{ "model": { "rank": 10311, "code": "thing-q956437", "model_id": "vr.tr.norm", "name": "norm", "purpose": "Let an agent explain norms in mathematics, relay axioms, examples, induced metrics and applications from mathematics sources, describe the named norms and flag misfiled aliases, and distinguish norms from metrics, inner products, seminorms and social or technical norms.", "family": "Thing Registry", "category": "Cross-cutting context", "status": "research-draft", "kind": "thing", "plane": "XCT", "domain": "XCT.QLT", "industry": "", "version": "", "url": "/models/thing/q956437/", "tier": 2, "score": 45, "payload": { "layer": "wikidata", "aliases": [ "Deficiency (statistics)", "canonical norm induced by inner product", "Euclidean norm", "p-norm", "Bombieri norm", "edit distance", "Schatten norm", "matrix norm", "operator norm", "natural norm" ], "aliasCount": 10, "merged": 10, "knownIn": 45, "facets": null, "markers": [], "lexicalClass": "", "senseRank": null, "alsoRegisteredAs": null, "source": { "dataset": "wikidata", "item": "Q956437", "url": "https://www.wikidata.org/wiki/Q956437", "license": "CC0 1.0" } }, "research": { "vercy": "1.0-draft", "publication": { "status": "research-draft", "adjudicationStatus": "unreviewed", "publishableCanonical": false, "generatedAt": "2026-09-13T23:07:57Z", "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-Q956437", "registryId": "vr.tr.norm", "name": "norm", "version": "0.2.0-wave.4", "entryKind": "thing", "family": "Thing Registry", "domain": [ "XCT.QLT" ], "status": "research-draft" }, "canonicalUrl": "https://ver.cy/models/thing/q956437/", "model": { "registry_id": "vr.tr.norm", "name": "norm", "purpose": "Let an agent explain norms in mathematics, relay axioms, examples, induced metrics and applications from mathematics sources, describe the named norms and flag misfiled aliases, and distinguish norms from metrics, inner products, seminorms and social or technical norms.", "definition": "A function assigning a non-negative length or size to each vector in a vector space, satisfying positive definiteness, absolute homogeneity and the triangle inequality, including the Euclidean norm, the canonical norm induced by an inner product, p-norms such as the taxicab norm for p equal 1 and the maximum norm, and specialised norms such as the Bombieri norm on polynomials; a seminorm relaxes positive definiteness. The registry aliases edit distance, a metric on strings, and Deficiency, a statistics term, are not norms and appear misfiled. The word norm also names social norms and standards, which are different senses.", "what_it_is_for": "Measuring size of vectors and functions.", "affordances": [ "explain axioms", "relay examples", "describe named norms", "flag misfiled aliases" ], "distinguishing_features": [ "Non-negative size", "Triangle inequality", "Induces a metric", "Many examples" ], "appearance": "Not a physical object; written with double vertical bars.", "visual_identification": [ "Length function on a vector space", "Deficiency (statistics), canonical norm induced by inner product, Euclidean norm, p-norm, Bombieri norm, edit distance", "Metrics measure distance between points; inner products give angles; seminorms allow zero length for nonzero vectors; social norms are behavioural" ], "physical_properties": [ { "quantity": "axioms", "typical_range": "3", "unit": "count", "note": "positivity, homogeneity, triangle inequality" }, { "quantity": "Euclidean norm", "typical_range": "square root of sum of squares", "unit": "note", "note": "" }, { "quantity": "Banach space", "typical_range": "complete normed space", "unit": "note", "note": "Banach, 1920s" } ], "families_and_kinds": [ "p-norms", "inner product norms", "operator and matrix norms", "function space norms", "polynomial norms" ], "related_models": [ { "relation": "is a kind of", "target": "seminorm", "why": "in registry terms" }, { "relation": "induces", "target": "metric (mathematics)", "why": "" }, { "relation": "includes", "target": "Euclidean norm", "why": "" }, { "relation": "is contrasted with", "target": "edit distance", "why": "misfiled alias" } ], "identifiers": [], "standards_and_regulation": [ "No regulation" ], "failure_modes_and_hazards": [ "Confusing norms and metrics", "Misfiled string and statistics aliases", "Conflating mathematical and social norms" ], "in_scope": [], "out_of_scope": [], "characteristics": [] }, "sources": [], "structure": { "bundles": [ { "id": "understand", "name": "Understand", "description": "What a norm is.", "rationale": "Definition.", "layers": [ { "id": "definition", "name": "Definition", "description": "Definition.", "findings": [ { "id": "definition-finding", "name": "Definition", "description": "Definition.", "questions": [ { "text": "What is a norm, and how does it differ from metrics, inner products, seminorms and social norms?", "kind": "definition" }, { "text": "Is the question about linear algebra, analysis, machine learning or another sense of norm?", "kind": "boundary" } ] } ] }, { "id": "named", "name": "Named norms", "description": "Named norms.", "findings": [ { "id": "named-finding", "name": "Named norms", "description": "Named norms.", "questions": [ { "text": "What are Euclidean, p-norms, inner product and Bombieri norms, and why are edit distance and Deficiency different?", "kind": "definition" }, { "text": "Which entry fits the specific norm?", "kind": "action" } ] } ] } ] }, { "id": "theory", "name": "Theory", "description": "Theory.", "rationale": "Science.", "layers": [ { "id": "axioms", "name": "Axioms", "description": "Axioms.", "findings": [ { "id": "axioms-finding", "name": "Axioms", "description": "Axioms.", "questions": [ { "text": "What do the norm axioms require, and how do seminorms differ?", "kind": "provenance" }, { "text": "Which references are standard?", "kind": "provenance" } ] } ] }, { "id": "banach", "name": "Banach spaces", "description": "Normed spaces.", "findings": [ { "id": "banach-finding", "name": "Banach spaces", "description": "Banach spaces.", "questions": [ { "text": "What are normed and Banach spaces?", "kind": "provenance" }, { "text": "Which sources are cited?", "kind": "provenance" } ] } ] } ] }, { "id": "applications", "name": "Applications", "description": "Applications.", "rationale": "Science.", "layers": [ { "id": "ml", "name": "Machine learning", "description": "Regularisation.", "findings": [ { "id": "ml-finding", "name": "Machine learning", "description": "Machine learning.", "questions": [ { "text": "How are L1 and L2 norms used in regularisation?", "kind": "provenance" }, { "text": "Which entry fits regularization (mathematics)?", "kind": "action" } ] } ] }, { "id": "numerical", "name": "Numerical", "description": "Error measures.", "findings": [ { "id": "numerical-finding", "name": "Numerical", "description": "Numerical.", "questions": [ { "text": "How are norms used to measure errors in numerical analysis?", "kind": "measurement" }, { "text": "Which entry fits matrix norm?", "kind": "action" } ] } ] } ] }, { "id": "context", "name": "Context", "description": "Other senses.", "rationale": "Context.", "layers": [ { "id": "strings", "name": "Strings", "description": "Edit distance.", "findings": [ { "id": "strings-finding", "name": "Strings", "description": "Strings.", "questions": [ { "text": "What is edit distance, and why is it a metric rather than a norm?", "kind": "provenance" }, { "text": "Which entry fits Levenshtein distance?", "kind": "action" } ] } ] }, { "id": "social", "name": "Social norms", "description": "Social norms.", "findings": [ { "id": "social-finding", "name": "Social norms", "description": "Social norms.", "questions": [ { "text": "How does the mathematical sense differ from social norms?", "kind": "provenance" }, { "text": "Which entry fits social norm?", "kind": "action" } ] } ] } ] } ] }, "openQuestions": [ "The registry aliases edit distance and Deficiency (statistics) should be moved to their own entries", "Should matrix norms be a separate entry?", "How should functional analysis references be linked?" ], "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 norm, record what state it is in, and decide what may be done with it.", "whatItIs": "Let an agent explain norms in mathematics, relay axioms, examples, induced metrics and applications from mathematics sources, describe the named norms and flag misfiled aliases, and distinguish norms from metrics, inner products, seminorms and social or technical norms.", "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: Deficiency (statistics), canonical norm induced by inner product, Euclidean norm, p-norm, Bombieri norm, edit distance, Schatten norm, matrix norm, operator norm, natural norm.", "10 finer distinctions are held as aliases rather than separate entries, because telling them apart needs a task that asks for it.", "Described in 45 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 norm, 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": [ "Deficiency (statistics)", "canonical norm induced by inner product", "Euclidean norm", "p-norm", "Bombieri norm", "edit distance", "Schatten norm", "matrix norm", "operator norm", "natural norm" ] } ], "standing": "Described in 45 Wikipedia languages, which measures how widely it is written about rather than how important or how common it is. 10 finer distinctions are held inside this entry as names rather than as separate models.", "structure": { "bundles": [ { "id": "identity-and-classification", "name": "Identity, naming and classification", "description": "How an agent tells one norm from another, and a norm 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 norm, 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 norm, 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 norm 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 norm, 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 norm, 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 norm 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 norm 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 norm, 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 norm, 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 norm 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 norm from the things most often confused with it.", "questions": [ { "id": "distinguishing-features-q01", "text": "What identifies and describes what distinguishes a norm, 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 norm, 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 norm 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 norm 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 norm between them.", "questions": [ { "id": "stages-and-transitions-q01", "text": "What identifies and describes the lifecycle of a norm, 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 norm, 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 norm 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 norm, how often and by whom.", "findings": [ { "id": "observation-record", "name": "Observation record", "description": "How an observation of a norm 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 norm, 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 norm, 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 norm 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 norm 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 norm 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 norm 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 norm 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 norm?", "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 norm?", "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 norm 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 norm and how confident it is.", "questions": [ { "id": "claim-provenance-q01", "text": "What identifies and describes a claim about a norm, 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 norm, 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 norm 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 norm is retired without being erased.", "questions": [ { "id": "validity-and-supersession-q01", "text": "What identifies and describes the validity of a claim about a norm, 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 norm, 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 norm 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 } } } }