{ "model": { "rank": 4247, "code": "thing-q601053", "model_id": "vr.tr.nth-root", "name": "nth root", "purpose": "Let an agent explain nth roots, relay definitions, notation, properties, computation and history from mathematics sources, describe the cube root, and distinguish nth roots from exponentiation, logarithms, roots of polynomials as zeros and square roots specifically.", "family": "Thing Registry", "category": "Cross-cutting context", "status": "research-draft", "kind": "thing", "plane": "XCT", "domain": "XCT.QLT", "industry": "", "version": "", "url": "/models/thing/q601053/", "tier": 2, "score": 77, "payload": { "layer": "wikidata", "aliases": [ "cube root" ], "aliasCount": 1, "merged": 1, "knownIn": 77, "facets": null, "markers": [], "lexicalClass": "", "senseRank": null, "alsoRegisteredAs": null, "source": { "dataset": "wikidata", "item": "Q601053", "url": "https://www.wikidata.org/wiki/Q601053", "license": "CC0 1.0" } }, "research": { "vercy": "1.0-draft", "publication": { "status": "research-draft", "adjudicationStatus": "unreviewed", "publishableCanonical": false, "generatedAt": "2026-09-13T22:29:46Z", "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-Q601053", "registryId": "vr.tr.nth-root", "name": "nth root", "version": "0.2.0-wave.4", "entryKind": "thing", "family": "Thing Registry", "domain": [ "XCT.QLT" ], "status": "research-draft" }, "canonicalUrl": "https://ver.cy/models/thing/q601053/", "model": { "registry_id": "vr.tr.nth-root", "name": "nth root", "purpose": "Let an agent explain nth roots, relay definitions, notation, properties, computation and history from mathematics sources, describe the cube root, and distinguish nth roots from exponentiation, logarithms, roots of polynomials as zeros and square roots specifically.", "definition": "For a number x and positive integer n, a number r such that r raised to the power n equals x, written with the radical sign or as x to the power 1/n, including the square root for n equal to 2 and the cube root for n equal to 3; every nonzero complex number has exactly n distinct nth roots, positive real numbers have one positive real nth root called the principal root, negative real numbers have a real nth root only when n is odd, and nth roots of unity lie evenly spaced on the unit circle. The Abel-Ruffini theorem shows that general polynomial equations of degree five or more cannot be solved by radicals.", "what_it_is_for": "Inverting powers in algebra and computation.", "affordances": [ "explain definition and notation", "relay properties and computation", "describe cube roots and roots of unity", "distinguish related concepts" ], "distinguishing_features": [ "Inverse of powers", "Principal root convention", "Complex roots", "Radical notation" ], "appearance": "Not a physical object; written with the radical sign and an index.", "visual_identification": [ "Inverse of raising to the nth power", "Cube root, radical, principal root", "Exponentiation raises to powers; logarithms find exponents; polynomial roots are zeros; square roots are the n equal 2 case" ], "physical_properties": [ { "quantity": "exponent form", "typical_range": "x to the power 1/n", "unit": "note", "note": "" }, { "quantity": "complex nth roots of a nonzero number", "typical_range": "n", "unit": "count", "note": "" }, { "quantity": "Abel-Ruffini theorem", "typical_range": "1824", "unit": "year", "note": "Abel s proof" } ], "families_and_kinds": [ "square roots", "cube roots", "higher roots", "roots of unity", "nested radicals" ], "related_models": [ { "relation": "is a kind of", "target": "algebraic function", "why": "in registry terms" }, { "relation": "is the inverse of", "target": "exponentiation", "why": "" }, { "relation": "includes", "target": "cube root", "why": "" }, { "relation": "is contrasted with", "target": "logarithm", "why": "" } ], "identifiers": [], "standards_and_regulation": [ "ISO 80000-2 mathematical notation", "IEEE 754 root functions" ], "failure_modes_and_hazards": [ "Ignoring multiple roots", "Misapplying rules to negative numbers", "Confusing roots with zeros" ], "in_scope": [], "out_of_scope": [], "characteristics": [] }, "sources": [], "structure": { "bundles": [ { "id": "understand", "name": "Understand", "description": "What an nth root is.", "rationale": "Definition.", "layers": [ { "id": "definition", "name": "Definition", "description": "Definition.", "findings": [ { "id": "definition-finding", "name": "Definition", "description": "Definition.", "questions": [ { "text": "What is an nth root, and how does it differ from exponentiation, logarithms, polynomial zeros and square roots?", "kind": "definition" }, { "text": "Is the question about arithmetic, complex numbers, computation or history?", "kind": "boundary" } ] } ] }, { "id": "cube", "name": "Cube root", "description": "Cube root.", "findings": [ { "id": "cube-finding", "name": "Cube root", "description": "Cube root.", "questions": [ { "text": "What is a cube root, and why do negative numbers have real cube roots?", "kind": "definition" }, { "text": "Which entry fits cube root?", "kind": "action" } ] } ] } ] }, { "id": "properties", "name": "Properties", "description": "Properties.", "rationale": "Science.", "layers": [ { "id": "principal", "name": "Principal root", "description": "Principal roots.", "findings": [ { "id": "principal-finding", "name": "Principal root", "description": "Principal root.", "questions": [ { "text": "How is the principal nth root defined for real and complex numbers?", "kind": "provenance" }, { "text": "Which references are standard?", "kind": "provenance" } ] } ] }, { "id": "unity", "name": "Roots of unity", "description": "Roots of unity.", "findings": [ { "id": "unity-finding", "name": "Roots of unity", "description": "Roots of unity.", "questions": [ { "text": "What are nth roots of unity and why are they evenly spaced?", "kind": "provenance" }, { "text": "Which sources are cited?", "kind": "provenance" } ] } ] } ] }, { "id": "computation", "name": "Computation", "description": "Computation.", "rationale": "Science.", "layers": [ { "id": "methods", "name": "Methods", "description": "Numerical methods.", "findings": [ { "id": "methods-finding", "name": "Methods", "description": "Methods.", "questions": [ { "text": "How do Newton s method and logarithms compute nth roots?", "kind": "measurement" }, { "text": "Which entry fits nth root algorithm?", "kind": "action" } ] } ] }, { "id": "radicals", "name": "Radicals", "description": "Simplifying radicals.", "findings": [ { "id": "radicals-finding", "name": "Radicals", "description": "Radicals.", "questions": [ { "text": "How are radical expressions simplified and denominators rationalised?", "kind": "provenance" }, { "text": "Which entry fits nested radical?", "kind": "action" } ] } ] } ] }, { "id": "context", "name": "Context", "description": "History.", "rationale": "Context.", "layers": [ { "id": "history", "name": "History", "description": "History.", "findings": [ { "id": "history-finding", "name": "History", "description": "History.", "questions": [ { "text": "How did Babylonian and later mathematicians compute roots?", "kind": "provenance" }, { "text": "Which entry fits Babylonian mathematics?", "kind": "action" } ] } ] }, { "id": "abel", "name": "Abel-Ruffini", "description": "Solvability by radicals.", "findings": [ { "id": "abel-finding", "name": "Abel-Ruffini", "description": "Abel-Ruffini.", "questions": [ { "text": "Why can quintic equations not generally be solved by radicals?", "kind": "provenance" }, { "text": "Which entry fits Abel-Ruffini theorem?", "kind": "action" } ] } ] } ] } ] }, "openQuestions": [ "Should cube root be a separate entry?", "How should mathematics references be linked?", "Should roots of unity be linked separately?" ], "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 nth root, record what state it is in, and decide what may be done with it.", "whatItIs": "Let an agent explain nth roots, relay definitions, notation, properties, computation and history from mathematics sources, describe the cube root, and distinguish nth roots from exponentiation, logarithms, roots of polynomials as zeros and square roots specifically.", "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: cube root.", "1 finer distinctions are held as aliases rather than separate entries, because telling them apart needs a task that asks for it.", "Described in 77 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 nth root, 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": [ "cube root" ] } ], "standing": "Described in 77 Wikipedia languages, which measures how widely it is written about rather than how important or how common it is. 1 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 nth root from another, and a nth root 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 nth root, 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 nth root, 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 nth root 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 nth root, 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 nth root, 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 nth root 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 nth root 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 nth root, 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 nth root, 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 nth root 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 nth root from the things most often confused with it.", "questions": [ { "id": "distinguishing-features-q01", "text": "What identifies and describes what distinguishes a nth root, 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 nth root, 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 nth root 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 nth root 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 nth root between them.", "questions": [ { "id": "stages-and-transitions-q01", "text": "What identifies and describes the lifecycle of a nth root, 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 nth root, 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 nth root 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 nth root, how often and by whom.", "findings": [ { "id": "observation-record", "name": "Observation record", "description": "How an observation of a nth root 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 nth root, 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 nth root, 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 nth root 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 nth root 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 nth root 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 nth root 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 nth root 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 nth root?", "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 nth root?", "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 nth root 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 nth root and how confident it is.", "questions": [ { "id": "claim-provenance-q01", "text": "What identifies and describes a claim about a nth root, 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 nth root, 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 nth root 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 nth root is retired without being erased.", "questions": [ { "id": "validity-and-supersession-q01", "text": "What identifies and describes the validity of a claim about a nth root, 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 nth root, 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 nth root 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 } } } }