{
  "vercy": "1.0-draft",
  "publication": {
    "status": "research-draft",
    "adjudicationStatus": "unreviewed",
    "publishableCanonical": false,
    "generatedAt": "2026-09-11T21:59:31Z",
    "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": 2,
    "engine": "claude",
    "enrichment": {
      "pass": 3,
      "engine": "claude",
      "producedAt": "2026-10-05T23:50:00Z",
      "ingestedAt": "2026-10-05T20:45:43+00:00",
      "fields": [
        "agent_conduct",
        "ethics",
        "owners"
      ]
    }
  },
  "metaModel": {
    "id": "THING-Q4440864",
    "registryId": "vr.tr.dimension",
    "name": "dimension",
    "version": "0.2.0-wave.2",
    "entryKind": "thing",
    "family": "Thing Registry",
    "domain": [
      "XCT.QLT"
    ],
    "status": "research-draft"
  },
  "canonicalUrl": "https://ver.cy/models/thing/q4440864/",
  "model": {
    "registry_id": "vr.tr.dimension",
    "name": "dimension",
    "purpose": "Let an agent explain mathematical dimension in its various senses, compute or identify the dimension of a given object, separate the measurement sense, and support learning across levels.",
    "definition": "A mathematical property of a space or object giving the number of independent coordinates needed to specify a point, generalised to notions such as the dimension of a vector space, topological and fractal dimensions, the Krull dimension of a ring and other algebraic and analytic dimensions; the word also denotes measured sizes such as length, width and height and, in engineering, specified sizes such as weld leg and throat dimensions.",
    "what_it_is_for": "Degrees of freedom and measured sizes.",
    "affordances": [
      "explain notions of dimension",
      "determine the dimension of a space or object",
      "separate measurement and engineering senses",
      "support learning"
    ],
    "distinguishing_features": [
      "Degrees of freedom",
      "Many generalisations",
      "Integer or fractional",
      "Also a size measure"
    ],
    "appearance": "Not physical; a number attached to a space or a measurement of size.",
    "visual_identification": [
      "Number of independent coordinates",
      "Generalised in many ways",
      "A measured length is the everyday sense"
    ],
    "physical_properties": [],
    "families_and_kinds": [
      "dimension of vector spaces",
      "topological dimension",
      "fractal and Hausdorff dimension",
      "algebraic dimensions such as Krull dimension",
      "measured dimensions and engineering sizes"
    ],
    "related_models": [
      {
        "relation": "is a kind of",
        "target": "mathematical property",
        "why": "category"
      },
      {
        "relation": "is related to",
        "target": "ordered pair",
        "why": "coordinates"
      },
      {
        "relation": "is related to",
        "target": "homomorphism",
        "why": "linear maps and rank"
      },
      {
        "relation": "is related to",
        "target": "intensive quantity",
        "why": "dimensional analysis contrast"
      }
    ],
    "identifiers": [],
    "standards_and_regulation": [
      "Mathematical conventions",
      "Engineering drawing and welding standards for sizes"
    ],
    "failure_modes_and_hazards": [
      "Confusing senses of dimension",
      "Assuming dimension is always an integer",
      "Misreading engineering dimensions"
    ],
    "in_scope": [],
    "out_of_scope": [],
    "characteristics": [],
    "agent_conduct": {
      "may": [
        "Explain which notion of dimension is meant and compute it where it is well defined.",
        "Check that measured dimensions are stated with units and tolerances."
      ],
      "must_not": [
        "Mix up different notions of dimension, such as fractal and topological, without saying so.",
        "Report measured sizes without units or in the wrong units.",
        "Change dimensions on a drawing or specification it is not authorized to edit.",
        "Present a contested or open dimension result as proven."
      ],
      "requires_human": [
        "Approving dimension changes on parts or structures that people depend on for safety."
      ]
    },
    "ethics": {
      "considerations": [
        "Wrong dimensions in engineering can make parts fail or not fit, with safety consequences.",
        "Mathematical claims should be stated precisely so learners are not misled."
      ],
      "affected_parties": [
        "Students and researchers",
        "Engineers and manufacturers",
        "Users of built things"
      ]
    },
    "owners": {
      "steward": "Nobody owns the concept; the author of a drawing or specification answers for its dimensions.",
      "master_systems": []
    }
  },
  "sources": [
    {
      "id": "wikidata",
      "title": "Wikidata item Q4440864: dimension",
      "url": "https://www.wikidata.org/wiki/Q4440864",
      "url_status": "live",
      "what_it_supports": "identity and sense of the item",
      "checked_by": "wikidata-api"
    },
    {
      "id": "wikipedia-en",
      "title": "Wikipedia: Dimension",
      "url": "https://en.wikipedia.org/wiki/Dimension",
      "url_status": "live",
      "what_it_supports": "general description of the item",
      "checked_by": "wikidata-api sitelink"
    }
  ],
  "structure": {
    "bundles": [
      {
        "id": "define",
        "name": "Define",
        "description": "What dimension means.",
        "rationale": "Senses.",
        "layers": [
          {
            "id": "senses",
            "name": "Senses",
            "description": "Which sense.",
            "findings": [
              {
                "id": "senses-finding",
                "name": "Senses",
                "description": "Senses.",
                "questions": [
                  {
                    "text": "Is the mathematical dimension of a space, a measured size, a physical dimension in unit analysis or an engineering specification meant?",
                    "kind": "boundary"
                  },
                  {
                    "text": "Which entry fits?",
                    "kind": "action"
                  }
                ]
              }
            ]
          },
          {
            "id": "basic",
            "name": "Basic",
            "description": "Dimension of a space.",
            "findings": [
              {
                "id": "basic-finding",
                "name": "Basic",
                "description": "Basic notion.",
                "questions": [
                  {
                    "text": "What is the dimension of a vector space or manifold, and why is it well defined?",
                    "kind": "definition"
                  },
                  {
                    "text": "How is the dimension of this object computed?",
                    "kind": "action"
                  }
                ]
              }
            ]
          }
        ]
      },
      {
        "id": "generalise",
        "name": "Generalise",
        "description": "Beyond the basics.",
        "rationale": "Advanced notions.",
        "layers": [
          {
            "id": "topological",
            "name": "Topological",
            "description": "Topological and fractal.",
            "findings": [
              {
                "id": "topological-finding",
                "name": "Topological",
                "description": "Topological and fractal.",
                "questions": [
                  {
                    "text": "What are topological, Hausdorff and box-counting dimensions, and how can dimension be fractional?",
                    "kind": "definition"
                  },
                  {
                    "text": "What is the dimension of a given fractal?",
                    "kind": "action"
                  }
                ]
              }
            ]
          },
          {
            "id": "algebraic",
            "name": "Algebraic",
            "description": "Algebraic dimensions.",
            "findings": [
              {
                "id": "algebraic-finding",
                "name": "Algebraic",
                "description": "Algebraic.",
                "questions": [
                  {
                    "text": "What is the Krull dimension of a ring, and how does it relate to geometric dimension?",
                    "kind": "definition"
                  },
                  {
                    "text": "Which other algebraic dimensions exist?",
                    "kind": "definition"
                  }
                ]
              }
            ]
          }
        ]
      },
      {
        "id": "apply",
        "name": "Apply",
        "description": "Uses.",
        "rationale": "Applications.",
        "layers": [
          {
            "id": "physics",
            "name": "Physics",
            "description": "Dimensions in physics.",
            "findings": [
              {
                "id": "physics-finding",
                "name": "Physics",
                "description": "Physics.",
                "questions": [
                  {
                    "text": "How is dimension used in physics, from spacetime to higher-dimensional theories, with speculative parts attributed?",
                    "kind": "provenance"
                  },
                  {
                    "text": "What is the curse of dimensionality in data?",
                    "kind": "definition"
                  }
                ]
              }
            ]
          },
          {
            "id": "engineering",
            "name": "Engineering",
            "description": "Engineering sizes.",
            "findings": [
              {
                "id": "engineering-finding",
                "name": "Engineering",
                "description": "Engineering.",
                "questions": [
                  {
                    "text": "What do weld dimensions such as leg size, throat thickness and root opening mean, and which standards specify them?",
                    "kind": "provenance"
                  },
                  {
                    "text": "How are dimensions shown on drawings?",
                    "kind": "provenance"
                  }
                ]
              }
            ]
          }
        ]
      },
      {
        "id": "learn",
        "name": "Learn",
        "description": "Teaching.",
        "rationale": "Education.",
        "layers": [
          {
            "id": "teach",
            "name": "Teach",
            "description": "Teaching dimension.",
            "findings": [
              {
                "id": "teach-finding",
                "name": "Teach",
                "description": "Teaching.",
                "questions": [
                  {
                    "text": "How can dimension be taught from coordinates to fractals?",
                    "kind": "action"
                  },
                  {
                    "text": "Which misconceptions arise?",
                    "kind": "provenance"
                  }
                ]
              }
            ]
          },
          {
            "id": "history",
            "name": "History",
            "description": "History.",
            "findings": [
              {
                "id": "history-finding",
                "name": "History",
                "description": "History.",
                "questions": [
                  {
                    "text": "How did the concept of dimension develop, from Euclid to Cantor, Hausdorff and beyond?",
                    "kind": "provenance"
                  },
                  {
                    "text": "Which references are standard?",
                    "kind": "provenance"
                  }
                ]
              }
            ]
          }
        ]
      }
    ]
  },
  "openQuestions": [
    "Should each notion of dimension be a separate entry?",
    "How should engineering standards be linked?",
    "How should physical dimension analysis be linked?"
  ],
  "statistics": {
    "bundles": 4,
    "layers": 8,
    "findings": 8,
    "questions": 16
  }
}