{
  "vercy": "1.0-draft",
  "publication": {
    "status": "research-draft",
    "adjudicationStatus": "unreviewed",
    "publishableCanonical": false,
    "generatedAt": "2026-09-11T12:56:33Z",
    "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": 1,
    "engine": "claude",
    "enrichment": {
      "pass": 3,
      "engine": "claude",
      "producedAt": "2026-10-05T18:00:00Z",
      "ingestedAt": "2026-10-05T13:27:07+00:00",
      "fields": [
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        "ethics",
        "owners",
        "standards_and_regulation"
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      "at": "2026-10-06T19:51:54+00:00",
      "evidence": [
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        "review by codex: pass"
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  "metaModel": {
    "id": "THING-Q1357788",
    "registryId": "vr.tr.angular-measure",
    "name": "angular measure",
    "version": "0.2.0-wave.1",
    "entryKind": "thing",
    "family": "Thing Registry",
    "domain": [
      "XCT.QLT"
    ],
    "status": "research-draft"
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  "canonicalUrl": "https://ver.cy/models/thing/q1357788/",
  "model": {
    "registry_id": "vr.tr.angular-measure",
    "name": "angular measure",
    "purpose": "Let an agent explain angular measures by unit, conversion, measurement and application in mathematics, physics, navigation and astronomy.",
    "definition": "A measure of the size of an angle or of a rotation, expressed in units such as the radian (the SI unit), degree, gradian, turn and arcminute or arcsecond; a full turn equals 360 degrees or 2 pi radians, and related quantities include phase angle and angular displacement.",
    "what_it_is_for": "Describing angles and rotations.",
    "affordances": [
      "convert between degrees, radians and other units",
      "measure angles with instruments",
      "use angles in trigonometry and physics",
      "read angular sizes in astronomy"
    ],
    "distinguishing_features": [
      "Measures rotation or opening",
      "Radian is dimensionless in SI",
      "Many units",
      "Used across sciences"
    ],
    "appearance": "Not physical; shown on protractors, dials, compasses and in formulas.",
    "visual_identification": [
      "Symbols such as deg, rad and arcsec",
      "Protractors and theodolites",
      "Slope as a percentage is a different measure"
    ],
    "physical_properties": [
      {
        "quantity": "full turn",
        "typical_range": "360 or 2 pi",
        "unit": "degrees or rad",
        "note": "exact"
      }
    ],
    "families_and_kinds": [
      "plane angles",
      "solid angles (steradian)",
      "phase angles",
      "angular displacement",
      "angles of scattering and diffraction"
    ],
    "related_models": [
      {
        "relation": "is a kind of",
        "target": "geometric measure",
        "why": "category"
      },
      {
        "relation": "is measured in",
        "target": "radian",
        "why": "unit"
      },
      {
        "relation": "is used in",
        "target": "trigonometry",
        "why": "field"
      },
      {
        "relation": "is measured by",
        "target": "protractor and theodolite",
        "why": "instrument"
      }
    ],
    "identifiers": [
      {
        "scheme": "SI unit",
        "value_or_pattern": "radian (rad)",
        "note": "plane angle"
      }
    ],
    "standards_and_regulation": [
      "SI Brochure (BIPM)",
      "ISO 80000-3 space and time quantities"
    ],
    "failure_modes_and_hazards": [
      "Mixing degrees and radians in calculations",
      "Sign and direction conventions"
    ],
    "in_scope": [],
    "out_of_scope": [],
    "characteristics": [],
    "agent_conduct": {
      "may": [
        "Convert and report angles between units with stated precision.",
        "Check that angular inputs to calculations use the expected unit."
      ],
      "must_not": [
        "Mix degrees and radians silently in calculations that control machines or navigation.",
        "Round angles in a way that hides errors relevant to safety.",
        "Present an angle without its unit where it could be misread."
      ],
      "requires_human": [
        "Changing angular settings on machinery, antennas or vehicles that people rely on."
      ]
    },
    "ethics": {
      "considerations": [
        "Unit confusion in angles has caused failures in engineering and navigation.",
        "Shared units let people across fields and countries check each other's work."
      ],
      "affected_parties": [
        "Engineers and navigators",
        "People relying on systems built with these measures"
      ]
    },
    "owners": {
      "steward": "Nobody owns it; the international metrology bodies define the SI unit.",
      "master_systems": []
    }
  },
  "sources": [
    {
      "id": "wikidata",
      "title": "Wikidata item Q1357788: angular measure",
      "url": "https://www.wikidata.org/wiki/Q1357788",
      "url_status": "live",
      "what_it_supports": "identity and sense of the item",
      "checked_by": "wikidata-api"
    },
    {
      "id": "wikipedia-en",
      "title": "Wikipedia: Angular distance",
      "url": "https://en.wikipedia.org/wiki/Angular_distance",
      "url_status": "live",
      "what_it_supports": "general description of the item",
      "checked_by": "wikidata-api sitelink"
    }
  ],
  "structure": {
    "bundles": [
      {
        "id": "units",
        "name": "Units",
        "description": "Which unit.",
        "rationale": "Units must be clear.",
        "layers": [
          {
            "id": "convert",
            "name": "Convert",
            "description": "Conversion.",
            "findings": [
              {
                "id": "convert-finding",
                "name": "Convert",
                "description": "Conversion.",
                "questions": [
                  {
                    "text": "What is this angle in radians or degrees?",
                    "kind": "measurement"
                  },
                  {
                    "text": "How precise must it be?",
                    "kind": "boundary"
                  }
                ]
              }
            ]
          },
          {
            "id": "small",
            "name": "Small angles",
            "description": "Arcminutes and arcseconds.",
            "findings": [
              {
                "id": "small-finding",
                "name": "Small angles",
                "description": "Small angles.",
                "questions": [
                  {
                    "text": "How are arcminutes and arcseconds used?",
                    "kind": "definition"
                  },
                  {
                    "text": "What is this in decimal degrees?",
                    "kind": "measurement"
                  }
                ]
              }
            ]
          }
        ]
      },
      {
        "id": "measure",
        "name": "Measure",
        "description": "Instruments.",
        "rationale": "Instruments differ.",
        "layers": [
          {
            "id": "instrument",
            "name": "Instrument",
            "description": "Tools.",
            "findings": [
              {
                "id": "instrument-finding",
                "name": "Instrument",
                "description": "Instruments.",
                "questions": [
                  {
                    "text": "Which instrument measures this angle to the required accuracy?",
                    "kind": "provenance"
                  },
                  {
                    "text": "How is it calibrated?",
                    "kind": "provenance"
                  }
                ]
              }
            ]
          },
          {
            "id": "convention",
            "name": "Convention",
            "description": "Direction and sign.",
            "findings": [
              {
                "id": "convention-finding",
                "name": "Convention",
                "description": "Conventions.",
                "questions": [
                  {
                    "text": "Is the angle measured clockwise or anticlockwise, and from which reference?",
                    "kind": "definition"
                  },
                  {
                    "text": "How are negative angles treated?",
                    "kind": "definition"
                  }
                ]
              }
            ]
          }
        ]
      },
      {
        "id": "mathematics",
        "name": "Mathematics",
        "description": "Trigonometry.",
        "rationale": "Angles feed formulas.",
        "layers": [
          {
            "id": "trig",
            "name": "Trigonometry",
            "description": "Functions.",
            "findings": [
              {
                "id": "trig-finding",
                "name": "Trigonometry",
                "description": "Trigonometry.",
                "questions": [
                  {
                    "text": "What are the sine, cosine and tangent of this angle?",
                    "kind": "measurement"
                  },
                  {
                    "text": "Is the calculator in degree or radian mode?",
                    "kind": "boundary"
                  }
                ]
              }
            ]
          },
          {
            "id": "radian",
            "name": "Radian",
            "description": "Why radians.",
            "findings": [
              {
                "id": "radian-finding",
                "name": "Radian",
                "description": "Radians.",
                "questions": [
                  {
                    "text": "Why are radians natural in calculus?",
                    "kind": "definition"
                  },
                  {
                    "text": "How is a radian defined?",
                    "kind": "definition"
                  }
                ]
              }
            ]
          }
        ]
      },
      {
        "id": "applications",
        "name": "Applications",
        "description": "Uses.",
        "rationale": "Angles are everywhere.",
        "layers": [
          {
            "id": "navigation",
            "name": "Navigation",
            "description": "Bearings.",
            "findings": [
              {
                "id": "navigation-finding",
                "name": "Navigation",
                "description": "Bearings.",
                "questions": [
                  {
                    "text": "How are bearings expressed in navigation?",
                    "kind": "definition"
                  },
                  {
                    "text": "What is the difference between true and magnetic bearings?",
                    "kind": "definition"
                  }
                ]
              }
            ]
          },
          {
            "id": "astronomy",
            "name": "Astronomy",
            "description": "Angular size.",
            "findings": [
              {
                "id": "astronomy-finding",
                "name": "Astronomy",
                "description": "Angular size.",
                "questions": [
                  {
                    "text": "What is the angular size of this object in the sky?",
                    "kind": "measurement"
                  },
                  {
                    "text": "How does it relate to distance and size?",
                    "kind": "definition"
                  }
                ]
              }
            ]
          }
        ]
      }
    ]
  },
  "openQuestions": [
    "Should units be separate entries?",
    "How should solid angle be linked?",
    "How should navigation bearings be linked?"
  ],
  "statistics": {
    "bundles": 4,
    "layers": 8,
    "findings": 8,
    "questions": 16
  }
}