{ "model": { "rank": 5481, "code": "thing-q179976", "model_id": "vr.tr.recursion", "name": "recursion", "purpose": "Let an agent explain recursion, relay definitions, programming techniques, termination and stack concerns, type theory uses and linguistic debates from computer science, mathematics and linguistics sources with positions attributed, describe the named forms, and distinguish recursion from iteration, induction, self-similarity and circular definitions.", "family": "Thing Registry", "category": "Cross-cutting context", "status": "research-draft", "kind": "thing", "plane": "XCT", "domain": "XCT.QLT", "industry": "", "version": "", "url": "/models/thing/q179976/", "tier": 2, "score": 67, "payload": { "layer": "wikidata", "aliases": [ "anonymous recursion", "nesting", "F-bounded quantification", "tail recursion", "linguistic recursivity" ], "aliasCount": 5, "merged": 5, "knownIn": 67, "facets": null, "markers": [], "lexicalClass": "", "senseRank": null, "alsoRegisteredAs": null, "source": { "dataset": "wikidata", "item": "Q179976", "url": "https://www.wikidata.org/wiki/Q179976", "license": "CC0 1.0" } }, "research": { "vercy": "1.0-draft", "publication": { "status": "research-draft", "adjudicationStatus": "unreviewed", "publishableCanonical": false, "generatedAt": "2026-09-13T22:13:41Z", "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-Q179976", "registryId": "vr.tr.recursion", "name": "recursion", "version": "0.2.0-wave.4", "entryKind": "thing", "family": "Thing Registry", "domain": [ "XCT.QLT" ], "status": "research-draft" }, "canonicalUrl": "https://ver.cy/models/thing/q179976/", "model": { "registry_id": "vr.tr.recursion", "name": "recursion", "purpose": "Let an agent explain recursion, relay definitions, programming techniques, termination and stack concerns, type theory uses and linguistic debates from computer science, mathematics and linguistics sources with positions attributed, describe the named forms, and distinguish recursion from iteration, induction, self-similarity and circular definitions.", "definition": "The process in which a function, structure or definition refers to itself, used in mathematics to define sequences and sets, in computer science where a function calls itself with base cases to stop, including tail recursion, which compilers can optimise into loops, and anonymous recursion through fixed-point combinators, in type theory in forms such as F-bounded quantification, and in linguistics, where recursivity lets phrases be nested inside phrases, a claim central to generative grammar whose universality is debated, as in discussions of the Piraha language; nesting and self-similarity in fractals are related ideas.", "what_it_is_for": "Defining and computing things in terms of themselves.", "affordances": [ "explain recursion across fields", "relay programming techniques and pitfalls", "describe named forms", "distinguish related concepts" ], "distinguishing_features": [ "Self-reference", "Base cases", "Call stack use", "Cross-disciplinary" ], "appearance": "Not a physical object; seen in code, formulas, nested structures and fractals.", "visual_identification": [ "Self-reference with a base case", "Anonymous recursion, nesting, F-bounded quantification, tail recursion, linguistic recursivity", "Iteration repeats with loops; induction is a proof method; self-similarity is geometric; circular definitions lack a base" ], "physical_properties": [ { "quantity": "key requirement", "typical_range": "base case for termination", "unit": "note", "note": "" }, { "quantity": "Y combinator", "typical_range": "fixed-point combinator for anonymous recursion", "unit": "note", "note": "Curry" }, { "quantity": "Piraha recursion debate", "typical_range": "from 2005", "unit": "note", "note": "Everett, attributed" } ], "families_and_kinds": [ "direct and mutual recursion", "tail recursion", "structural recursion", "anonymous recursion", "recursive types and bounded quantification", "recursion in syntax" ], "related_models": [ { "relation": "is a kind of", "target": "self-similarity", "why": "in registry terms" }, { "relation": "is related to", "target": "mathematical induction", "why": "" }, { "relation": "includes", "target": "tail call", "why": "" }, { "relation": "is contrasted with", "target": "iteration", "why": "" } ], "identifiers": [], "standards_and_regulation": [ "No regulation; language standards specify tail call behaviour in some languages such as Scheme" ], "failure_modes_and_hazards": [ "Infinite recursion without base cases", "Stack overflow", "Overstating linguistic universality claims" ], "in_scope": [], "out_of_scope": [], "characteristics": [] }, "sources": [], "structure": { "bundles": [ { "id": "understand", "name": "Understand", "description": "What recursion is.", "rationale": "Definition.", "layers": [ { "id": "definition", "name": "Definition", "description": "Definition.", "findings": [ { "id": "definition-finding", "name": "Definition", "description": "Definition.", "questions": [ { "text": "What is recursion, and how does it differ from iteration, induction, self-similarity and circular definitions?", "kind": "definition" }, { "text": "Is the question about programming, mathematics, type theory or linguistics?", "kind": "boundary" } ] } ] }, { "id": "forms", "name": "Forms", "description": "Named forms.", "findings": [ { "id": "forms-finding", "name": "Forms", "description": "Forms.", "questions": [ { "text": "What are anonymous recursion, nesting, F-bounded quantification, tail recursion and linguistic recursivity?", "kind": "definition" }, { "text": "Which entry fits the specific form?", "kind": "action" } ] } ] } ] }, { "id": "computing", "name": "Computing", "description": "Programming.", "rationale": "Sources.", "layers": [ { "id": "base", "name": "Base cases", "description": "Base cases and termination.", "findings": [ { "id": "base-finding", "name": "Base cases", "description": "Base cases.", "questions": [ { "text": "How do base cases stop recursion, and what causes stack overflow?", "kind": "provenance" }, { "text": "Which references are standard?", "kind": "provenance" } ] } ] }, { "id": "tail", "name": "Tail calls", "description": "Tail call optimisation.", "findings": [ { "id": "tail-finding", "name": "Tail calls", "description": "Tail calls.", "questions": [ { "text": "How do compilers turn tail recursion into loops, and which languages guarantee it?", "kind": "provenance" }, { "text": "Which sources are cited?", "kind": "provenance" } ] } ] } ] }, { "id": "theory", "name": "Theory", "description": "Mathematics and types.", "rationale": "Science.", "layers": [ { "id": "functions", "name": "Functions", "description": "Recursive functions.", "findings": [ { "id": "functions-finding", "name": "Functions", "description": "Functions.", "questions": [ { "text": "How did recursive function theory shape computability?", "kind": "provenance" }, { "text": "Which entry fits computable function?", "kind": "action" } ] } ] }, { "id": "types", "name": "Types", "description": "Recursive types.", "findings": [ { "id": "types-finding", "name": "Types", "description": "Types.", "questions": [ { "text": "What is F-bounded quantification in object-oriented type systems?", "kind": "provenance" }, { "text": "Which entry fits bounded quantification?", "kind": "action" } ] } ] } ] }, { "id": "context", "name": "Context", "description": "Language.", "rationale": "Attribution.", "layers": [ { "id": "syntax", "name": "Syntax", "description": "Recursion in syntax.", "findings": [ { "id": "syntax-finding", "name": "Syntax", "description": "Syntax.", "questions": [ { "text": "Why do generative linguists treat recursion as central to language?", "kind": "provenance" }, { "text": "Which entry fits generative grammar?", "kind": "action" } ] } ] }, { "id": "piraha", "name": "Piraha debate", "description": "Piraha debate.", "findings": [ { "id": "piraha-finding", "name": "Piraha debate", "description": "Piraha debate.", "questions": [ { "text": "What did Everett and his critics argue about recursion in Piraha, with positions attributed?", "kind": "provenance" }, { "text": "Is the presentation neutral and attributed?", "kind": "boundary" } ] } ] } ] } ] }, "openQuestions": [ "Should linguistic recursion be a separate entry?", "How should computer science sources be linked?", "Should F-bounded quantification be moved to type theory entries?" ], "statistics": { "bundles": 4, "layers": 8, "findings": 8, "questions": 16 } }, "draft": { "generator": "vr.draft.v3", "status": "draft-generated", "researched": false, "archetype": "abstract concept", "method": "Written from the archetype playbook - what this kind of thing needs beyond identity and provenance - and from the structure that recurred across 6,333 models already researched by two engines. Applied to this entry by rule. No source was read for this thing and no claim here is researched. This entry carries no facets of its own, so they were inferred from its domain - a guess about a whole domain applied to one thing.", "facetsInferred": true, "nextPass": "A researcher replaces this draft with a sourced specification. Treat every sentence below as a proposal to argue with.", "purpose": "Give an agent a durable, checkable way to recognise a recursion, record what state it is in, and decide what may be done with it.", "whatItIs": "Let an agent explain recursion, relay definitions, programming techniques, termination and stack concerns, type theory uses and linguistic debates from computer science, mathematics and linguistics sources with positions attributed, describe the named forms, and distinguish recursion from iteration, induction, self-similarity and circular definitions.", "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: anonymous recursion, nesting, F-bounded quantification, tail recursion, linguistic recursivity.", "5 finer distinctions are held as aliases rather than separate entries, because telling them apart needs a task that asks for it.", "Described in 67 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 recursion, 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": [ "anonymous recursion", "nesting", "F-bounded quantification", "tail recursion", "linguistic recursivity" ] } ], "standing": "Described in 67 Wikipedia languages, which measures how widely it is written about rather than how important or how common it is. 5 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 recursion from another, and a recursion 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 recursion, 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 recursion, 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 recursion 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 recursion, 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 recursion, 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 recursion 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 recursion 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 recursion, 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 recursion, 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 recursion 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 recursion from the things most often confused with it.", "questions": [ { "id": "distinguishing-features-q01", "text": "What identifies and describes what distinguishes a recursion, 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 recursion, 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 recursion 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 recursion 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 recursion between them.", "questions": [ { "id": "stages-and-transitions-q01", "text": "What identifies and describes the lifecycle of a recursion, 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 recursion, 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 recursion 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 recursion, how often and by whom.", "findings": [ { "id": "observation-record", "name": "Observation record", "description": "How an observation of a recursion 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 recursion, 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 recursion, 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 recursion 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 recursion 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 recursion 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 recursion 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 recursion 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 recursion?", "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 recursion?", "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 recursion 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 recursion and how confident it is.", "questions": [ { "id": "claim-provenance-q01", "text": "What identifies and describes a claim about a recursion, 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 recursion, 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 recursion 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 recursion is retired without being erased.", "questions": [ { "id": "validity-and-supersession-q01", "text": "What identifies and describes the validity of a claim about a recursion, 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 recursion, 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 recursion 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 } } } }