{
  "vercy": "1.0-draft",
  "publication": {
    "status": "research-draft",
    "adjudicationStatus": "unreviewed",
    "publishableCanonical": false,
    "generatedAt": "2026-09-13T01:10:31Z",
    "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": "2026-10-06T07:04:07+00:00",
      "fields": [
        "agent_conduct",
        "ethics",
        "owners"
      ]
    },
    "gate": {
      "passed": true,
      "version": "1.0",
      "at": "2026-10-06T19:51:53+00:00",
      "evidence": [
        "completeness 1.00",
        "sense: Wikidata description",
        "2 live sources",
        "review by codex: pass"
      ]
    }
  },
  "metaModel": {
    "id": "THING-Q1193504",
    "registryId": "vr.tr.untouchable-number",
    "name": "untouchable number",
    "version": "0.2.0-wave.3",
    "entryKind": "thing",
    "family": "Thing Registry",
    "domain": [
      "XCT.QTY"
    ],
    "status": "research-draft"
  },
  "canonicalUrl": "https://ver.cy/models/thing/q1193504/",
  "model": {
    "registry_id": "vr.tr.untouchable-number",
    "name": "untouchable number",
    "purpose": "Let an agent define untouchable numbers, relay their sequence, known results and open conjectures from number theory references, and distinguish them from related concepts such as aliquot sequences and perfect numbers.",
    "definition": "A positive integer that cannot be expressed as the sum of all the proper divisors of any positive integer, that is, one that is not the aliquot sum of any number, the sequence beginning 2, 5, 52, 88, 96, 120, 124, 146; Erdos proved there are infinitely many untouchable numbers, 5 is conjectured to be the only odd one, a claim that follows from a strong form of the Goldbach conjecture, and the numbers are catalogued in the OEIS.",
    "what_it_is_for": "Not applicable; a class of integers.",
    "affordances": [
      "define and list",
      "relay known results",
      "relay conjectures",
      "distinguish related concepts"
    ],
    "distinguishing_features": [
      "Defined via aliquot sums",
      "Infinitely many",
      "Link to Goldbach conjecture",
      "Mostly even"
    ],
    "appearance": "The sequence 2, 5, 52, 88, 96, 120, 124, 146, ...",
    "visual_identification": [
      "Integers that are no number aliquot sum",
      "Sequence OEIS A005114",
      "Perfect numbers equal their own aliquot sum; abundant numbers are less than it"
    ],
    "physical_properties": [
      {
        "quantity": "smallest",
        "typical_range": "2",
        "unit": "number",
        "note": ""
      },
      {
        "quantity": "only known odd",
        "typical_range": "5",
        "unit": "number",
        "note": "conjectured unique"
      }
    ],
    "families_and_kinds": [
      "untouchable numbers in general",
      "the odd untouchable number 5",
      "related classes: aliquot sequences, perfect, abundant and deficient numbers"
    ],
    "related_models": [
      {
        "relation": "is a kind of",
        "target": "positive integer",
        "why": "in registry terms"
      },
      {
        "relation": "is defined by",
        "target": "aliquot sum",
        "why": "the sum of proper divisors"
      },
      {
        "relation": "is related to",
        "target": "Goldbach conjecture",
        "why": "through the odd case"
      },
      {
        "relation": "is listed in",
        "target": "OEIS",
        "why": "as A005114"
      }
    ],
    "identifiers": [
      {
        "scheme": "OEIS",
        "value_or_pattern": "A005114",
        "note": ""
      }
    ],
    "standards_and_regulation": [
      "No regulation; mathematical conventions"
    ],
    "failure_modes_and_hazards": [
      "Confusing with other divisor-based classes",
      "Stating conjectures as theorems",
      "Computation errors"
    ],
    "in_scope": [],
    "out_of_scope": [],
    "characteristics": [],
    "agent_conduct": {
      "may": [
        "State the defining property of untouchable numbers and the start of the sequence.",
        "Test whether a given number is untouchable within stated computational limits."
      ],
      "must_not": [
        "State a number is untouchable without a proof or a cited verified result.",
        "Present the infinitude result without naming the proof it rests on.",
        "Confuse untouchable numbers with other aliquot sequence notions such as amicable or perfect numbers.",
        "Publish computed sequence terms as verified when the search bound is unstated."
      ],
      "requires_human": [
        "Publishing a claimed new result about the sequence."
      ]
    },
    "ethics": {
      "considerations": [
        "Published number sequences are reused by others, so unverified terms spread errors.",
        "Credit for mathematical results belongs to those who proved them."
      ],
      "affected_parties": [
        "Mathematicians",
        "Students",
        "Maintainers of sequence databases"
      ]
    },
    "owners": {
      "steward": "Nobody owns a mathematical fact; sequence databases record it by convention.",
      "master_systems": []
    }
  },
  "sources": [
    {
      "id": "wikidata",
      "title": "Wikidata item Q1193504: untouchable number",
      "url": "https://www.wikidata.org/wiki/Q1193504",
      "url_status": "live",
      "what_it_supports": "identity and sense of the item",
      "checked_by": "wikidata-api"
    },
    {
      "id": "wikipedia-en",
      "title": "Wikipedia: Untouchable number",
      "url": "https://en.wikipedia.org/wiki/Untouchable_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 an untouchable number, and how is it checked?",
                    "kind": "definition"
                  },
                  {
                    "text": "Is the question about untouchable numbers or another divisor-based class?",
                    "kind": "boundary"
                  }
                ]
              }
            ]
          },
          {
            "id": "sequence",
            "name": "Sequence",
            "description": "Sequence.",
            "findings": [
              {
                "id": "sequence-finding",
                "name": "Sequence",
                "description": "Sequence.",
                "questions": [
                  {
                    "text": "What are the first untouchable numbers, and where is the sequence catalogued?",
                    "kind": "measurement"
                  },
                  {
                    "text": "Which entry fits aliquot sum?",
                    "kind": "action"
                  }
                ]
              }
            ]
          }
        ]
      },
      {
        "id": "results",
        "name": "Results",
        "description": "Results and conjectures.",
        "rationale": "Mathematics.",
        "layers": [
          {
            "id": "theorems",
            "name": "Theorems",
            "description": "Known results.",
            "findings": [
              {
                "id": "theorems-finding",
                "name": "Theorems",
                "description": "Theorems.",
                "questions": [
                  {
                    "text": "What did Erdos prove about infinitude, and what density results exist?",
                    "kind": "provenance"
                  },
                  {
                    "text": "Which references are standard?",
                    "kind": "provenance"
                  }
                ]
              }
            ]
          },
          {
            "id": "conjectures",
            "name": "Conjectures",
            "description": "Conjectures.",
            "findings": [
              {
                "id": "conjectures-finding",
                "name": "Conjectures",
                "description": "Conjectures.",
                "questions": [
                  {
                    "text": "Why does the uniqueness of 5 follow from a strong Goldbach conjecture?",
                    "kind": "provenance"
                  },
                  {
                    "text": "Which entry fits Goldbach conjecture?",
                    "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 untouchable 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 untouchable numbers relate to aliquot sequences, perfect and amicable numbers?",
                    "kind": "provenance"
                  },
                  {
                    "text": "Which entry fits aliquot sequence?",
                    "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": "When were untouchable numbers introduced and studied?",
                    "kind": "provenance"
                  },
                  {
                    "text": "Which entry fits the history of number theory?",
                    "kind": "action"
                  }
                ]
              }
            ]
          },
          {
            "id": "recreational",
            "name": "Recreational",
            "description": "Recreational mathematics.",
            "findings": [
              {
                "id": "recreational-finding",
                "name": "Recreational",
                "description": "Recreational.",
                "questions": [
                  {
                    "text": "How do untouchable numbers appear in recreational mathematics?",
                    "kind": "provenance"
                  },
                  {
                    "text": "Which entry fits recreational mathematics?",
                    "kind": "action"
                  }
                ]
              }
            ]
          }
        ]
      }
    ]
  },
  "openQuestions": [
    "Is 5 the only odd untouchable number?",
    "How should OEIS and literature be linked?",
    "What is the asymptotic density of untouchable numbers?"
  ],
  "statistics": {
    "bundles": 4,
    "layers": 8,
    "findings": 8,
    "questions": 16
  }
}