{ "model": { "rank": 6926, "code": "thing-q189114", "model_id": "vr.tr.spiral", "name": "spiral", "purpose": "Let an agent explain spirals and their main kinds, relay equations and properties from mathematical references, describe occurrences in nature and technology, and distinguish planar spirals from helices and from loose usage.", "family": "Thing Registry", "category": "Cross-cutting context", "status": "research-draft", "kind": "thing", "plane": "XCT", "domain": "XCT.QLT", "industry": "", "version": "", "url": "/models/thing/q189114/", "tier": 2, "score": 58, "payload": { "layer": "wikidata", "aliases": [ "trumpet spiral", "generalized Archimedean spiral", "lituus", "spiral of Theodorus", "rhumb line", "Archimedean spiral", "logarithmic spiral", "hyperbolic spiral", "spirangle", "golden spiral", "Ulam spiral", "neoid" ], "aliasCount": 12, "merged": 12, "knownIn": 58, "facets": null, "markers": [], "lexicalClass": "", "senseRank": null, "alsoRegisteredAs": "vr.tr.spiral-artifact", "source": { "dataset": "wikidata", "item": "Q189114", "url": "https://www.wikidata.org/wiki/Q189114", "license": "CC0 1.0" } }, "research": { "vercy": "1.0-draft", "publication": { "status": "research-draft", "adjudicationStatus": "unreviewed", "publishableCanonical": false, "generatedAt": "2026-09-13T04:34:01Z", "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": 3, "engine": "claude" }, "metaModel": { "id": "THING-Q189114", "registryId": "vr.tr.spiral", "name": "spiral", "version": "0.2.0-wave.3", "entryKind": "thing", "family": "Thing Registry", "domain": [ "XCT.QLT" ], "status": "research-draft" }, "canonicalUrl": "https://ver.cy/models/thing/q189114/", "model": { "registry_id": "vr.tr.spiral", "name": "spiral", "purpose": "Let an agent explain spirals and their main kinds, relay equations and properties from mathematical references, describe occurrences in nature and technology, and distinguish planar spirals from helices and from loose usage.", "definition": "A curve that winds around a central point while moving progressively farther from or closer to it, including the Archimedean spiral with constant spacing, generalised Archimedean spirals such as the lituus and the hyperbolic spiral, the logarithmic spiral found in shells and galaxies, the spiral of Theodorus built from right triangles, Fermat and Euler spirals, trumpet spirals, and rhumb lines that spiral toward the poles on a sphere; spirals appear throughout nature, art, engineering and mathematics.", "what_it_is_for": "Not applicable; a family of curves.", "affordances": [ "explain kinds and equations", "relay properties", "describe occurrences", "distinguish from helices" ], "distinguishing_features": [ "Radius changing with angle", "Many named families", "Self-similarity in logarithmic spirals", "Natural occurrence" ], "appearance": "A curve coiling around a centre.", "visual_identification": [ "Curve winding around a point", "Archimedean, logarithmic, hyperbolic, lituus, Theodorus, Fermat, Euler, trumpet spirals, rhumb lines", "A helix winds around an axis in three dimensions; a circle does not change radius" ], "physical_properties": [ { "quantity": "Archimedean spiral", "typical_range": "r = a + b theta", "unit": "equation", "note": "" }, { "quantity": "logarithmic spiral", "typical_range": "r = a e^(b theta)", "unit": "equation", "note": "" }, { "quantity": "lituus", "typical_range": "r^2 theta = a^2", "unit": "equation", "note": "" } ], "families_and_kinds": [ "Archimedean spiral", "generalised Archimedean spirals including the hyperbolic spiral and lituus", "logarithmic or equiangular spiral", "Fermat spiral", "Euler or Cornu spiral", "spiral of Theodorus", "trumpet and other named spirals", "rhumb lines or loxodromes on spheres" ], "related_models": [ { "relation": "is a kind of", "target": "curve", "why": "in registry terms" }, { "relation": "is exemplified by", "target": "Archimedean spiral", "why": "with constant spacing" }, { "relation": "is contrasted with", "target": "helix", "why": "in three dimensions" }, { "relation": "appears in", "target": "nautilus", "why": "shells as logarithmic spirals" } ], "identifiers": [], "standards_and_regulation": [ "No regulation; standard mathematical definitions" ], "failure_modes_and_hazards": [ "Confusing spirals with helices", "Confusing spiral kinds", "Overstating golden spiral claims in nature and art" ], "in_scope": [], "out_of_scope": [], "characteristics": [] }, "sources": [], "structure": { "bundles": [ { "id": "understand", "name": "Understand", "description": "What a spiral is.", "rationale": "Mathematics.", "layers": [ { "id": "definition", "name": "Definition", "description": "Definition.", "findings": [ { "id": "definition-finding", "name": "Definition", "description": "Definition.", "questions": [ { "text": "What is a spiral, and how does it differ from a helix and a circle?", "kind": "definition" }, { "text": "Is the question about a planar spiral, a helix or loose usage?", "kind": "boundary" } ] } ] }, { "id": "kinds", "name": "Kinds", "description": "Kinds.", "findings": [ { "id": "kinds-finding", "name": "Kinds", "description": "Kinds.", "questions": [ { "text": "What are the Archimedean, logarithmic, hyperbolic, lituus, Theodorus, Fermat, Euler and trumpet spirals, and what are rhumb lines?", "kind": "definition" }, { "text": "Which entry fits the specific spiral?", "kind": "action" } ] } ] } ] }, { "id": "mathematics", "name": "Mathematics", "description": "Equations and properties.", "rationale": "Mathematics.", "layers": [ { "id": "equations", "name": "Equations", "description": "Equations.", "findings": [ { "id": "equations-finding", "name": "Equations", "description": "Equations.", "questions": [ { "text": "What are the polar equations of the main spirals, and how are arc length and curvature computed?", "kind": "action" }, { "text": "Which references are standard?", "kind": "provenance" } ] } ] }, { "id": "properties", "name": "Properties", "description": "Properties.", "findings": [ { "id": "properties-finding", "name": "Properties", "description": "Properties.", "questions": [ { "text": "What properties such as self-similarity and constant angle characterise logarithmic spirals?", "kind": "provenance" }, { "text": "Which entry fits logarithmic spiral?", "kind": "action" } ] } ] } ] }, { "id": "occur", "name": "Occur", "description": "Occurrences.", "rationale": "Science.", "layers": [ { "id": "nature", "name": "Nature", "description": "Nature.", "findings": [ { "id": "nature-finding", "name": "Nature", "description": "Nature.", "questions": [ { "text": "Where do spirals occur in shells, galaxies, hurricanes and plants, and what is overstated about golden spirals?", "kind": "provenance" }, { "text": "Which sources are cited?", "kind": "provenance" } ] } ] }, { "id": "technology", "name": "Technology", "description": "Technology and art.", "findings": [ { "id": "technology-finding", "name": "Technology", "description": "Technology.", "questions": [ { "text": "How are spirals used in springs, road transitions with Euler spirals, antennas, navigation with rhumb lines and art?", "kind": "provenance" }, { "text": "Which entry fits the specific application?", "kind": "action" } ] } ] } ] }, { "id": "context", "name": "Context", "description": "History and culture.", "rationale": "Context.", "layers": [ { "id": "history", "name": "History", "description": "History.", "findings": [ { "id": "history-finding", "name": "History", "description": "History.", "questions": [ { "text": "How did Archimedes, Theodorus, Bernoulli and others study spirals?", "kind": "provenance" }, { "text": "Which entry fits the history of geometry?", "kind": "action" } ] } ] }, { "id": "culture", "name": "Culture", "description": "Culture.", "findings": [ { "id": "culture-finding", "name": "Culture", "description": "Culture.", "questions": [ { "text": "How do spirals appear in prehistoric art, symbolism and design?", "kind": "provenance" }, { "text": "Which entry fits spiral in art?", "kind": "action" } ] } ] } ] } ] }, "openQuestions": [ "Should logarithmic spiral and rhumb line be separate primary entries?", "How should mathematical references be linked?", "The registry entry has merged aliases naming specific spirals and rhumb lines; should they be split off?" ], "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 spiral, record what state it is in, and decide what may be done with it.", "whatItIs": "Let an agent explain spirals and their main kinds, relay equations and properties from mathematical references, describe occurrences in nature and technology, and distinguish planar spirals from helices and from loose usage.", "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: trumpet spiral, generalized Archimedean spiral, lituus, spiral of Theodorus, rhumb line, Archimedean spiral, logarithmic spiral, hyperbolic spiral, spirangle, golden spiral, Ulam spiral, neoid.", "12 finer distinctions are held as aliases rather than separate entries, because telling them apart needs a task that asks for it.", "Described in 58 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 spiral, 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": [ "trumpet spiral", "generalized Archimedean spiral", "lituus", "spiral of Theodorus", "rhumb line", "Archimedean spiral", "logarithmic spiral", "hyperbolic spiral", "spirangle", "golden spiral", "Ulam spiral", "neoid" ] } ], "standing": "Described in 58 Wikipedia languages, which measures how widely it is written about rather than how important or how common it is. 12 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 spiral from another, and a spiral 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 spiral, 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 spiral, 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 spiral 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 spiral, 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 spiral, 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 spiral 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 spiral 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 spiral, 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 spiral, 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 spiral 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 spiral from the things most often confused with it.", "questions": [ { "id": "distinguishing-features-q01", "text": "What identifies and describes what distinguishes a spiral, 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 spiral, 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 spiral 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 spiral 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 spiral between them.", "questions": [ { "id": "stages-and-transitions-q01", "text": "What identifies and describes the lifecycle of a spiral, 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 spiral, 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 spiral 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 spiral, how often and by whom.", "findings": [ { "id": "observation-record", "name": "Observation record", "description": "How an observation of a spiral 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 spiral, 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 spiral, 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 spiral 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 spiral 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 spiral 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 spiral 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 spiral 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 spiral?", "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 spiral?", "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 spiral 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 spiral and how confident it is.", "questions": [ { "id": "claim-provenance-q01", "text": "What identifies and describes a claim about a spiral, 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 spiral, 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 spiral 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 spiral is retired without being erased.", "questions": [ { "id": "validity-and-supersession-q01", "text": "What identifies and describes the validity of a claim about a spiral, 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 spiral, 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 spiral 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 } } } }