{ "model": { "rank": 3032, "code": "thing-q177239", "model_id": "vr.tr.limit", "name": "limit", "purpose": "Let an agent explain and compute mathematical limits, explain their rigorous definition and role, and separate the everyday and regulatory senses of limit.", "family": "Thing Registry", "category": "Cross-cutting context", "status": "research-draft", "kind": "thing", "plane": "XCT", "domain": "XCT.QLT", "industry": "", "version": "", "url": "/models/thing/q177239/", "tier": 2, "score": 92, "payload": { "layer": "wikidata", "aliases": [ "set-theoretic limit", "mutation limit", "Cesaro summation", "liability limit", "maximum residue limit", "limit of a function", "control limit", "resolution limit", "engineering tolerance", "limit from below", "limit from above", "critical value", "warning limit", "action limit", "Shewhart control limit", "upper control limit", "lower control limit", "engineering fit", "ABEC scale", "fit", "yield criterion", "threshold value", "Herd immunity threshold" ], "aliasCount": 23, "merged": 23, "knownIn": 92, "facets": null, "markers": [], "lexicalClass": "", "senseRank": null, "alsoRegisteredAs": "vr.tr.limit-3", "source": { "dataset": "wikidata", "item": "Q177239", "url": "https://www.wikidata.org/wiki/Q177239", "license": "CC0 1.0" } }, "research": { "vercy": "1.0-draft", "publication": { "status": "research-draft", "adjudicationStatus": "unreviewed", "publishableCanonical": false, "generatedAt": "2026-09-11T19:59:16Z", "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-Q177239", "registryId": "vr.tr.limit", "name": "limit", "version": "0.2.0-wave.2", "entryKind": "thing", "family": "Thing Registry", "domain": [ "XCT.QLT" ], "status": "research-draft" }, "canonicalUrl": "https://ver.cy/models/thing/q177239/", "model": { "registry_id": "vr.tr.limit", "name": "limit", "purpose": "Let an agent explain and compute mathematical limits, explain their rigorous definition and role, and separate the everyday and regulatory senses of limit.", "definition": "In mathematics, the value that a function or sequence approaches as the input or index approaches some value or infinity, defined rigorously by epsilon-delta and related definitions and underpinning continuity, derivatives, integrals and series, with extensions such as set-theoretic limits and summation methods; outside mathematics the word denotes a boundary or maximum, as in speed limits, liability limits and residue limits.", "what_it_is_for": "Foundations of calculus and analysis.", "affordances": [ "compute limits of functions and sequences", "explain the rigorous definition", "explain the role of limits in calculus", "separate regulatory and everyday senses" ], "distinguishing_features": [ "Value approached", "Rigorous definition", "Foundation of calculus", "Homonym with bounds and rules" ], "appearance": "Not physical; notation and definitions.", "visual_identification": [ "lim notation", "Approach to a value", "A bound is not necessarily a limit" ], "physical_properties": [], "families_and_kinds": [ "limits of sequences", "limits of functions", "one-sided and infinite limits", "set-theoretic limits and summation methods", "limits in the sense of bounds and rules (separate sense)" ], "related_models": [ { "relation": "is a kind of", "target": "mathematical concept", "why": "category" }, { "relation": "is a kind of", "target": "upper and lower bounds", "why": "category" }, { "relation": "is studied in", "target": "mathematical analysis", "why": "field" }, { "relation": "underlies", "target": "integral", "why": "definition" } ], "identifiers": [], "standards_and_regulation": [ "ISO 80000-2 notation", "Regulatory limits are governed by domain-specific rules" ], "failure_modes_and_hazards": [ "Treating limits as values reached", "Ignoring one-sided differences", "Confusing senses" ], "in_scope": [], "out_of_scope": [], "characteristics": [] }, "sources": [], "structure": { "bundles": [ { "id": "compute", "name": "Compute", "description": "Finding limits.", "rationale": "Techniques.", "layers": [ { "id": "evaluate", "name": "Evaluate", "description": "Evaluating a limit.", "findings": [ { "id": "evaluate-finding", "name": "Evaluate", "description": "Evaluation.", "questions": [ { "text": "What is the limit of this function or sequence, and which technique shows it?", "kind": "measurement" }, { "text": "Does the limit exist, and are one-sided limits equal?", "kind": "boundary" } ] } ] }, { "id": "indeterminate", "name": "Indeterminate", "description": "Indeterminate forms.", "findings": [ { "id": "indeterminate-finding", "name": "Indeterminate", "description": "Indeterminate forms.", "questions": [ { "text": "How are indeterminate forms resolved, for example by algebra or the rule of l Hopital?", "kind": "action" }, { "text": "When does the rule apply?", "kind": "boundary" } ] } ] } ] }, { "id": "define", "name": "Define", "description": "Rigorous definition.", "rationale": "Epsilon and delta.", "layers": [ { "id": "epsilon", "name": "Epsilon", "description": "Formal definition.", "findings": [ { "id": "epsilon-finding", "name": "Epsilon", "description": "Formal definition.", "questions": [ { "text": "What is the epsilon-delta definition of this limit, and how is it used in a proof?", "kind": "definition" }, { "text": "How does the sequence definition differ?", "kind": "definition" } ] } ] }, { "id": "role", "name": "Role", "description": "Role in calculus.", "findings": [ { "id": "role-finding", "name": "Role", "description": "Role.", "questions": [ { "text": "How do limits define continuity, derivatives, integrals and series?", "kind": "definition" }, { "text": "Why were limits introduced historically?", "kind": "provenance" } ] } ] } ] }, { "id": "advanced", "name": "Advanced", "description": "Generalisations.", "rationale": "Beyond the basics.", "layers": [ { "id": "sets", "name": "Sets", "description": "Set-theoretic limits.", "findings": [ { "id": "sets-finding", "name": "Sets", "description": "Set limits.", "questions": [ { "text": "What are the limit superior and inferior of a sequence of sets or numbers?", "kind": "definition" }, { "text": "Where are they used?", "kind": "provenance" } ] } ] }, { "id": "summation", "name": "Summation", "description": "Summation methods.", "findings": [ { "id": "summation-finding", "name": "Summation", "description": "Summation methods.", "questions": [ { "text": "What does Cesaro summation assign to a divergent series, and how does it relate to limits?", "kind": "definition" }, { "text": "When are such methods legitimate?", "kind": "boundary" } ] } ] } ] }, { "id": "senses", "name": "Senses", "description": "Other senses.", "rationale": "Bounds and rules.", "layers": [ { "id": "regulatory", "name": "Regulatory", "description": "Limits as rules.", "findings": [ { "id": "regulatory-finding", "name": "Regulatory", "description": "Regulatory limits.", "questions": [ { "text": "Is a regulatory or contractual limit meant, such as a speed, liability or residue limit?", "kind": "boundary" }, { "text": "Which entry or authority applies?", "kind": "action" } ] } ] }, { "id": "teach", "name": "Teach", "description": "Teaching limits.", "findings": [ { "id": "teach-finding", "name": "Teach", "description": "Teaching.", "questions": [ { "text": "How can limits be taught intuitively before formalising?", "kind": "action" }, { "text": "Which misconceptions arise?", "kind": "provenance" } ] } ] } ] } ] }, "openQuestions": [ "Should sequence and function limits be separate entries?", "How should teaching resources be linked?", "How should regulatory senses be split?" ], "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 limit, record what state it is in, and decide what may be done with it.", "whatItIs": "Let an agent explain and compute mathematical limits, explain their rigorous definition and role, and separate the everyday and regulatory senses of limit.", "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: set-theoretic limit, mutation limit, Cesaro summation, liability limit, maximum residue limit, limit of a function, control limit, resolution limit, engineering tolerance, limit from below, limit from above, critical value.", "23 finer distinctions are held as aliases rather than separate entries, because telling them apart needs a task that asks for it.", "Described in 92 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 limit, 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": [ "set-theoretic limit", "mutation limit", "Cesaro summation", "liability limit", "maximum residue limit", "limit of a function", "control limit", "resolution limit", "engineering tolerance", "limit from below", "limit from above", "critical value" ] } ], "standing": "Described in 92 Wikipedia languages, which measures how widely it is written about rather than how important or how common it is. 23 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 limit from another, and a limit 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 limit, 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 limit, 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 limit 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 limit, 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 limit, 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 limit 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 limit 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 limit, 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 limit, 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 limit 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 limit from the things most often confused with it.", "questions": [ { "id": "distinguishing-features-q01", "text": "What identifies and describes what distinguishes a limit, 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 limit, 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 limit 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 limit 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 limit between them.", "questions": [ { "id": "stages-and-transitions-q01", "text": "What identifies and describes the lifecycle of a limit, 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 limit, 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 limit 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 limit, how often and by whom.", "findings": [ { "id": "observation-record", "name": "Observation record", "description": "How an observation of a limit 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 limit, 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 limit, 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 limit 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 limit 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 limit 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 limit 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 limit 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 limit?", "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 limit?", "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 limit 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 limit and how confident it is.", "questions": [ { "id": "claim-provenance-q01", "text": "What identifies and describes a claim about a limit, 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 limit, 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 limit 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 limit is retired without being erased.", "questions": [ { "id": "validity-and-supersession-q01", "text": "What identifies and describes the validity of a claim about a limit, 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 limit, 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 limit 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 } } } }