{ "model": { "rank": 17754, "code": "thing-q1473607", "model_id": "vr.tr.degree-of-a-polynomial", "name": "degree of a polynomial", "purpose": "Let an agent explain the degree of a polynomial and its properties, support finding degrees and using them in algebra, describe the role of degree in roots and graphs, and support learning.", "family": "Thing Registry", "category": "Cross-cutting context", "status": "research-draft", "kind": "thing", "plane": "XCT", "domain": "XCT.QTY", "industry": "", "version": "", "url": "/models/thing/q1473607/", "tier": 2, "score": 30, "payload": { "layer": "wikidata", "aliases": [], "aliasCount": 0, "merged": 0, "knownIn": 30, "facets": null, "markers": [], "lexicalClass": "", "senseRank": null, "alsoRegisteredAs": null, "source": { "dataset": "wikidata", "item": "Q1473607", "url": "https://www.wikidata.org/wiki/Q1473607", "license": "CC0 1.0" } }, "research": { "vercy": "1.0-draft", "publication": { "status": "research-draft", "adjudicationStatus": "unreviewed", "publishableCanonical": false, "generatedAt": "2026-09-12T04:34:36Z", "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": 2, "engine": "claude" }, "metaModel": { "id": "THING-Q1473607", "registryId": "vr.tr.degree-of-a-polynomial", "name": "degree of a polynomial", "version": "0.2.0-wave.2", "entryKind": "thing", "family": "Thing Registry", "domain": [ "XCT.QTY" ], "status": "research-draft" }, "canonicalUrl": "https://ver.cy/models/thing/q1473607/", "model": { "registry_id": "vr.tr.degree-of-a-polynomial", "name": "degree of a polynomial", "purpose": "Let an agent explain the degree of a polynomial and its properties, support finding degrees and using them in algebra, describe the role of degree in roots and graphs, and support learning.", "definition": "The highest power of the variable with a non-zero coefficient in a polynomial, or for polynomials in several variables the largest total degree of any term, a non-negative integer that determines the number of roots over the complex numbers, the shape of the graph, and the behaviour under operations such as addition, multiplication and differentiation; the degree of a polynomial is fundamental in algebra and is used to classify polynomials as constant, linear, quadratic, cubic and higher.", "what_it_is_for": "Highest power in a polynomial.", "affordances": [ "explain the concept", "support finding degrees", "describe role in roots and graphs", "support learning" ], "distinguishing_features": [ "Non-negative integer", "Determines root count", "Behaves under operations", "Classifies polynomials" ], "appearance": "Not physical; a number attached to an expression.", "visual_identification": [ "Highest exponent with non-zero coefficient", "Non-negative integer", "The order of a differential equation is a different notion; leading coefficient is the coefficient of the top term" ], "physical_properties": [], "families_and_kinds": [ "degree of univariate polynomials", "total degree of multivariate polynomials", "degree conventions for the zero polynomial", "degree in rings and fields", "degree of rational functions and curves" ], "related_models": [ { "relation": "is a kind of", "target": "non-negative integer", "why": "category" }, { "relation": "is related to", "target": "factor", "why": "factoring polynomials" }, { "relation": "is related to", "target": "real", "why": "coefficients and roots" }, { "relation": "is related to", "target": "mathematical proof", "why": "proofs about polynomials" } ], "identifiers": [], "standards_and_regulation": [ "Mathematical conventions", "No regulation" ], "failure_modes_and_hazards": [ "Miscounting degree in unsimplified expressions", "Confusing degree with number of terms", "Zero polynomial conventions" ], "in_scope": [], "out_of_scope": [], "characteristics": [] }, "sources": [], "structure": { "bundles": [ { "id": "understand", "name": "Understand", "description": "What degree is.", "rationale": "Mathematics.", "layers": [ { "id": "definition", "name": "Definition", "description": "Definition.", "findings": [ { "id": "definition-finding", "name": "Definition", "description": "Definition.", "questions": [ { "text": "How is the degree of a polynomial defined for one and several variables, and how is the zero polynomial handled?", "kind": "definition" }, { "text": "Which entry fits polynomials?", "kind": "action" } ] } ] }, { "id": "classes", "name": "Classes", "description": "Classification by degree.", "findings": [ { "id": "classes-finding", "name": "Classes", "description": "Classes.", "questions": [ { "text": "How are polynomials classified as constant, linear, quadratic, cubic and higher?", "kind": "definition" }, { "text": "Which entry fits a specific class?", "kind": "action" } ] } ] } ] }, { "id": "compute", "name": "Compute", "description": "Finding and using degree.", "rationale": "Practice.", "layers": [ { "id": "find", "name": "Find", "description": "Finding the degree.", "findings": [ { "id": "find-finding", "name": "Find", "description": "Finding.", "questions": [ { "text": "What is the degree of this polynomial, and how does simplification affect it?", "kind": "action" }, { "text": "Which entry fits algebraic simplification?", "kind": "action" } ] } ] }, { "id": "operations", "name": "Operations", "description": "Degree under operations.", "findings": [ { "id": "operations-finding", "name": "Operations", "description": "Operations.", "questions": [ { "text": "How does degree behave under addition, multiplication, composition and differentiation?", "kind": "definition" }, { "text": "Which entry fits polynomial arithmetic?", "kind": "action" } ] } ] } ] }, { "id": "theory", "name": "Theory", "description": "Roots and graphs.", "rationale": "Algebra.", "layers": [ { "id": "roots", "name": "Roots", "description": "Roots.", "findings": [ { "id": "roots-finding", "name": "Roots", "description": "Roots.", "questions": [ { "text": "How does degree bound the number of roots, and what does the fundamental theorem of algebra say?", "kind": "definition" }, { "text": "Which entry fits the fundamental theorem of algebra?", "kind": "action" } ] } ] }, { "id": "graphs", "name": "Graphs", "description": "Graphs.", "findings": [ { "id": "graphs-finding", "name": "Graphs", "description": "Graphs.", "questions": [ { "text": "How does degree shape the end behaviour and turning points of polynomial graphs?", "kind": "definition" }, { "text": "Which entry fits graphing?", "kind": "action" } ] } ] } ] }, { "id": "learn", "name": "Learn", "description": "History and teaching.", "rationale": "Education.", "layers": [ { "id": "history", "name": "History", "description": "History.", "findings": [ { "id": "history-finding", "name": "History", "description": "History.", "questions": [ { "text": "How did the study of polynomial degree develop in the history of algebra?", "kind": "provenance" }, { "text": "Which references are standard?", "kind": "provenance" } ] } ] }, { "id": "teach", "name": "Teach", "description": "Teaching.", "findings": [ { "id": "teach-finding", "name": "Teach", "description": "Teaching.", "questions": [ { "text": "How can degree be taught in school algebra?", "kind": "action" }, { "text": "Which misconceptions arise?", "kind": "provenance" } ] } ] } ] } ] }, "openQuestions": [ "Should polynomials be a separate entry?", "How should algebra resources be linked?", "How should conventions be documented?" ], "statistics": { "bundles": 4, "layers": 8, "findings": 8, "questions": 16 } }, "draft": { "generator": "vr.draft.v3", "status": "draft-generated", "researched": false, "archetype": "unit, quantity or measure", "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 degree of a polynomial, record what state it is in, and decide what may be done with it.", "whatItIs": "Let an agent explain the degree of a polynomial and its properties, support finding degrees and using them in algebra, describe the role of degree in roots and graphs, and support learning.", "characteristics": { "substance": "abstract", "origin": "conceptual", "agency": "inert" }, "whatYouCanDoWithIt": [ "observed and measured" ], "distinguishingFeatures": [ "Described in 30 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 degree of a polynomial, 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: a unit is a convention. What is seen is an instrument reading in it." ], "relatedModels": [], "standing": "Described in 30 Wikipedia languages, which measures how widely it is written about rather than how important or how common it is.", "structure": { "bundles": [ { "id": "identity-and-classification", "name": "Identity, naming and classification", "description": "How an agent tells one degree of a polynomial from another, and a degree of a polynomial 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 degree of a polynomial, 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 degree of a polynomial, 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 degree of a polynomial 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 degree of a polynomial, 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 degree of a polynomial, 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 degree of a polynomial 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 degree of a polynomial 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 degree of a polynomial, 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 degree of a polynomial, 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 degree of a polynomial 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 degree of a polynomial from the things most often confused with it.", "questions": [ { "id": "distinguishing-features-q01", "text": "What identifies and describes what distinguishes a degree of a polynomial, 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 degree of a polynomial, 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 degree of a polynomial 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 degree of a polynomial 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 degree of a polynomial between them.", "questions": [ { "id": "stages-and-transitions-q01", "text": "What identifies and describes the lifecycle of a degree of a polynomial, 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 degree of a polynomial, 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 degree of a polynomial 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 degree of a polynomial, how often and by whom.", "findings": [ { "id": "observation-record", "name": "Observation record", "description": "How an observation of a degree of a polynomial 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 degree of a polynomial, 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 degree of a polynomial, 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 degree of a polynomial is known, and what must it refuse?", "kind": "action", "answer_data": [ "permitted actions", "preconditions", "refusals", "escalation" ] } ] } ] } ] }, { "id": "definition-and-realisation", "name": "Definition, dimension and realisation", "description": "What degree of a polynomial is defined as and how it is realised in practice.", "rationale": "A unit is not the quantity it measures, and its definition has a history that older data still depends on.", "layers": [ { "id": "definition", "name": "Definition and dimension", "description": "The defining relation and the quantity it measures.", "findings": [ { "id": "definition-record", "name": "Definition, body and date", "description": "What defines it now, and what defined it before.", "questions": [ { "id": "definition-record-q01", "text": "How is degree of a polynomial defined, by which body, and since when?", "kind": "definition" }, { "id": "definition-record-q02", "text": "What was the previous definition, and what data still depends on it?", "kind": "provenance" } ] } ] }, { "id": "conversion", "name": "Conversion and compatibility", "description": "Relations to other units, exact or approximate.", "findings": [ { "id": "conversion-record", "name": "Conversions and their exactness", "description": "Factors, and whether each is exact by definition.", "questions": [ { "id": "conversion-record-q01", "text": "What conversions relate degree of a polynomial to other units, and which are exact by definition?", "kind": "measurement" }, { "id": "conversion-record-q02", "text": "Where does rounding a conversion change a decision, and how should that be recorded?", "kind": "action" } ] } ] } ] }, { "id": "provenance-and-evidence", "name": "Provenance, evidence and time", "description": "Where every claim about a degree of a polynomial 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 degree of a polynomial and how confident it is.", "questions": [ { "id": "claim-provenance-q01", "text": "What identifies and describes a claim about a degree of a polynomial, 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 degree of a polynomial, 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 degree of a polynomial 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 degree of a polynomial is retired without being erased.", "questions": [ { "id": "validity-and-supersession-q01", "text": "What identifies and describes the validity of a claim about a degree of a polynomial, 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 degree of a polynomial, 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 degree of a polynomial is known, and what must it refuse?", "kind": "action", "answer_data": [ "permitted actions", "preconditions", "refusals", "escalation" ] } ] } ] } ] } ] }, "statistics": { "bundles": 4, "layers": 8, "findings": 10, "questions": 28 } } } }