{
  "vercy": "1.0-draft",
  "publication": {
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    "adjudicationStatus": "unreviewed",
    "publishableCanonical": false,
    "generatedAt": "2026-09-12T06:14:37Z",
    "providers": [
      "Claude"
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    "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": "2026-10-06T00:10:00Z",
      "ingestedAt": "2026-10-05T20:53:16+00:00",
      "fields": [
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        "owners"
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        "review by codex: pass"
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  "metaModel": {
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    "registryId": "vr.tr.logarithm",
    "name": "logarithm",
    "version": "0.2.0-wave.2",
    "entryKind": "thing",
    "family": "Thing Registry",
    "domain": [
      "XCT.QLT"
    ],
    "status": "research-draft"
  },
  "canonicalUrl": "https://ver.cy/models/thing/q11197/",
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    "registry_id": "vr.tr.logarithm",
    "name": "logarithm",
    "purpose": "Let an agent explain logarithms and their definition, properties and bases, support calculations and use of logarithmic scales, describe applications in science, statistics and computing, and support learning.",
    "definition": "The exponent to which a fixed base must be raised to produce a given number, the inverse of exponentiation, in forms such as the common logarithm to base ten, the natural logarithm to base e and the binary logarithm to base two, with properties turning multiplication into addition and powers into products, and extensions such as complex and discrete logarithms; logarithms underlie logarithmic scales such as decibels and pH, log-likelihood and log probability in statistics, and computation from slide rules to algorithms.",
    "what_it_is_for": "Inverse of exponentiation.",
    "affordances": [
      "explain definition and properties",
      "support calculations",
      "describe applications",
      "support learning"
    ],
    "distinguishing_features": [
      "Inverse of powers",
      "Product to sum rule",
      "Choice of base",
      "Logarithmic scales"
    ],
    "appearance": "Not physical; a mathematical function.",
    "visual_identification": [
      "Exponent giving a number from a base",
      "Common, natural, binary, discrete, complex logarithms",
      "An exponential is the inverse; a root is a different inverse of powers"
    ],
    "physical_properties": [],
    "families_and_kinds": [
      "common logarithm",
      "natural logarithm",
      "binary logarithm",
      "discrete logarithm",
      "complex logarithm and logarithmic units"
    ],
    "related_models": [
      {
        "relation": "is a kind of",
        "target": "transcendental function",
        "why": "category"
      },
      {
        "relation": "is a kind of",
        "target": "multivalued function",
        "why": "category"
      },
      {
        "relation": "is related to",
        "target": "root",
        "why": "another inverse of exponentiation"
      },
      {
        "relation": "is related to",
        "target": "trillion",
        "why": "large numbers expressed on logarithmic scales"
      }
    ],
    "identifiers": [],
    "standards_and_regulation": [
      "Mathematical notation conventions",
      "Standards for logarithmic units such as the decibel",
      "Curriculum standards for algebra"
    ],
    "failure_modes_and_hazards": [
      "Confusing bases",
      "Misreading logarithmic scales",
      "Domain errors with zero and negatives"
    ],
    "in_scope": [],
    "out_of_scope": [],
    "characteristics": [],
    "agent_conduct": {
      "may": [
        "Explain logarithms, their bases, rules and uses.",
        "Compute logarithms and show the working."
      ],
      "must_not": [
        "Present numerical results without stating the base when it matters.",
        "Mislead with a logarithmic scale presented as linear, or the reverse.",
        "Give results beyond the precision the input supports."
      ],
      "requires_human": [
        "Relying on a computed value for engineering, dosing or financial decisions."
      ]
    },
    "ethics": {
      "considerations": [
        "Log scales on charts can hide or exaggerate risk, for example in epidemics or earthquakes.",
        "Misunderstood exponential growth leads to poor public decisions."
      ],
      "affected_parties": [
        "Students",
        "Readers of charts"
      ]
    },
    "owners": {
      "steward": "Nobody: a mathematical concept held in common.",
      "master_systems": []
    }
  },
  "sources": [
    {
      "id": "wikidata",
      "title": "Wikidata item Q11197: logarithm",
      "url": "https://www.wikidata.org/wiki/Q11197",
      "url_status": "live",
      "what_it_supports": "identity and sense of the item",
      "checked_by": "wikidata-api"
    },
    {
      "id": "wikipedia-en",
      "title": "Wikipedia: Logarithm",
      "url": "https://en.wikipedia.org/wiki/Logarithm",
      "url_status": "live",
      "what_it_supports": "general description of the item",
      "checked_by": "wikidata-api sitelink"
    }
  ],
  "structure": {
    "bundles": [
      {
        "id": "understand",
        "name": "Understand",
        "description": "What a logarithm is.",
        "rationale": "Mathematics.",
        "layers": [
          {
            "id": "concept",
            "name": "Concept",
            "description": "Definition and bases.",
            "findings": [
              {
                "id": "concept-finding",
                "name": "Concept",
                "description": "Concept.",
                "questions": [
                  {
                    "text": "What is a logarithm, and how do common, natural and binary logarithms differ?",
                    "kind": "definition"
                  },
                  {
                    "text": "Which base is meant?",
                    "kind": "boundary"
                  }
                ]
              }
            ]
          },
          {
            "id": "properties",
            "name": "Properties",
            "description": "Properties.",
            "findings": [
              {
                "id": "properties-finding",
                "name": "Properties",
                "description": "Properties.",
                "questions": [
                  {
                    "text": "What are the product, quotient, power and change of base rules, and why do they hold?",
                    "kind": "definition"
                  },
                  {
                    "text": "Which entry fits exponentials?",
                    "kind": "action"
                  }
                ]
              }
            ]
          }
        ]
      },
      {
        "id": "calculate",
        "name": "Calculate",
        "description": "Calculation and scales.",
        "rationale": "Practice.",
        "layers": [
          {
            "id": "compute",
            "name": "Compute",
            "description": "Computing logarithms.",
            "findings": [
              {
                "id": "compute-finding",
                "name": "Compute",
                "description": "Computation.",
                "questions": [
                  {
                    "text": "How can this logarithm be computed or an equation with logarithms solved?",
                    "kind": "action"
                  },
                  {
                    "text": "Which entry fits solving equations?",
                    "kind": "action"
                  }
                ]
              }
            ]
          },
          {
            "id": "scales",
            "name": "Scales",
            "description": "Logarithmic scales.",
            "findings": [
              {
                "id": "scales-finding",
                "name": "Scales",
                "description": "Scales.",
                "questions": [
                  {
                    "text": "How do logarithmic scales such as decibels, pH and earthquake magnitude work, and how are they read?",
                    "kind": "provenance"
                  },
                  {
                    "text": "Which entry fits a specific scale?",
                    "kind": "action"
                  }
                ]
              }
            ]
          }
        ]
      },
      {
        "id": "apply",
        "name": "Apply",
        "description": "Applications.",
        "rationale": "Applications.",
        "layers": [
          {
            "id": "statistics",
            "name": "Statistics",
            "description": "Statistics and science.",
            "findings": [
              {
                "id": "statistics-finding",
                "name": "Statistics",
                "description": "Statistics.",
                "questions": [
                  {
                    "text": "How are log-likelihood, log probability and log transformations used in statistics and science?",
                    "kind": "provenance"
                  },
                  {
                    "text": "Which entry fits likelihood?",
                    "kind": "action"
                  }
                ]
              }
            ]
          },
          {
            "id": "computing",
            "name": "Computing",
            "description": "Computing and cryptography.",
            "findings": [
              {
                "id": "computing-finding",
                "name": "Computing",
                "description": "Computing.",
                "questions": [
                  {
                    "text": "How do binary logarithms describe algorithm complexity, and what is the discrete logarithm problem in cryptography?",
                    "kind": "provenance"
                  },
                  {
                    "text": "Which entry fits computational complexity?",
                    "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 Napier and others develop logarithms, and how did tables and slide rules transform calculation?",
                    "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 logarithms be taught?",
                    "kind": "action"
                  },
                  {
                    "text": "Which misconceptions arise?",
                    "kind": "provenance"
                  }
                ]
              }
            ]
          }
        ]
      }
    ]
  },
  "openQuestions": [
    "Should the natural logarithm be a separate entry?",
    "How should textbooks be linked?",
    "How should scale standards be linked?"
  ],
  "statistics": {
    "bundles": 4,
    "layers": 8,
    "findings": 8,
    "questions": 16
  }
}