{ "vercy": "1.0-draft", "publication": { "status": "research-draft", "adjudicationStatus": "unreviewed", "publishableCanonical": false, "generatedAt": "2026-09-11T14:24:29Z", "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": "2026-10-05T17:00:00Z", "ingestedAt": "2026-10-05T13:29:53+00:00", "fields": [ "agent_conduct", "ethics", "owners" ] }, "gate": { "passed": true, "version": "1.0", "at": "2026-10-06T19:51:55+00:00", "evidence": [ "completeness 1.00", "sense: Wikidata description", "2 live sources", "review by codex: pass" ] } }, "metaModel": { "id": "THING-Q17278", "registryId": "vr.tr.circle", "name": "circle", "version": "0.2.0-wave.1", "entryKind": "thing", "family": "Thing Registry", "domain": [ "XCT.QLT" ], "status": "research-draft" }, "canonicalUrl": "https://ver.cy/models/thing/q17278/", "model": { "registry_id": "vr.tr.circle", "name": "circle", "purpose": "Let an agent explain circles by definition, formulas, theorems and applications, and separate geographic and other senses.", "definition": "The set of all points in a plane at a fixed distance, the radius, from a centre point; its circumference is 2 pi r and its area pi r squared, and the unit circle underlies trigonometry; the word also names circles of latitude and circular shapes such as colour wheels.", "what_it_is_for": "Geometry, trigonometry, engineering and design.", "affordances": [ "calculate circumference, area and arc length", "use the unit circle in trigonometry", "explain circle theorems", "separate other senses of circle" ], "distinguishing_features": [ "Constant distance from centre", "Special conic section", "Defines pi", "Symmetric in every direction" ], "appearance": "A round closed curve, as in wheels, coins and drawings.", "visual_identification": [ "Constant radius from a centre", "Symbol pi in formulas", "Ellipses have two foci" ], "physical_properties": [ { "quantity": "circumference", "typical_range": "2 pi r", "unit": "", "note": "formula" }, { "quantity": "area", "typical_range": "pi r squared", "unit": "", "note": "formula" } ], "families_and_kinds": [ "unit circle", "great and small circles", "circles of latitude", "inscribed and circumscribed circles", "circle packing" ], "related_models": [ { "relation": "is a kind of", "target": "conic section", "why": "category" }, { "relation": "is related to", "target": "angular measure", "why": "angles" }, { "relation": "is used in", "target": "trigonometry", "why": "field" }, { "relation": "is related to", "target": "orbit", "why": "circular orbits" } ], "identifiers": [], "standards_and_regulation": [ "No specific regulation" ], "failure_modes_and_hazards": [ "Confusing radius and diameter", "Rounding pi too early" ], "in_scope": [], "out_of_scope": [], "characteristics": [], "agent_conduct": { "may": [ "Compute circle properties and explain them.", "Distinguish the geometric circle from circles of latitude and other uses of the word." ], "must_not": [ "Present approximations of pi as exact.", "Claim to have squared the circle or present disproven results as valid." ], "requires_human": [ "Relying on calculations for a design used by people." ] }, "ethics": { "considerations": [ "Accurate mathematics underlies engineering and teaching.", "Misleading claims about famous problems can deceive learners." ], "affected_parties": [ "Students and teachers", "Users of designs" ] }, "owners": { "steward": "Nobody: a mathematical concept held in common.", "master_systems": [] } }, "sources": [ { "id": "wikidata", "title": "Wikidata item Q17278: circle", "url": "https://www.wikidata.org/wiki/Q17278", "url_status": "live", "what_it_supports": "identity and sense of the item", "checked_by": "wikidata-api" }, { "id": "wikipedia-en", "title": "Wikipedia: Circle", "url": "https://en.wikipedia.org/wiki/Circle", "url_status": "live", "what_it_supports": "general description of the item", "checked_by": "wikidata-api sitelink" } ], "structure": { "bundles": [ { "id": "measure", "name": "Measure", "description": "Formulas.", "rationale": "Formulas are exact.", "layers": [ { "id": "formulas", "name": "Formulas", "description": "Circumference and area.", "findings": [ { "id": "formulas-finding", "name": "Formulas", "description": "Formulas.", "questions": [ { "text": "What are the circumference and area for this radius?", "kind": "measurement" }, { "text": "How precise should pi be?", "kind": "boundary" } ] } ] }, { "id": "arcs", "name": "Arcs", "description": "Arcs and sectors.", "findings": [ { "id": "arcs-finding", "name": "Arcs", "description": "Arcs and sectors.", "questions": [ { "text": "What are the arc length and sector area for this angle?", "kind": "measurement" }, { "text": "Is the angle in radians?", "kind": "boundary" } ] } ] } ] }, { "id": "theory", "name": "Theory", "description": "Theorems.", "rationale": "Circles have rich theory.", "layers": [ { "id": "theorems", "name": "Theorems", "description": "Circle theorems.", "findings": [ { "id": "theorems-finding", "name": "Theorems", "description": "Circle theorems.", "questions": [ { "text": "Which circle theorem applies here, such as the inscribed angle theorem?", "kind": "definition" }, { "text": "How is it proved?", "kind": "definition" } ] } ] }, { "id": "unit", "name": "Unit circle", "description": "Trigonometry.", "findings": [ { "id": "unit-finding", "name": "Unit circle", "description": "Unit circle.", "questions": [ { "text": "How does the unit circle define sine and cosine?", "kind": "definition" }, { "text": "What are the values at key angles?", "kind": "measurement" } ] } ] } ] }, { "id": "applications", "name": "Applications", "description": "Uses.", "rationale": "Circles are everywhere.", "layers": [ { "id": "engineering", "name": "Engineering", "description": "Design.", "findings": [ { "id": "engineering-finding", "name": "Engineering", "description": "Engineering.", "questions": [ { "text": "How are circles used in wheels, gears and pipes?", "kind": "definition" }, { "text": "Which tolerances apply?", "kind": "provenance" } ] } ] }, { "id": "geography", "name": "Geography", "description": "Circles of latitude.", "findings": [ { "id": "geography-finding", "name": "Geography", "description": "Circles of latitude.", "questions": [ { "text": "What are circles of latitude and the tropics?", "kind": "definition" }, { "text": "Where are they located?", "kind": "provenance" } ] } ] } ] }, { "id": "senses", "name": "Senses", "description": "Disambiguation.", "rationale": "Circle has other senses.", "layers": [ { "id": "social", "name": "Social", "description": "Social circles.", "findings": [ { "id": "social-finding", "name": "Social", "description": "Social sense.", "questions": [ { "text": "Is a social circle or group meant?", "kind": "boundary" }, { "text": "Which entry fits?", "kind": "action" } ] } ] }, { "id": "design", "name": "Design", "description": "Colour wheels and icons.", "findings": [ { "id": "design-finding", "name": "Design", "description": "Design sense.", "questions": [ { "text": "Is a colour wheel or a loading icon meant?", "kind": "boundary" }, { "text": "Which entry fits?", "kind": "action" } ] } ] } ] } ] }, "openQuestions": [ "Should circle theorems be separate entries?", "How should geographic circles be linked?", "How should other senses be split off?" ], "statistics": { "bundles": 4, "layers": 8, "findings": 8, "questions": 16 } }