{ "model": { "rank": 7404, "code": "thing-q190046", "model_id": "vr.tr.ellipsoid", "name": "ellipsoid", "purpose": "Let an agent explain ellipsoids, relay geometry, formulas and applications from mathematics, geodesy and physics sources, describe the named ellipsoids, and distinguish ellipsoids from spheres, spheroids as a special case, ellipses and other quadrics such as hyperboloids and paraboloids.", "family": "Thing Registry", "category": "Cross-cutting context", "status": "research-draft", "kind": "thing", "plane": "XCT", "domain": "XCT.QLT", "industry": "", "version": "", "url": "/models/thing/q190046/", "tier": 2, "score": 55, "payload": { "layer": "wikidata", "aliases": [ "Poinsot's ellipsoid", "index ellipsoid", "tri-axial ellipsoid" ], "aliasCount": 3, "merged": 3, "knownIn": 55, "facets": null, "markers": [], "lexicalClass": "", "senseRank": null, "alsoRegisteredAs": null, "source": { "dataset": "wikidata", "item": "Q190046", "url": "https://www.wikidata.org/wiki/Q190046", "license": "CC0 1.0" } }, "research": { "vercy": "1.0-draft", "publication": { "status": "research-draft", "adjudicationStatus": "unreviewed", "publishableCanonical": false, "generatedAt": "2026-09-13T19:38:08Z", "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": 4, "engine": "claude" }, "metaModel": { "id": "THING-Q190046", "registryId": "vr.tr.ellipsoid", "name": "ellipsoid", "version": "0.2.0-wave.4", "entryKind": "thing", "family": "Thing Registry", "domain": [ "XCT.QLT" ], "status": "research-draft" }, "canonicalUrl": "https://ver.cy/models/thing/q190046/", "model": { "registry_id": "vr.tr.ellipsoid", "name": "ellipsoid", "purpose": "Let an agent explain ellipsoids, relay geometry, formulas and applications from mathematics, geodesy and physics sources, describe the named ellipsoids, and distinguish ellipsoids from spheres, spheroids as a special case, ellipses and other quadrics such as hyperboloids and paraboloids.", "definition": "A closed quadric surface that is a three-dimensional analogue of an ellipse, defined in standard form by x2/a2 + y2/b2 + z2/c2 = 1 with semi-axes a, b and c, called tri-axial when all three differ and a spheroid when two are equal, with volume four-thirds pi abc, used as reference ellipsoids for the shape of the Earth in geodesy, and in physics as Poinsot s ellipsoid, the inertia ellipsoid describing free rigid-body rotation, and the index ellipsoid or optical indicatrix describing refractive index in crystals.", "what_it_is_for": "Not applicable; a geometric surface, used as a model.", "affordances": [ "explain geometry", "relay formulas", "describe named ellipsoids", "distinguish related surfaces" ], "distinguishing_features": [ "Three semi-axes", "Closed quadric", "Earth model", "Physical applications" ], "appearance": "A stretched or squashed sphere shape.", "visual_identification": [ "Closed quadric surface", "Tri-axial ellipsoid, Poinsot s ellipsoid, index ellipsoid", "Spheres have equal axes; spheroids have two equal axes; ellipses are 2D; hyperboloids and paraboloids are open" ], "physical_properties": [ { "quantity": "volume", "typical_range": "4/3 pi a b c", "unit": "formula", "note": "" }, { "quantity": "WGS 84 semi-major axis", "typical_range": "6378137", "unit": "m", "note": "" }, { "quantity": "WGS 84 flattening", "typical_range": "1/298.257223563", "unit": "ratio", "note": "" } ], "families_and_kinds": [ "spheres as degenerate cases", "oblate and prolate spheroids", "tri-axial ellipsoids", "reference ellipsoids", "inertia and index ellipsoids" ], "related_models": [ { "relation": "is a kind of", "target": "quadric", "why": "in registry terms" }, { "relation": "includes", "target": "spheroid", "why": "" }, { "relation": "is used in", "target": "geodesy", "why": "as a reference ellipsoid" }, { "relation": "is contrasted with", "target": "ellipse", "why": "the 2D analogue" } ], "identifiers": [], "standards_and_regulation": [ "WGS 84 and GRS 80 reference ellipsoids" ], "failure_modes_and_hazards": [ "No simple closed formula for surface area of a tri-axial ellipsoid", "Mixing reference ellipsoids in mapping", "Confusing ellipsoid and spheroid" ], "in_scope": [], "out_of_scope": [], "characteristics": [] }, "sources": [], "structure": { "bundles": [ { "id": "understand", "name": "Understand", "description": "What an ellipsoid is.", "rationale": "Science.", "layers": [ { "id": "definition", "name": "Definition", "description": "Definition.", "findings": [ { "id": "definition-finding", "name": "Definition", "description": "Definition.", "questions": [ { "text": "What is an ellipsoid, and how does it differ from spheres, spheroids, ellipses and other quadrics?", "kind": "definition" }, { "text": "Is the question about geometry, geodesy, mechanics or optics?", "kind": "boundary" } ] } ] }, { "id": "named", "name": "Named", "description": "Named ellipsoids.", "findings": [ { "id": "named-finding", "name": "Named", "description": "Named.", "questions": [ { "text": "What are tri-axial ellipsoids, Poinsot s ellipsoid and the index ellipsoid?", "kind": "definition" }, { "text": "Which entry fits the specific ellipsoid?", "kind": "action" } ] } ] } ] }, { "id": "geometry", "name": "Geometry", "description": "Geometry.", "rationale": "Science.", "layers": [ { "id": "formulas", "name": "Formulas", "description": "Formulas.", "findings": [ { "id": "formulas-finding", "name": "Formulas", "description": "Formulas.", "questions": [ { "text": "What are the equation, volume and surface area approximations?", "kind": "measurement" }, { "text": "Which references are standard?", "kind": "provenance" } ] } ] }, { "id": "quadrics", "name": "Quadrics", "description": "Quadrics.", "findings": [ { "id": "quadrics-finding", "name": "Quadrics", "description": "Quadrics.", "questions": [ { "text": "How do ellipsoids fit among quadric surfaces?", "kind": "provenance" }, { "text": "Which sources are cited?", "kind": "provenance" } ] } ] } ] }, { "id": "applications", "name": "Applications", "description": "Applications.", "rationale": "Application.", "layers": [ { "id": "earth", "name": "Earth", "description": "Earth models.", "findings": [ { "id": "earth-finding", "name": "Earth", "description": "Earth.", "questions": [ { "text": "How are reference ellipsoids used for GPS and mapping?", "kind": "provenance" }, { "text": "Which entry fits reference ellipsoid?", "kind": "action" } ] } ] }, { "id": "physics", "name": "Physics", "description": "Mechanics and optics.", "findings": [ { "id": "physics-finding", "name": "Physics", "description": "Physics.", "questions": [ { "text": "How do the inertia and index ellipsoids describe rotation and birefringence?", "kind": "provenance" }, { "text": "Which entry fits birefringence?", "kind": "action" } ] } ] } ] }, { "id": "context", "name": "Context", "description": "Other uses.", "rationale": "Context.", "layers": [ { "id": "statistics", "name": "Statistics", "description": "Confidence ellipsoids.", "findings": [ { "id": "statistics-finding", "name": "Statistics", "description": "Statistics.", "questions": [ { "text": "How are ellipsoids used in multivariate statistics?", "kind": "provenance" }, { "text": "Which entry fits multivariate normal distribution?", "kind": "action" } ] } ] }, { "id": "nature", "name": "Nature", "description": "Astronomy.", "findings": [ { "id": "nature-finding", "name": "Nature", "description": "Nature.", "questions": [ { "text": "Why are rotating planets and some asteroids ellipsoidal?", "kind": "provenance" }, { "text": "Which entry fits hydrostatic equilibrium?", "kind": "action" } ] } ] } ] } ] }, "openQuestions": [ "Should reference ellipsoid be a separate entry?", "How should geodesy sources be linked?", "Should Poinsot s and index ellipsoids be separate entries?" ], "statistics": { "bundles": 4, "layers": 8, "findings": 8, "questions": 16 } }, "draft": { "generator": "vr.draft.v3", "status": "draft-generated", "researched": false, "archetype": "abstract concept", "method": "Written from the archetype playbook - what this kind of thing needs beyond identity and provenance - and from the structure that recurred across 6,333 models already researched by two engines. Applied to this entry by rule. No source was read for this thing and no claim here is researched. This entry carries no facets of its own, so they were inferred from its domain - a guess about a whole domain applied to one thing.", "facetsInferred": true, "nextPass": "A researcher replaces this draft with a sourced specification. Treat every sentence below as a proposal to argue with.", "purpose": "Give an agent a durable, checkable way to recognise a ellipsoid, record what state it is in, and decide what may be done with it.", "whatItIs": "Let an agent explain ellipsoids, relay geometry, formulas and applications from mathematics, geodesy and physics sources, describe the named ellipsoids, and distinguish ellipsoids from spheres, spheroids as a special case, ellipses and other quadrics such as hyperboloids and paraboloids.", "characteristics": { "substance": "abstract", "origin": "conceptual", "agency": "inert" }, "whatYouCanDoWithIt": [ "observed and measured" ], "distinguishingFeatures": [ "Names folded into this entry, which a task may need to split apart again: Poinsot's ellipsoid, index ellipsoid, tri-axial ellipsoid.", "3 finer distinctions are held as aliases rather than separate entries, because telling them apart needs a task that asks for it.", "Described in 55 Wikipedia languages, which is a measure of how widely the thing is known, not of how important it is." ], "openQuestionsForResearch": [ "Which of the bundles below does a real task actually need, and which are ceremony?", "What does this thing have that the facets do not capture at all?", "Which neighbouring kind is most often confused with a ellipsoid, and on what evidence are they told apart?" ], "whatItIsMadeOf": "an abstraction with no physical instance", "physicalCharacter": [ "Does nothing on its own; everything it does, something else did to it.", "These come from the domain this entry sits in rather than from the entry itself, so treat them as a first guess about the whole domain applied to one thing." ], "whatCanBeDoneWithIt": [ "observe it, measure it, record its state" ], "howItIsRecognised": [ "Nothing to see. What is recognised is an instance of it, and which instances count is exactly what is argued about." ], "relatedModels": [ { "relation": "covers", "note": "Finer kinds folded into this entry because telling them apart needs a task that asks for it. Each is a model waiting to be split out when one does.", "targets": [ "Poinsot's ellipsoid", "index ellipsoid", "tri-axial ellipsoid" ] } ], "standing": "Described in 55 Wikipedia languages, which measures how widely it is written about rather than how important or how common it is. 3 finer distinctions are held inside this entry as names rather than as separate models.", "structure": { "bundles": [ { "id": "identity-and-classification", "name": "Identity, naming and classification", "description": "How an agent tells one ellipsoid from another, and a ellipsoid from things that resemble it.", "rationale": "Recognition comes before every other claim. Without stable identity nothing else in the model can be trusted to be about the same thing twice.", "layers": [ { "id": "naming-and-identifiers", "name": "Names and identifiers", "description": "The names this thing goes by and the identifiers that survive translation and time.", "findings": [ { "id": "preferred-name-and-aliases", "name": "Preferred name, aliases and local names", "description": "Which name to use, which names mean the same thing, and which merely sound similar.", "questions": [ { "id": "preferred-name-and-aliases-q01", "text": "What identifies and describes the name of a ellipsoid, and in what units or vocabulary?", "kind": "definition", "answer_data": [ "identifiers", "types and classes", "values with units", "explicit unknowns" ] }, { "id": "preferred-name-and-aliases-q02", "text": "Who or what asserted this about the name of a ellipsoid, by which method, and when was it true?", "kind": "provenance", "answer_data": [ "authority", "method", "evidence", "event time", "knowledge time" ] }, { "id": "preferred-name-and-aliases-q03", "text": "What may an agent decide or do once the name of a ellipsoid is known, and what must it refuse?", "kind": "action", "answer_data": [ "permitted actions", "preconditions", "refusals", "escalation" ] } ] }, { "id": "stable-identifiers", "name": "Stable identifiers and external keys", "description": "Identifiers that keep pointing at this kind of thing across systems and languages.", "questions": [ { "id": "stable-identifiers-q01", "text": "What identifies and describes an identifier for a ellipsoid, and in what units or vocabulary?", "kind": "definition", "answer_data": [ "identifiers", "types and classes", "values with units", "explicit unknowns" ] }, { "id": "stable-identifiers-q02", "text": "Who or what asserted this about an identifier for a ellipsoid, by which method, and when was it true?", "kind": "provenance", "answer_data": [ "authority", "method", "evidence", "event time", "knowledge time" ] }, { "id": "stable-identifiers-q03", "text": "What may an agent decide or do once an identifier for a ellipsoid is known, and what must it refuse?", "kind": "action", "answer_data": [ "permitted actions", "preconditions", "refusals", "escalation" ] } ] } ] }, { "id": "classification-and-granularity", "name": "Classification and granularity", "description": "Where a ellipsoid sits among kinds, and how finely a task needs to cut it.", "findings": [ { "id": "kind-and-parents", "name": "Kind, parents and neighbouring kinds", "description": "The classes this thing belongs to and the ones it is next to.", "questions": [ { "id": "kind-and-parents-q01", "text": "What identifies and describes the kind of a ellipsoid, and in what units or vocabulary?", "kind": "definition", "answer_data": [ "identifiers", "types and classes", "values with units", "explicit unknowns" ] }, { "id": "kind-and-parents-q02", "text": "Who or what asserted this about the kind of a ellipsoid, by which method, and when was it true?", "kind": "provenance", "answer_data": [ "authority", "method", "evidence", "event time", "knowledge time" ] }, { "id": "kind-and-parents-q03", "text": "What may an agent decide or do once the kind of a ellipsoid is known, and what must it refuse?", "kind": "action", "answer_data": [ "permitted actions", "preconditions", "refusals", "escalation" ] } ] }, { "id": "distinguishing-features", "name": "Distinguishing features", "description": "What separates a ellipsoid from the things most often confused with it.", "questions": [ { "id": "distinguishing-features-q01", "text": "What identifies and describes what distinguishes a ellipsoid, and in what units or vocabulary?", "kind": "definition", "answer_data": [ "identifiers", "types and classes", "values with units", "explicit unknowns" ] }, { "id": "distinguishing-features-q02", "text": "Who or what asserted this about what distinguishes a ellipsoid, by which method, and when was it true?", "kind": "provenance", "answer_data": [ "authority", "method", "evidence", "event time", "knowledge time" ] }, { "id": "distinguishing-features-q03", "text": "What may an agent decide or do once what distinguishes a ellipsoid is known, and what must it refuse?", "kind": "action", "answer_data": [ "permitted actions", "preconditions", "refusals", "escalation" ] } ] } ] } ] }, { "id": "state-and-lifecycle", "name": "State and lifecycle", "description": "The states a ellipsoid passes through and the events that move it between them.", "rationale": "Most decisions about a thing depend on what state it is in now, which is a claim with a time on it, not a property.", "layers": [ { "id": "lifecycle-stages", "name": "Lifecycle stages", "description": "From coming into existence to ceasing to be one of these.", "findings": [ { "id": "stages-and-transitions", "name": "Stages and transitions", "description": "The stages worth naming and what moves a ellipsoid between them.", "questions": [ { "id": "stages-and-transitions-q01", "text": "What identifies and describes the lifecycle of a ellipsoid, and in what units or vocabulary?", "kind": "definition", "answer_data": [ "identifiers", "types and classes", "values with units", "explicit unknowns" ] }, { "id": "stages-and-transitions-q02", "text": "Who or what asserted this about the lifecycle of a ellipsoid, by which method, and when was it true?", "kind": "provenance", "answer_data": [ "authority", "method", "evidence", "event time", "knowledge time" ] }, { "id": "stages-and-transitions-q03", "text": "What may an agent decide or do once the lifecycle of a ellipsoid is known, and what must it refuse?", "kind": "action", "answer_data": [ "permitted actions", "preconditions", "refusals", "escalation" ] } ] } ] }, { "id": "observations-and-status", "name": "Observations and current status", "description": "What is observed about a ellipsoid, how often and by whom.", "findings": [ { "id": "observation-record", "name": "Observation record", "description": "How an observation of a ellipsoid is recorded so that it can be superseded rather than overwritten.", "questions": [ { "id": "observation-record-q01", "text": "What identifies and describes an observation of a ellipsoid, and in what units or vocabulary?", "kind": "definition", "answer_data": [ "identifiers", "types and classes", "values with units", "explicit unknowns" ] }, { "id": "observation-record-q02", "text": "Who or what asserted this about an observation of a ellipsoid, by which method, and when was it true?", "kind": "provenance", "answer_data": [ "authority", "method", "evidence", "event time", "knowledge time" ] }, { "id": "observation-record-q03", "text": "What may an agent decide or do once an observation of a ellipsoid is known, and what must it refuse?", "kind": "action", "answer_data": [ "permitted actions", "preconditions", "refusals", "escalation" ] } ] } ] } ] }, { "id": "definitions-in-contest", "name": "Definitions and who holds them", "description": "What ellipsoid is taken to mean, and by whom.", "rationale": "When a field disagrees about a concept, the disagreement is the content. A model that picks one definition silently destroys the information.", "layers": [ { "id": "competing-definitions", "name": "Competing definitions", "description": "The main readings and the traditions behind them.", "findings": [ { "id": "definition-map", "name": "Definitions and their holders", "description": "Each definition with the school or body that holds it.", "questions": [ { "id": "definition-map-q01", "text": "Which definitions of ellipsoid are in use, and which tradition or body holds each?", "kind": "definition" }, { "id": "definition-map-q02", "text": "What turns on the difference between them in practice?", "kind": "boundary" } ] } ] }, { "id": "operationalisation", "name": "Operationalisation", "description": "How it is measured or applied when it has to be.", "findings": [ { "id": "operational-record", "name": "Measures and proxies", "description": "Instruments and indicators used to stand in for it.", "questions": [ { "id": "operational-record-q01", "text": "How is ellipsoid operationalised or measured in practice, and by what instrument?", "kind": "measurement" }, { "id": "operational-record-q02", "text": "What does that operationalisation leave out, and when does that matter?", "kind": "boundary" } ] } ] } ] }, { "id": "instances-and-use", "name": "Instances, use and consequence", "description": "What counts as an instance of ellipsoid and what follows from calling something that.", "rationale": "Applying a concept is an act with consequences, so a model must say what the label licenses and what it does not.", "layers": [ { "id": "instances", "name": "What counts as an instance", "description": "Clear cases, borderline cases and non-cases.", "findings": [ { "id": "instance-tests", "name": "Tests for an instance", "description": "What would settle whether something falls under it.", "questions": [ { "id": "instance-tests-q01", "text": "What would settle whether something is an instance of ellipsoid?", "kind": "boundary" }, { "id": "instance-tests-q02", "text": "Which borderline cases are argued about, and on what grounds?", "kind": "definition" } ] } ] }, { "id": "consequence", "name": "Consequence of application", "description": "Rights, duties or decisions that follow from the label.", "findings": [ { "id": "consequence-record", "name": "What the label licenses", "description": "What an agent may do once something is classified this way.", "questions": [ { "id": "consequence-record-q01", "text": "What follows practically once something is treated as ellipsoid?", "kind": "action" }, { "id": "consequence-record-q02", "text": "What must an agent not infer from the label alone?", "kind": "action" } ] } ] } ] }, { "id": "provenance-and-evidence", "name": "Provenance, evidence and time", "description": "Where every claim about a ellipsoid came from and when it held.", "rationale": "A claim without a source and a time cannot be superseded, only overwritten, and an agent that overwrites loses the ability to explain itself.", "layers": [ { "id": "source-and-authority", "name": "Source and authority", "description": "Who said it, on what evidence, and how strongly.", "findings": [ { "id": "claim-provenance", "name": "Claim provenance and confidence", "description": "The authority behind each claim about a ellipsoid and how confident it is.", "questions": [ { "id": "claim-provenance-q01", "text": "What identifies and describes a claim about a ellipsoid, and in what units or vocabulary?", "kind": "definition", "answer_data": [ "identifiers", "types and classes", "values with units", "explicit unknowns" ] }, { "id": "claim-provenance-q02", "text": "Who or what asserted this about a claim about a ellipsoid, by which method, and when was it true?", "kind": "provenance", "answer_data": [ "authority", "method", "evidence", "event time", "knowledge time" ] }, { "id": "claim-provenance-q03", "text": "What may an agent decide or do once a claim about a ellipsoid is known, and what must it refuse?", "kind": "action", "answer_data": [ "permitted actions", "preconditions", "refusals", "escalation" ] } ] } ] }, { "id": "time-and-versions", "name": "Time, versions and supersession", "description": "When a claim was true, when it was learnt, and what replaced it.", "findings": [ { "id": "validity-and-supersession", "name": "Validity period and supersession", "description": "How an old claim about a ellipsoid is retired without being erased.", "questions": [ { "id": "validity-and-supersession-q01", "text": "What identifies and describes the validity of a claim about a ellipsoid, and in what units or vocabulary?", "kind": "definition", "answer_data": [ "identifiers", "types and classes", "values with units", "explicit unknowns" ] }, { "id": "validity-and-supersession-q02", "text": "Who or what asserted this about the validity of a claim about a ellipsoid, by which method, and when was it true?", "kind": "provenance", "answer_data": [ "authority", "method", "evidence", "event time", "knowledge time" ] }, { "id": "validity-and-supersession-q03", "text": "What may an agent decide or do once the validity of a claim about a ellipsoid is known, and what must it refuse?", "kind": "action", "answer_data": [ "permitted actions", "preconditions", "refusals", "escalation" ] } ] } ] } ] } ] }, "statistics": { "bundles": 5, "layers": 10, "findings": 12, "questions": 32 } } } }