{
  "vercy": "1.0-draft",
  "publication": {
    "status": "research-draft",
    "adjudicationStatus": "unreviewed",
    "publishableCanonical": false,
    "generatedAt": "2026-09-12T23:55:53Z",
    "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": "2026-10-06T07:02:59+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-Q3232444",
    "registryId": "vr.tr.achilles-number",
    "name": "Achilles number",
    "version": "0.2.0-wave.3",
    "entryKind": "thing",
    "family": "Thing Registry",
    "domain": [
      "XCT.QTY"
    ],
    "status": "research-draft"
  },
  "canonicalUrl": "https://ver.cy/models/thing/q3232444/",
  "model": {
    "registry_id": "vr.tr.achilles-number",
    "name": "Achilles number",
    "purpose": "Let an agent define Achilles numbers, distinguish them from powerful numbers and perfect powers, give examples, and help test whether a number qualifies.",
    "definition": "A positive integer that is powerful, meaning every prime factor appears at least squared, but is not a perfect power, such as 72, 108, 200, 288, 392, 432, 500, 648, 675 and 800; Achilles numbers are named for the hero who was powerful but imperfect, and they include strong Achilles numbers whose Euler totient is also an Achilles number.",
    "what_it_is_for": "A recreational and number-theoretic classification.",
    "affordances": [
      "define the class and its conditions",
      "distinguish from powerful numbers and perfect powers",
      "give examples",
      "test numbers"
    ],
    "distinguishing_features": [
      "Every prime factor at least squared",
      "Not a perfect power",
      "Named after Achilles",
      "Strong subclass via totient"
    ],
    "appearance": "Not a visible object; integers of a special form.",
    "visual_identification": [
      "Powerful but not a perfect power",
      "Sequence 72, 108, 200, 288, 392",
      "Perfect powers such as 64 are powerful but excluded; squarefree numbers are not powerful"
    ],
    "physical_properties": [
      {
        "quantity": "first terms",
        "typical_range": "72, 108, 200, 288, 392, 432, 500, 648, 675, 800",
        "unit": "sequence",
        "note": ""
      }
    ],
    "families_and_kinds": [
      "Achilles numbers",
      "strong Achilles numbers",
      "powerful numbers as the parent class",
      "perfect powers as the excluded class"
    ],
    "related_models": [
      {
        "relation": "is a kind of",
        "target": "powerful number",
        "why": "in registry terms"
      },
      {
        "relation": "is contrasted with",
        "target": "perfect power",
        "why": "the excluded case"
      },
      {
        "relation": "is related to",
        "target": "Euler totient function",
        "why": "in the strong subclass"
      },
      {
        "relation": "is studied in",
        "target": "recreational mathematics",
        "why": "the field"
      }
    ],
    "identifiers": [
      {
        "scheme": "OEIS",
        "value_or_pattern": "A052486",
        "note": "Achilles numbers"
      }
    ],
    "standards_and_regulation": [
      "No regulation; the OEIS is the reference database"
    ],
    "failure_modes_and_hazards": [
      "Forgetting to exclude perfect powers",
      "Misidentifying powerful numbers",
      "Overstating mathematical significance"
    ],
    "in_scope": [],
    "out_of_scope": [],
    "characteristics": [],
    "agent_conduct": {
      "may": [
        "Define Achilles numbers and check whether a number is one, showing why.",
        "Explain the link to powerful numbers and perfect powers."
      ],
      "must_not": [
        "Forget to exclude perfect powers.",
        "Misidentify powerful numbers.",
        "Overstate the mathematical significance of Achilles numbers.",
        "Confuse the mathematical term with the mythological figure."
      ],
      "requires_human": [
        "Publishing new claimed results."
      ]
    },
    "ethics": {
      "considerations": [
        "Accurate definitions matter for students.",
        "Mathematical play deserves honesty about significance."
      ],
      "affected_parties": [
        "Students",
        "Puzzle enthusiasts"
      ]
    },
    "owners": {
      "steward": "Nobody: a mathematical concept held in common.",
      "master_systems": []
    }
  },
  "sources": [
    {
      "id": "wikidata",
      "title": "Wikidata item Q3232444: Achilles number",
      "url": "https://www.wikidata.org/wiki/Q3232444",
      "url_status": "live",
      "what_it_supports": "identity and sense of the item",
      "checked_by": "wikidata-api"
    },
    {
      "id": "wikipedia-en",
      "title": "Wikipedia: Achilles number",
      "url": "https://en.wikipedia.org/wiki/Achilles_number",
      "url_status": "live",
      "what_it_supports": "general description of the item",
      "checked_by": "wikidata-api sitelink"
    }
  ],
  "structure": {
    "bundles": [
      {
        "id": "define",
        "name": "Define",
        "description": "What Achilles numbers are.",
        "rationale": "Definition.",
        "layers": [
          {
            "id": "definition",
            "name": "Definition",
            "description": "Definition and examples.",
            "findings": [
              {
                "id": "definition-finding",
                "name": "Definition",
                "description": "Definition.",
                "questions": [
                  {
                    "text": "What is an Achilles number, and what are the first examples?",
                    "kind": "definition"
                  },
                  {
                    "text": "Is the number powerful, and is it a perfect power?",
                    "kind": "boundary"
                  }
                ]
              }
            ]
          },
          {
            "id": "relations",
            "name": "Relations",
            "description": "Related classes.",
            "findings": [
              {
                "id": "relations-finding",
                "name": "Relations",
                "description": "Relations.",
                "questions": [
                  {
                    "text": "How do Achilles numbers relate to powerful numbers and perfect powers?",
                    "kind": "definition"
                  },
                  {
                    "text": "Which entry fits powerful number?",
                    "kind": "action"
                  }
                ]
              }
            ]
          }
        ]
      },
      {
        "id": "compute",
        "name": "Compute",
        "description": "Testing and generating.",
        "rationale": "Computation.",
        "layers": [
          {
            "id": "test",
            "name": "Test",
            "description": "Testing a number.",
            "findings": [
              {
                "id": "test-finding",
                "name": "Test",
                "description": "Test.",
                "questions": [
                  {
                    "text": "How is a number tested for the Achilles property by factorisation and exponent gcd?",
                    "kind": "action"
                  },
                  {
                    "text": "Is the number in question an Achilles number?",
                    "kind": "measurement"
                  }
                ]
              }
            ]
          },
          {
            "id": "strong",
            "name": "Strong",
            "description": "Strong Achilles numbers.",
            "findings": [
              {
                "id": "strong-finding",
                "name": "Strong",
                "description": "Strong.",
                "questions": [
                  {
                    "text": "What are strong Achilles numbers, and how are they found?",
                    "kind": "provenance"
                  },
                  {
                    "text": "Which references are standard?",
                    "kind": "provenance"
                  }
                ]
              }
            ]
          }
        ]
      },
      {
        "id": "theory",
        "name": "Theory",
        "description": "Properties.",
        "rationale": "Theory.",
        "layers": [
          {
            "id": "density",
            "name": "Density",
            "description": "Density and structure.",
            "findings": [
              {
                "id": "density-finding",
                "name": "Density",
                "description": "Density.",
                "questions": [
                  {
                    "text": "How are Achilles numbers distributed, and what structure do they have?",
                    "kind": "provenance"
                  },
                  {
                    "text": "Which sources are cited?",
                    "kind": "provenance"
                  }
                ]
              }
            ]
          },
          {
            "id": "related",
            "name": "Related",
            "description": "Related problems.",
            "findings": [
              {
                "id": "related-finding",
                "name": "Related",
                "description": "Related.",
                "questions": [
                  {
                    "text": "How do powerful numbers figure in problems such as consecutive powerful numbers?",
                    "kind": "provenance"
                  },
                  {
                    "text": "Which entry fits the specific problem?",
                    "kind": "action"
                  }
                ]
              }
            ]
          }
        ]
      },
      {
        "id": "context",
        "name": "Context",
        "description": "Naming and status.",
        "rationale": "Context.",
        "layers": [
          {
            "id": "naming",
            "name": "Naming",
            "description": "Naming.",
            "findings": [
              {
                "id": "naming-finding",
                "name": "Naming",
                "description": "Naming.",
                "questions": [
                  {
                    "text": "Why are they named after Achilles, and who introduced the term?",
                    "kind": "provenance"
                  },
                  {
                    "text": "Which entry fits recreational mathematics?",
                    "kind": "action"
                  }
                ]
              }
            ]
          },
          {
            "id": "status",
            "name": "Status",
            "description": "Mathematical status.",
            "findings": [
              {
                "id": "status-finding",
                "name": "Status",
                "description": "Status.",
                "questions": [
                  {
                    "text": "How do mathematicians regard the class, with positions attributed?",
                    "kind": "provenance"
                  },
                  {
                    "text": "Is the presentation neutral?",
                    "kind": "boundary"
                  }
                ]
              }
            ]
          }
        ]
      }
    ]
  },
  "openQuestions": [
    "Should powerful number be the primary entry?",
    "How should the OEIS be linked?",
    "How should the naming story be sourced?"
  ],
  "statistics": {
    "bundles": 4,
    "layers": 8,
    "findings": 8,
    "questions": 16
  }
}