{ "model": { "rank": 12203, "code": "thing-q213723", "model_id": "vr.tr.hypercube", "name": "hypercube", "purpose": "Let an agent explain hypercubes and their properties in n dimensions, support calculations of vertices, edges and facets, describe applications in computing and mathematics, and support visualisation and learning.", "family": "Thing Registry", "category": "Cross-cutting context", "status": "research-draft", "kind": "thing", "plane": "XCT", "domain": "XCT.QLT", "industry": "", "version": "", "url": "/models/thing/q213723/", "tier": 2, "score": 40, "payload": { "layer": "wikidata", "aliases": [ "11-cube", "12-cube", "13-cube", "7-cube", "8-cube", "9-cube", "10-cubeihgq", "tesseract", "5-cube", "6-cube", "21-cube", "19-cube", "17-cube", "16-cube", "20-cube", "18-cube", "15-cube", "14-cube", "magic hypercube", "unit hypercube", "magic tesseract" ], "aliasCount": 21, "merged": 21, "knownIn": 40, "facets": null, "markers": [], "lexicalClass": "", "senseRank": null, "alsoRegisteredAs": null, "source": { "dataset": "wikidata", "item": "Q213723", "url": "https://www.wikidata.org/wiki/Q213723", "license": "CC0 1.0" } }, "research": { "vercy": "1.0-draft", "publication": { "status": "research-draft", "adjudicationStatus": "unreviewed", "publishableCanonical": false, "generatedAt": "2026-09-12T03:55:22Z", "providers": [ "Claude" ], "breadth": "written by Claude from model knowledge without web access - no source was read, every claim is a lead to verify", "pass": 2, "wave": 2, "engine": "claude" }, "metaModel": { "id": "THING-Q213723", "registryId": "vr.tr.hypercube", "name": "hypercube", "version": "0.2.0-wave.2", "entryKind": "thing", "family": "Thing Registry", "domain": [ "XCT.QLT" ], "status": "research-draft" }, "canonicalUrl": "https://ver.cy/models/thing/q213723/", "model": { "registry_id": "vr.tr.hypercube", "name": "hypercube", "purpose": "Let an agent explain hypercubes and their properties in n dimensions, support calculations of vertices, edges and facets, describe applications in computing and mathematics, and support visualisation and learning.", "definition": "The generalisation of the square and the cube to n dimensions, a regular convex polytope with vertices at all combinations of coordinates zero and one, so that the n-cube has two to the power n vertices and two n facets, including the tesseract in four dimensions and higher cubes up to the thirteen-cube and beyond; hypercubes appear in geometry, combinatorics, coding theory, computer network topology and data analysis.", "what_it_is_for": "n-dimensional cubes.", "affordances": [ "explain properties", "support calculations", "describe applications", "support visualisation" ], "distinguishing_features": [ "Regular polytope", "Binary coordinates", "Recursive construction", "Graph structure" ], "appearance": "Not physical; projections and models in lower dimensions.", "visual_identification": [ "Generalised cube in n dimensions", "Two to the n vertices", "A hyperrectangle has unequal sides; a simplex generalises the triangle" ], "physical_properties": [], "families_and_kinds": [ "square and cube as low-dimensional cases", "tesseract", "five-cube to thirteen-cube", "hypercube graphs", "hypercubes in coding and networks" ], "related_models": [ { "relation": "is a kind of", "target": "regular convex polytope", "why": "category" }, { "relation": "is a kind of", "target": "hyperrectangle", "why": "category" }, { "relation": "is related to", "target": "simplex", "why": "another family of polytopes" }, { "relation": "is related to", "target": "convex set", "why": "hypercubes as convex sets" } ], "identifiers": [], "standards_and_regulation": [ "Mathematical conventions", "No regulation" ], "failure_modes_and_hazards": [ "Misreading projections as the object", "Counting errors for faces", "Confusing hypercube with hyperrectangle" ], "in_scope": [], "out_of_scope": [], "characteristics": [] }, "sources": [], "structure": { "bundles": [ { "id": "understand", "name": "Understand", "description": "What hypercubes are.", "rationale": "Mathematics.", "layers": [ { "id": "definition", "name": "Definition", "description": "Definition and construction.", "findings": [ { "id": "definition-finding", "name": "Definition", "description": "Definition.", "questions": [ { "text": "How is the n-cube defined and constructed recursively, and what are its vertices, edges and facets?", "kind": "definition" }, { "text": "Which dimension is meant?", "kind": "boundary" } ] } ] }, { "id": "properties", "name": "Properties", "description": "Properties.", "findings": [ { "id": "properties-finding", "name": "Properties", "description": "Properties.", "questions": [ { "text": "What symmetry, volume, diagonal and graph properties do hypercubes have?", "kind": "definition" }, { "text": "Which entry fits polytopes?", "kind": "action" } ] } ] } ] }, { "id": "compute", "name": "Compute", "description": "Calculations.", "rationale": "Practice.", "layers": [ { "id": "counts", "name": "Counts", "description": "Counting elements.", "findings": [ { "id": "counts-finding", "name": "Counts", "description": "Counting.", "questions": [ { "text": "How many k-dimensional faces does the n-cube have, and how are they counted?", "kind": "action" }, { "text": "Which entry fits combinatorics?", "kind": "action" } ] } ] }, { "id": "visualise", "name": "Visualise", "description": "Visualisation.", "findings": [ { "id": "visualise-finding", "name": "Visualise", "description": "Visualisation.", "questions": [ { "text": "How can a tesseract or higher cube be visualised through projections and nets?", "kind": "action" }, { "text": "Which entry fits four-dimensional geometry?", "kind": "action" } ] } ] } ] }, { "id": "apply", "name": "Apply", "description": "Applications.", "rationale": "Computing.", "layers": [ { "id": "networks", "name": "Networks", "description": "Networks and coding.", "findings": [ { "id": "networks-finding", "name": "Networks", "description": "Networks.", "questions": [ { "text": "How are hypercube graphs used in parallel computer networks and error-correcting codes?", "kind": "provenance" }, { "text": "Which entry fits network topology?", "kind": "action" } ] } ] }, { "id": "data", "name": "Data", "description": "Data and other uses.", "findings": [ { "id": "data-finding", "name": "Data", "description": "Data.", "questions": [ { "text": "How do hypercubes appear in data cubes, Boolean functions and random walks?", "kind": "provenance" }, { "text": "Which entry fits a specific application?", "kind": "action" } ] } ] } ] }, { "id": "learn", "name": "Learn", "description": "History and teaching.", "rationale": "Education.", "layers": [ { "id": "history", "name": "History", "description": "History.", "findings": [ { "id": "history-finding", "name": "History", "description": "History.", "questions": [ { "text": "How did higher-dimensional geometry and the tesseract enter mathematics and culture?", "kind": "provenance" }, { "text": "Which references are standard?", "kind": "provenance" } ] } ] }, { "id": "teach", "name": "Teach", "description": "Teaching.", "findings": [ { "id": "teach-finding", "name": "Teach", "description": "Teaching.", "questions": [ { "text": "How can hypercubes be taught with models and analogy?", "kind": "action" }, { "text": "Which misconceptions arise?", "kind": "provenance" } ] } ] } ] } ] }, "openQuestions": [ "Should the tesseract be a separate entry?", "How should polytope databases be linked?", "How should visualisation tools 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 hypercube, record what state it is in, and decide what may be done with it.", "whatItIs": "Let an agent explain hypercubes and their properties in n dimensions, support calculations of vertices, edges and facets, describe applications in computing and mathematics, and support visualisation and learning.", "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: 11-cube, 12-cube, 13-cube, 7-cube, 8-cube, 9-cube, 10-cubeihgq, tesseract, 5-cube, 6-cube, 21-cube, 19-cube.", "21 finer distinctions are held as aliases rather than separate entries, because telling them apart needs a task that asks for it.", "Described in 40 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 hypercube, 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": [ "11-cube", "12-cube", "13-cube", "7-cube", "8-cube", "9-cube", "10-cubeihgq", "tesseract", "5-cube", "6-cube", "21-cube", "19-cube" ] } ], "standing": "Described in 40 Wikipedia languages, which measures how widely it is written about rather than how important or how common it is. 21 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 hypercube from another, and a hypercube 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 hypercube, 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 hypercube, 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 hypercube 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 hypercube, 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 hypercube, 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 hypercube 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 hypercube 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 hypercube, 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 hypercube, 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 hypercube 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 hypercube from the things most often confused with it.", "questions": [ { "id": "distinguishing-features-q01", "text": "What identifies and describes what distinguishes a hypercube, 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 hypercube, 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 hypercube 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 hypercube 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 hypercube between them.", "questions": [ { "id": "stages-and-transitions-q01", "text": "What identifies and describes the lifecycle of a hypercube, 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 hypercube, 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 hypercube 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 hypercube, how often and by whom.", "findings": [ { "id": "observation-record", "name": "Observation record", "description": "How an observation of a hypercube 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 hypercube, 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 hypercube, 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 hypercube 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 hypercube 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 hypercube 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 hypercube 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 hypercube 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 hypercube?", "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 hypercube?", "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 hypercube 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 hypercube and how confident it is.", "questions": [ { "id": "claim-provenance-q01", "text": "What identifies and describes a claim about a hypercube, 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 hypercube, 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 hypercube 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 hypercube is retired without being erased.", "questions": [ { "id": "validity-and-supersession-q01", "text": "What identifies and describes the validity of a claim about a hypercube, 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 hypercube, 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 hypercube 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 } } } }