{ "model": { "rank": 1666, "code": "thing-q40276", "model_id": "vr.tr.multiplication", "name": "multiplication", "purpose": "Let an agent explain multiplication and its properties across number systems, describe generalisations such as scalar, matrix and Hadamard products, relay algorithms and teaching approaches, and help compute or check products.", "family": "Thing Registry", "category": "Cross-cutting context", "status": "research-draft", "kind": "thing", "plane": "XCT", "domain": "XCT.QLT", "industry": "", "version": "", "url": "/models/thing/q40276/", "tier": 2, "score": 133, "payload": { "layer": "wikidata", "aliases": [ "scalar multiplication", "matrix multiplication", "doubling", "Hadamard product" ], "aliasCount": 4, "merged": 4, "knownIn": 133, "facets": null, "markers": [], "lexicalClass": "", "senseRank": null, "alsoRegisteredAs": null, "source": { "dataset": "wikidata", "item": "Q40276", "url": "https://www.wikidata.org/wiki/Q40276", "license": "CC0 1.0" } }, "research": { "vercy": "1.0-draft", "publication": { "status": "research-draft", "adjudicationStatus": "unreviewed", "publishableCanonical": false, "generatedAt": "2026-09-12T23:20:25Z", "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-Q40276", "registryId": "vr.tr.multiplication", "name": "multiplication", "version": "0.2.0-wave.3", "entryKind": "thing", "family": "Thing Registry", "domain": [ "XCT.QLT" ], "status": "research-draft" }, "canonicalUrl": "https://ver.cy/models/thing/q40276/", "model": { "registry_id": "vr.tr.multiplication", "name": "multiplication", "purpose": "Let an agent explain multiplication and its properties across number systems, describe generalisations such as scalar, matrix and Hadamard products, relay algorithms and teaching approaches, and help compute or check products.", "definition": "A binary arithmetic operation that combines two numbers to give their product, defined for natural numbers as repeated addition and extended to integers, rationals, reals and complex numbers, and generalised to scalar multiplication of vectors, matrix multiplication, the element-wise Hadamard product and multiplication in rings and groups; multiplication is commutative and associative for numbers, distributes over addition, and is a foundation of arithmetic and algebra.", "what_it_is_for": "Combining quantities by scaling.", "affordances": [ "explain the operation and properties", "describe generalisations", "relay algorithms and teaching", "compute or check products" ], "distinguishing_features": [ "Commutative and associative for numbers", "Distributive over addition", "Identity one and inverses for nonzero numbers", "Non-commutative generalisations" ], "appearance": "Not a visible object; expressions with times signs, dots or juxtaposition.", "visual_identification": [ "Binary operation giving a product", "Numbers, vectors, matrices and abstract structures", "Addition combines by summing; exponentiation is repeated multiplication" ], "physical_properties": [], "families_and_kinds": [ "multiplication of natural numbers, integers, rationals, reals and complex numbers", "scalar multiplication of vectors", "matrix multiplication", "Hadamard element-wise product", "multiplication in rings, fields and groups", "doubling as a special case" ], "related_models": [ { "relation": "is a kind of", "target": "binary operation", "why": "in registry terms" }, { "relation": "is inverse to", "target": "division", "why": "for nonzero divisors" }, { "relation": "generalises to", "target": "matrix multiplication", "why": "in linear algebra" }, { "relation": "distributes over", "target": "addition", "why": "the distributive law" } ], "identifiers": [ { "scheme": "symbols", "value_or_pattern": "times sign, middle dot, asterisk", "note": "notation" } ], "standards_and_regulation": [ "ISO 80000-2 notation for multiplication", "Curriculum standards for arithmetic" ], "failure_modes_and_hazards": [ "Assuming commutativity in matrix multiplication", "Overflow in computer arithmetic", "Confusing element-wise and matrix products" ], "in_scope": [], "out_of_scope": [], "characteristics": [] }, "sources": [], "structure": { "bundles": [ { "id": "define", "name": "Define", "description": "What multiplication is.", "rationale": "Definition.", "layers": [ { "id": "definition", "name": "Definition", "description": "Definition and properties.", "findings": [ { "id": "definition-finding", "name": "Definition", "description": "Definition.", "questions": [ { "text": "What is multiplication, and what properties does it have across number systems?", "kind": "definition" }, { "text": "Is the question about number multiplication or a generalisation?", "kind": "boundary" } ] } ] }, { "id": "generalisations", "name": "Generalisations", "description": "Generalisations.", "findings": [ { "id": "generalisations-finding", "name": "Generalisations", "description": "Generalisations.", "questions": [ { "text": "How do scalar, matrix, Hadamard and abstract multiplications differ?", "kind": "definition" }, { "text": "Which entry fits the specific generalisation?", "kind": "action" } ] } ] } ] }, { "id": "compute", "name": "Compute", "description": "Computation.", "rationale": "Computation.", "layers": [ { "id": "algorithms", "name": "Algorithms", "description": "Algorithms.", "findings": [ { "id": "algorithms-finding", "name": "Algorithms", "description": "Algorithms.", "questions": [ { "text": "How are products computed by hand and by algorithms such as long multiplication and Karatsuba?", "kind": "action" }, { "text": "What is the result for the values in question?", "kind": "measurement" } ] } ] }, { "id": "computers", "name": "Computers", "description": "Computer arithmetic.", "findings": [ { "id": "computers-finding", "name": "Computers", "description": "Computers.", "questions": [ { "text": "How do computers multiply integers and floating-point numbers, and where do errors arise?", "kind": "provenance" }, { "text": "Which entry fits computer arithmetic?", "kind": "action" } ] } ] } ] }, { "id": "theory", "name": "Theory", "description": "Algebraic structure.", "rationale": "Theory.", "layers": [ { "id": "structure", "name": "Structure", "description": "Rings and groups.", "findings": [ { "id": "structure-finding", "name": "Structure", "description": "Structure.", "questions": [ { "text": "How is multiplication axiomatised in rings, fields and groups?", "kind": "provenance" }, { "text": "Which references are standard?", "kind": "provenance" } ] } ] }, { "id": "matrices", "name": "Matrices", "description": "Matrix multiplication.", "findings": [ { "id": "matrices-finding", "name": "Matrices", "description": "Matrices.", "questions": [ { "text": "Why is matrix multiplication non-commutative, and how does it represent composition?", "kind": "provenance" }, { "text": "Which entry fits linear algebra?", "kind": "action" } ] } ] } ] }, { "id": "context", "name": "Context", "description": "History and teaching.", "rationale": "Context.", "layers": [ { "id": "history", "name": "History", "description": "History.", "findings": [ { "id": "history-finding", "name": "History", "description": "History.", "questions": [ { "text": "How did multiplication methods develop, from Egyptian doubling to modern algorithms?", "kind": "provenance" }, { "text": "Which entry fits the history of arithmetic?", "kind": "action" } ] } ] }, { "id": "teach", "name": "Teach", "description": "Teaching.", "findings": [ { "id": "teach-finding", "name": "Teach", "description": "Teaching.", "questions": [ { "text": "How is multiplication taught, and which misconceptions arise?", "kind": "provenance" }, { "text": "Which sources are cited?", "kind": "provenance" } ] } ] } ] } ] }, "openQuestions": [ "Should matrix multiplication be a separate primary entry?", "How should notation standards be linked?", "The registry entry has merged aliases naming generalisations; 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 multiplication, record what state it is in, and decide what may be done with it.", "whatItIs": "Let an agent explain multiplication and its properties across number systems, describe generalisations such as scalar, matrix and Hadamard products, relay algorithms and teaching approaches, and help compute or check products.", "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: scalar multiplication, matrix multiplication, doubling, Hadamard product.", "4 finer distinctions are held as aliases rather than separate entries, because telling them apart needs a task that asks for it.", "Described in 133 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 multiplication, 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": [ "scalar multiplication", "matrix multiplication", "doubling", "Hadamard product" ] } ], "standing": "Described in 133 Wikipedia languages, which measures how widely it is written about rather than how important or how common it is. 4 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 multiplication from another, and a multiplication 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 multiplication, 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 multiplication, 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 multiplication 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 multiplication, 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 multiplication, 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 multiplication 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 multiplication 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 multiplication, 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 multiplication, 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 multiplication 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 multiplication from the things most often confused with it.", "questions": [ { "id": "distinguishing-features-q01", "text": "What identifies and describes what distinguishes a multiplication, 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 multiplication, 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 multiplication 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 multiplication 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 multiplication between them.", "questions": [ { "id": "stages-and-transitions-q01", "text": "What identifies and describes the lifecycle of a multiplication, 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 multiplication, 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 multiplication 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 multiplication, how often and by whom.", "findings": [ { "id": "observation-record", "name": "Observation record", "description": "How an observation of a multiplication 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 multiplication, 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 multiplication, 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 multiplication 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 multiplication 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 multiplication 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 multiplication 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 multiplication 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 multiplication?", "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 multiplication?", "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 multiplication 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 multiplication and how confident it is.", "questions": [ { "id": "claim-provenance-q01", "text": "What identifies and describes a claim about a multiplication, 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 multiplication, 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 multiplication 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 multiplication is retired without being erased.", "questions": [ { "id": "validity-and-supersession-q01", "text": "What identifies and describes the validity of a claim about a multiplication, 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 multiplication, 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 multiplication 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 } } } }