{ "model": { "rank": 8024, "code": "thing-q838611", "model_id": "vr.tr.ball-q838611", "name": "ball", "purpose": "Let an agent explain balls in mathematics and their kinds, relay definitions, properties and uses in topology, analysis and coding theory from mathematics references, describe unit and Hamming balls, and distinguish balls from spheres, discs, neighbourhoods and physical balls.", "family": "Thing Registry", "category": "Cross-cutting context", "status": "research-draft", "kind": "thing", "plane": "XCT", "domain": "XCT.QLT", "industry": "", "version": "", "url": "/models/thing/q838611/", "tier": 2, "score": 52, "payload": { "layer": "wikidata", "aliases": [ "unit ball", "closed ball", "closed unit ball", "Hamming ball" ], "aliasCount": 4, "merged": 4, "knownIn": 52, "facets": null, "markers": [], "lexicalClass": "", "senseRank": null, "alsoRegisteredAs": "vr.tr.ball-act", "source": { "dataset": "wikidata", "item": "Q838611", "url": "https://www.wikidata.org/wiki/Q838611", "license": "CC0 1.0" } }, "research": { "vercy": "1.0-draft", "publication": { "status": "research-draft", "adjudicationStatus": "unreviewed", "publishableCanonical": false, "generatedAt": "2026-09-13T14:57:12Z", "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-Q838611", "registryId": "vr.tr.ball-q838611", "name": "ball", "version": "0.2.0-wave.4", "entryKind": "thing", "family": "Thing Registry", "domain": [ "XCT.QLT" ], "status": "research-draft" }, "canonicalUrl": "https://ver.cy/models/thing/q838611/", "model": { "registry_id": "vr.tr.ball-q838611", "name": "ball", "purpose": "Let an agent explain balls in mathematics and their kinds, relay definitions, properties and uses in topology, analysis and coding theory from mathematics references, describe unit and Hamming balls, and distinguish balls from spheres, discs, neighbourhoods and physical balls.", "definition": "In mathematics, the set of all points within a given distance of a centre point, a solid figure generalising the disc and the solid sphere to any metric space, either open, excluding the boundary, or closed, including it, with the unit ball of radius one in a normed space and the Hamming ball of strings within a given Hamming distance in coding theory; balls are convex in normed spaces and are the basic neighbourhoods of metric topology.", "what_it_is_for": "Not applicable; a mathematical object.", "affordances": [ "explain the concept", "relay properties", "describe kinds", "distinguish related concepts" ], "distinguishing_features": [ "Metric definition", "Open and closed", "Convex in normed spaces", "Basis of topology" ], "appearance": "Not a visible object; a solid sphere in three dimensions.", "visual_identification": [ "Set of points within a distance of a centre", "Open ball, closed ball, unit ball, closed unit ball, Hamming ball", "A sphere is the boundary; a disc is a 2D ball; neighbourhoods are more general; physical balls are objects" ], "physical_properties": [ { "quantity": "volume, 3D radius r", "typical_range": "4/3 pi r cubed", "unit": "note", "note": "" }, { "quantity": "unit ball volume, dimension n", "typical_range": "tends to zero as n grows", "unit": "note", "note": "" }, { "quantity": "Hamming ball size", "typical_range": "sum of binomial coefficients", "unit": "note", "note": "" } ], "families_and_kinds": [ "open and closed balls in metric spaces", "unit balls in normed spaces", "balls in Euclidean space", "Hamming balls in coding theory", "p-adic and ultrametric balls" ], "related_models": [ { "relation": "is a kind of", "target": "convex set", "why": "in normed spaces, in registry terms" }, { "relation": "is a kind of", "target": "solid figure", "why": "in registry terms" }, { "relation": "is bounded by", "target": "sphere", "why": "its boundary" }, { "relation": "is used in", "target": "metric space", "why": "as a neighbourhood" } ], "identifiers": [], "standards_and_regulation": [ "No regulation" ], "failure_modes_and_hazards": [ "Confusing ball with sphere", "Assuming Euclidean intuition in other metrics", "Registry aliases mixing analysis and coding theory" ], "in_scope": [], "out_of_scope": [], "characteristics": [] }, "sources": [], "structure": { "bundles": [ { "id": "understand", "name": "Understand", "description": "What a ball is.", "rationale": "Science.", "layers": [ { "id": "definition", "name": "Definition", "description": "Definition.", "findings": [ { "id": "definition-finding", "name": "Definition", "description": "Definition.", "questions": [ { "text": "What is a ball in mathematics, and how does it differ from a sphere, disc, neighbourhood and physical ball?", "kind": "definition" }, { "text": "Is the question about topology, analysis, geometry or coding theory?", "kind": "boundary" } ] } ] }, { "id": "kinds", "name": "Kinds", "description": "Kinds.", "findings": [ { "id": "kinds-finding", "name": "Kinds", "description": "Kinds.", "questions": [ { "text": "What are open, closed, unit and Hamming balls?", "kind": "definition" }, { "text": "Which entry fits the specific kind?", "kind": "action" } ] } ] } ] }, { "id": "properties", "name": "Properties", "description": "Properties.", "rationale": "Science.", "layers": [ { "id": "geometry", "name": "Geometry", "description": "Geometry.", "findings": [ { "id": "geometry-finding", "name": "Geometry", "description": "Geometry.", "questions": [ { "text": "What are the volume and surface formulas, and how do they behave in high dimensions?", "kind": "provenance" }, { "text": "Which references are standard?", "kind": "provenance" } ] } ] }, { "id": "topology", "name": "Topology", "description": "Topology.", "findings": [ { "id": "topology-finding", "name": "Topology", "description": "Topology.", "questions": [ { "text": "How do balls define open sets and neighbourhoods in metric spaces?", "kind": "provenance" }, { "text": "Which sources are cited?", "kind": "provenance" } ] } ] } ] }, { "id": "applications", "name": "Applications", "description": "Applications.", "rationale": "Application.", "layers": [ { "id": "analysis", "name": "Analysis", "description": "Analysis.", "findings": [ { "id": "analysis-finding", "name": "Analysis", "description": "Analysis.", "questions": [ { "text": "How are unit balls used in functional analysis and convexity?", "kind": "provenance" }, { "text": "Which entry fits normed vector space?", "kind": "action" } ] } ] }, { "id": "coding", "name": "Coding", "description": "Coding theory.", "findings": [ { "id": "coding-finding", "name": "Coding", "description": "Coding.", "questions": [ { "text": "How are Hamming balls used in error-correcting code bounds?", "kind": "provenance" }, { "text": "Which entry fits Hamming bound?", "kind": "action" } ] } ] } ] }, { "id": "context", "name": "Context", "description": "Beyond Euclid.", "rationale": "Context.", "layers": [ { "id": "metrics", "name": "Metrics", "description": "Other metrics.", "findings": [ { "id": "metrics-finding", "name": "Metrics", "description": "Metrics.", "questions": [ { "text": "How do balls look in taxicab, ultrametric and p-adic spaces?", "kind": "provenance" }, { "text": "Which entry fits ultrametric space?", "kind": "action" } ] } ] }, { "id": "history", "name": "History", "description": "History.", "findings": [ { "id": "history-finding", "name": "History", "description": "History.", "questions": [ { "text": "How did the abstract ball arise with metric spaces?", "kind": "provenance" }, { "text": "Which entry fits the history of topology?", "kind": "action" } ] } ] } ] } ] }, "openQuestions": [ "Should unit ball and Hamming ball be separate primary entries?", "How should mathematics references be linked?", "The registry entry has merged aliases from analysis and coding theory; 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 ball, record what state it is in, and decide what may be done with it.", "whatItIs": "Let an agent explain balls in mathematics and their kinds, relay definitions, properties and uses in topology, analysis and coding theory from mathematics references, describe unit and Hamming balls, and distinguish balls from spheres, discs, neighbourhoods and physical balls.", "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: unit ball, closed ball, closed unit ball, Hamming ball.", "4 finer distinctions are held as aliases rather than separate entries, because telling them apart needs a task that asks for it.", "Described in 52 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 ball, 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": [ "unit ball", "closed ball", "closed unit ball", "Hamming ball" ] } ], "standing": "Described in 52 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 ball from another, and a ball 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 ball, 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 ball, 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 ball 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 ball, 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 ball, 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 ball 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 ball 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 ball, 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 ball, 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 ball 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 ball from the things most often confused with it.", "questions": [ { "id": "distinguishing-features-q01", "text": "What identifies and describes what distinguishes a ball, 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 ball, 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 ball 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 ball 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 ball between them.", "questions": [ { "id": "stages-and-transitions-q01", "text": "What identifies and describes the lifecycle of a ball, 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 ball, 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 ball 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 ball, how often and by whom.", "findings": [ { "id": "observation-record", "name": "Observation record", "description": "How an observation of a ball 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 ball, 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 ball, 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 ball 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 ball 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 ball 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 ball 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 ball 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 ball?", "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 ball?", "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 ball 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 ball and how confident it is.", "questions": [ { "id": "claim-provenance-q01", "text": "What identifies and describes a claim about a ball, 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 ball, 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 ball 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 ball is retired without being erased.", "questions": [ { "id": "validity-and-supersession-q01", "text": "What identifies and describes the validity of a claim about a ball, 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 ball, 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 ball 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 } } } }