{ "model": { "rank": 1431, "code": "thing-q12503", "model_id": "vr.tr.integer", "name": "integer", "purpose": "Let an agent reason about integers mathematically and in computing, where fixed-width representations add overflow and signedness issues.", "family": "Thing Registry", "category": "Cross-cutting context", "status": "research-draft", "kind": "thing", "plane": "XCT", "domain": "XCT.QTY", "industry": "", "version": "", "url": "/models/thing/q12503/", "tier": 2, "score": 147, "payload": { "layer": "wikidata", "aliases": [ "process identifier", "even house number", "odd house number", "logical block address", "intersection number", "non-negative integer", "order of reflexion", "Miller index", "Skewes' number", "minimum vertex degree", "sphericity", "Takeuchi number", "trinomial coefficient", "Entringer number", "order of a difference equation", "Belgian number", "trimorphic number", "Loeschian number", "perfect digital invariant", "negative index of inertia", "order of a differential equation", "Wieferich number", "Descartes number", "Riesel number", "Sierpinski number", "product of two integers", "nonzero integer", "non-positive integer", "even number", "odd number", "Pell number", "almost perfect number", "Ramsey number", "heptanacci number", "Markov number", "Friedman number", "cyclic number", "self number", "cabtaxi number", "powerful number" ], "aliasCount": 53, "merged": 53, "knownIn": 147, "facets": null, "markers": [], "lexicalClass": "", "senseRank": null, "alsoRegisteredAs": "vr.tr.integer", "source": { "dataset": "wikidata", "item": "Q12503", "url": "https://www.wikidata.org/wiki/Q12503", "license": "CC0 1.0" } }, "research": { "vercy": "1.0-draft", "publication": { "status": "research-draft", "adjudicationStatus": "unreviewed", "publishableCanonical": false, "generatedAt": "2026-09-11T05:00:00Z", "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": 1, "engine": "claude" }, "metaModel": { "id": "THING-Q12503", "registryId": "vr.tr.integer", "name": "integer", "version": "0.2.0-wave.1", "entryKind": "thing", "family": "Thing Registry", "domain": [ "XCT.QTY" ], "status": "research-draft" }, "canonicalUrl": "https://ver.cy/models/thing/q12503/", "model": { "registry_id": "vr.tr.integer", "name": "integer", "purpose": "Let an agent reason about integers mathematically and in computing, where fixed-width representations add overflow and signedness issues.", "definition": "A number that is zero, a positive whole number or the negative of one: ..., -2, -1, 0, 1, 2, ...; the set Z.", "what_it_is_for": "Counting, indexing, identifiers and exact arithmetic.", "affordances": [ "add, subtract and multiply, staying within the integers", "divide with remainder", "store it, in fixed or arbitrary precision", "use it as an identifier, such as a process id or block address" ], "distinguishing_features": [ "Whole numbers, positive, negative and zero", "Closed under addition, subtraction and multiplication, not division", "Computer integers have fixed ranges unless arbitrary precision", "Numeric identifiers are not quantities" ], "appearance": "Digits without a fractional part, optionally with a minus sign.", "visual_identification": [ "Numerals with no decimal point", "Types such as int32, int64, BigInt in code", "Identifiers that look like integers are labels, not quantities" ], "physical_properties": [ { "quantity": "int32 range", "typical_range": "-2147483648 to 2147483647", "unit": "dimensionless", "note": "" }, { "quantity": "int64 maximum", "typical_range": "9223372036854775807", "unit": "dimensionless", "note": "" } ], "families_and_kinds": [ "natural numbers and non-negative integers", "even and odd integers", "primes", "signed and unsigned machine integers" ], "related_models": [ { "relation": "is a kind of", "target": "number", "why": "the set Z" }, { "relation": "has property", "target": "sign", "why": "positive, negative or zero" }, { "relation": "is used as", "target": "identifier", "why": "numeric labels" }, { "relation": "is confused with", "target": "floating-point number", "why": "approximate reals" } ], "identifiers": [ { "scheme": "OEIS", "value_or_pattern": "A-numbers", "note": "integer sequences" } ], "standards_and_regulation": [ "ISO 80000-2 notation", "ISO/IEC 9899 C and other language standards defining integer types" ], "failure_modes_and_hazards": [ "Integer overflow and wraparound", "Signed and unsigned mismatches", "Rounding when integers pass through floating point, such as in JSON beyond 2^53", "Doing arithmetic on identifiers" ], "in_scope": [], "out_of_scope": [], "characteristics": [] }, "sources": [], "structure": { "bundles": [ { "id": "mathematics", "name": "Mathematics", "description": "Properties of integers.", "rationale": "Mathematical properties underpin all use.", "layers": [ { "id": "arithmetic", "name": "Arithmetic", "description": "Operations and closure.", "findings": [ { "id": "arithmetic-finding", "name": "Operations", "description": "Operations and results.", "questions": [ { "text": "Does the operation stay within the integers?", "kind": "definition" }, { "text": "How is division with remainder defined here for negatives?", "kind": "boundary" } ] } ] }, { "id": "properties", "name": "Properties", "description": "Parity, primality, divisibility.", "findings": [ { "id": "properties-finding", "name": "Properties", "description": "Number-theoretic properties.", "questions": [ { "text": "Is it even or odd, prime or composite?", "kind": "measurement" }, { "text": "What are its divisors?", "kind": "measurement" } ] } ] } ] }, { "id": "representation", "name": "Representation", "description": "In computers.", "rationale": "Fixed-width integers behave differently from mathematical ones.", "layers": [ { "id": "width", "name": "Width and sign", "description": "int32, int64, unsigned.", "findings": [ { "id": "width-finding", "name": "Type", "description": "The type and range.", "questions": [ { "text": "Which integer type holds this value, and what is its range?", "kind": "definition" }, { "text": "Is it signed or unsigned?", "kind": "definition" } ] } ] }, { "id": "overflow", "name": "Overflow", "description": "Wraparound and errors.", "findings": [ { "id": "overflow-finding", "name": "Overflow handling", "description": "How overflow is handled.", "questions": [ { "text": "Can this calculation overflow?", "kind": "boundary" }, { "text": "Is overflow checked, wrapped or saturated?", "kind": "definition" } ] } ] } ] }, { "id": "interchange", "name": "Interchange", "description": "Passing integers between systems.", "rationale": "Formats can silently lose precision.", "layers": [ { "id": "formats", "name": "Formats", "description": "JSON, CSV, databases.", "findings": [ { "id": "formats-finding", "name": "Format limits", "description": "Limits of formats.", "questions": [ { "text": "Will this integer survive the format without loss?", "kind": "boundary" }, { "text": "Should it be sent as a string?", "kind": "action" } ] } ] }, { "id": "parsing", "name": "Parsing", "description": "Leading zeros and separators.", "findings": [ { "id": "parsing-finding", "name": "Parsing rules", "description": "Parsing rules.", "questions": [ { "text": "How are leading zeros and separators handled?", "kind": "boundary" }, { "text": "Is the value an identifier rather than a number?", "kind": "definition" } ] } ] } ] }, { "id": "identifiers", "name": "Identifiers", "description": "Integers as labels.", "rationale": "Many integers are labels, not quantities.", "layers": [ { "id": "label", "name": "Label or quantity", "description": "Nature of the value.", "findings": [ { "id": "label-finding", "name": "Nature", "description": "Whether the integer is a label.", "questions": [ { "text": "Is this integer a quantity or a label?", "kind": "definition" }, { "text": "What operations make sense on it?", "kind": "boundary" } ] } ] }, { "id": "uniqueness", "name": "Uniqueness", "description": "Scope of identifiers.", "findings": [ { "id": "uniqueness-finding", "name": "Scope", "description": "Where the identifier is unique.", "questions": [ { "text": "Within what scope is this identifier unique?", "kind": "boundary" }, { "text": "Can it be reused?", "kind": "boundary" } ] } ] } ] } ] }, "openQuestions": [ "Should machine integer types be separate entries?", "How should identifiers be marked so they are not treated as quantities?", "The registry entry has merged aliases such as house numbers; 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": "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 integer, record what state it is in, and decide what may be done with it.", "whatItIs": "Let an agent reason about integers mathematically and in computing, where fixed-width representations add overflow and signedness issues.", "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: process identifier, even house number, odd house number, logical block address, intersection number, non-negative integer, order of reflexion, Miller index, Skewes' number, minimum vertex degree, sphericity, Takeuchi number.", "53 finer distinctions are held as aliases rather than separate entries, because telling them apart needs a task that asks for it.", "Described in 147 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 integer, 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": [ { "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": [ "process identifier", "even house number", "odd house number", "logical block address", "intersection number", "non-negative integer", "order of reflexion", "Miller index", "Skewes' number", "minimum vertex degree", "sphericity", "Takeuchi number" ] } ], "standing": "Described in 147 Wikipedia languages, which measures how widely it is written about rather than how important or how common it is. 53 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 integer from another, and a integer 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 integer, 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 integer, 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 integer 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 integer, 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 integer, 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 integer 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 integer 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 integer, 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 integer, 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 integer 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 integer from the things most often confused with it.", "questions": [ { "id": "distinguishing-features-q01", "text": "What identifies and describes what distinguishes a integer, 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 integer, 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 integer 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 integer 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 integer between them.", "questions": [ { "id": "stages-and-transitions-q01", "text": "What identifies and describes the lifecycle of a integer, 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 integer, 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 integer 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 integer, how often and by whom.", "findings": [ { "id": "observation-record", "name": "Observation record", "description": "How an observation of a integer 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 integer, 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 integer, 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 integer 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 integer 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 integer 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 integer 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 integer 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 integer and how confident it is.", "questions": [ { "id": "claim-provenance-q01", "text": "What identifies and describes a claim about a integer, 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 integer, 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 integer 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 integer is retired without being erased.", "questions": [ { "id": "validity-and-supersession-q01", "text": "What identifies and describes the validity of a claim about a integer, 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 integer, 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 integer 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 } } } }