{ "model": { "rank": 6324, "code": "thing-q184743", "model_id": "vr.tr.periodic-function", "name": "periodic function", "purpose": "Let an agent define periodic functions and their period, frequency and harmonics, identify periodicity in data and models, explain Fourier analysis at an introductory level, and route applied questions to the relevant physical or signal-processing entries.", "family": "Thing Registry", "category": "Cross-cutting context", "status": "research-draft", "kind": "thing", "plane": "XCT", "domain": "XCT.QLT", "industry": "", "version": "", "url": "/models/thing/q184743/", "tier": 2, "score": 61, "payload": { "layer": "wikidata", "aliases": [ "molecular vibrations", "bending vibrations", "stretching vibrations", "Crenel function", "trigonometric polynomial", "periodic sequence", "Dirichlet kernel", "elliptic function", "Jacobi elliptic functions", "Weierstrass's elliptic functions" ], "aliasCount": 10, "merged": 10, "knownIn": 61, "facets": null, "markers": [], "lexicalClass": "", "senseRank": null, "alsoRegisteredAs": null, "source": { "dataset": "wikidata", "item": "Q184743", "url": "https://www.wikidata.org/wiki/Q184743", "license": "CC0 1.0" } }, "research": { "vercy": "1.0-draft", "publication": { "status": "research-draft", "adjudicationStatus": "unreviewed", "publishableCanonical": false, "generatedAt": "2026-09-12T20:21:37Z", "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-Q184743", "registryId": "vr.tr.periodic-function", "name": "periodic function", "version": "0.2.0-wave.3", "entryKind": "thing", "family": "Thing Registry", "domain": [ "XCT.QLT" ], "status": "research-draft" }, "canonicalUrl": "https://ver.cy/models/thing/q184743/", "model": { "registry_id": "vr.tr.periodic-function", "name": "periodic function", "purpose": "Let an agent define periodic functions and their period, frequency and harmonics, identify periodicity in data and models, explain Fourier analysis at an introductory level, and route applied questions to the relevant physical or signal-processing entries.", "definition": "A function whose values repeat at regular intervals, so that f of x plus P equals f of x for some fixed period P and all x; sine and cosine are the basic examples, and periodic functions describe waves, vibrations, rotations, tides and seasonal patterns, and are analysed through Fourier series into sums of sinusoids.", "what_it_is_for": "Describing repeating phenomena mathematically.", "affordances": [ "define period, frequency and fundamental period", "test whether a function or signal is periodic", "explain Fourier series and harmonics", "give examples from physics and signals" ], "distinguishing_features": [ "Invariance under shift by the period", "Fundamental period and its multiples", "Decomposable into sinusoids by Fourier series", "Continuous and discrete versions" ], "appearance": "Not visible in itself; a graph that repeats the same shape along the axis.", "visual_identification": [ "Graph repeating with a fixed period", "Sinusoids as the basic building blocks", "Quasi-periodic and almost periodic functions repeat only approximately" ], "physical_properties": [], "families_and_kinds": [ "trigonometric functions and trigonometric polynomials", "square, sawtooth and other waveforms", "periodic sequences", "elliptic and doubly periodic functions", "almost periodic functions, related", "periodic signals in engineering" ], "related_models": [ { "relation": "is a kind of", "target": "function", "why": "a mathematical function" }, { "relation": "is analysed by", "target": "Fourier series", "why": "decomposition into sinusoids" }, { "relation": "includes", "target": "sine function", "why": "the basic example" }, { "relation": "describes", "target": "oscillation", "why": "a physical application" } ], "identifiers": [], "standards_and_regulation": [ "No regulation; definitions follow standard mathematics" ], "failure_modes_and_hazards": [ "Confusing a period with the fundamental period", "Treating approximately repeating data as exactly periodic", "Aliasing when sampling periodic signals" ], "in_scope": [], "out_of_scope": [], "characteristics": [] }, "sources": [], "structure": { "bundles": [ { "id": "define", "name": "Define", "description": "What periodicity is.", "rationale": "Definition.", "layers": [ { "id": "definition", "name": "Definition", "description": "Definition.", "findings": [ { "id": "definition-finding", "name": "Definition", "description": "Definition.", "questions": [ { "text": "What defines a periodic function, and what are its period, fundamental period and frequency?", "kind": "definition" }, { "text": "Is the function exactly periodic, almost periodic or merely oscillating?", "kind": "boundary" } ] } ] }, { "id": "examples", "name": "Examples", "description": "Examples.", "findings": [ { "id": "examples-finding", "name": "Examples", "description": "Examples.", "questions": [ { "text": "What are the standard examples and waveforms?", "kind": "definition" }, { "text": "Which entry fits a specific function?", "kind": "action" } ] } ] } ] }, { "id": "analyse", "name": "Analyse", "description": "Fourier analysis.", "rationale": "Theory.", "layers": [ { "id": "fourier", "name": "Fourier", "description": "Fourier series.", "findings": [ { "id": "fourier-finding", "name": "Fourier", "description": "Fourier.", "questions": [ { "text": "How does a Fourier series decompose a periodic function, and what are harmonics?", "kind": "definition" }, { "text": "Which entry fits Fourier analysis?", "kind": "action" } ] } ] }, { "id": "properties", "name": "Properties", "description": "Properties.", "findings": [ { "id": "properties-finding", "name": "Properties", "description": "Properties.", "questions": [ { "text": "What properties do periodic functions have under sums, products and derivatives?", "kind": "provenance" }, { "text": "Which references are standard?", "kind": "provenance" } ] } ] } ] }, { "id": "detect", "name": "Detect", "description": "Periodicity in data.", "rationale": "Practice.", "layers": [ { "id": "data", "name": "Data", "description": "Detecting periods.", "findings": [ { "id": "data-finding", "name": "Data", "description": "Data.", "questions": [ { "text": "How is periodicity detected and the period estimated in data?", "kind": "measurement" }, { "text": "What uncertainty applies?", "kind": "measurement" } ] } ] }, { "id": "sampling", "name": "Sampling", "description": "Sampling and aliasing.", "findings": [ { "id": "sampling-finding", "name": "Sampling", "description": "Sampling.", "questions": [ { "text": "How does sampling affect periodic signals, and what is aliasing?", "kind": "provenance" }, { "text": "Which entry fits signal processing?", "kind": "action" } ] } ] } ] }, { "id": "apply", "name": "Apply", "description": "Applications and teaching.", "rationale": "Applications.", "layers": [ { "id": "physics", "name": "Physics", "description": "Physical applications.", "findings": [ { "id": "physics-finding", "name": "Physics", "description": "Physics.", "questions": [ { "text": "How do periodic functions describe waves, vibrations and rotations?", "kind": "provenance" }, { "text": "Which entry fits oscillation?", "kind": "action" } ] } ] }, { "id": "teach", "name": "Teach", "description": "Teaching.", "findings": [ { "id": "teach-finding", "name": "Teach", "description": "Teaching.", "questions": [ { "text": "How are periodic functions taught, and which misconceptions arise?", "kind": "provenance" }, { "text": "Which entry fits trigonometry?", "kind": "action" } ] } ] } ] } ] }, "openQuestions": [ "Should waveforms and Fourier series be separate entries?", "How should signal-processing applications be linked?", "The registry entry has merged aliases for molecular vibrations, which belong to physics; 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 periodic function, record what state it is in, and decide what may be done with it.", "whatItIs": "Let an agent define periodic functions and their period, frequency and harmonics, identify periodicity in data and models, explain Fourier analysis at an introductory level, and route applied questions to the relevant physical or signal-processing entries.", "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: molecular vibrations, bending vibrations, stretching vibrations, Crenel function, trigonometric polynomial, periodic sequence, Dirichlet kernel, elliptic function, Jacobi elliptic functions, Weierstrass's elliptic functions.", "10 finer distinctions are held as aliases rather than separate entries, because telling them apart needs a task that asks for it.", "Described in 61 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 periodic function, 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": [ "molecular vibrations", "bending vibrations", "stretching vibrations", "Crenel function", "trigonometric polynomial", "periodic sequence", "Dirichlet kernel", "elliptic function", "Jacobi elliptic functions", "Weierstrass's elliptic functions" ] } ], "standing": "Described in 61 Wikipedia languages, which measures how widely it is written about rather than how important or how common it is. 10 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 periodic function from another, and a periodic function 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 periodic function, 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 periodic function, 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 periodic function 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 periodic function, 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 periodic function, 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 periodic function 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 periodic function 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 periodic function, 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 periodic function, 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 periodic function 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 periodic function from the things most often confused with it.", "questions": [ { "id": "distinguishing-features-q01", "text": "What identifies and describes what distinguishes a periodic function, 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 periodic function, 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 periodic function 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 periodic function 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 periodic function between them.", "questions": [ { "id": "stages-and-transitions-q01", "text": "What identifies and describes the lifecycle of a periodic function, 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 periodic function, 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 periodic function 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 periodic function, how often and by whom.", "findings": [ { "id": "observation-record", "name": "Observation record", "description": "How an observation of a periodic function 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 periodic function, 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 periodic function, 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 periodic function 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 periodic function 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 periodic function 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 periodic function 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 periodic function 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 periodic function?", "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 periodic function?", "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 periodic function 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 periodic function and how confident it is.", "questions": [ { "id": "claim-provenance-q01", "text": "What identifies and describes a claim about a periodic function, 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 periodic function, 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 periodic function 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 periodic function is retired without being erased.", "questions": [ { "id": "validity-and-supersession-q01", "text": "What identifies and describes the validity of a claim about a periodic function, 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 periodic function, 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 periodic function 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 } } } }