}