{ "model": { "rank": 7454, "code": "thing-q192089", "model_id": "vr.tr.magic-square", "name": "magic square", "purpose": "Let an agent explain magic squares and their varieties, relay construction methods, properties and open problems from mathematical references, describe their cultural history, and distinguish magic squares from Latin squares and sudoku.", "family": "Thing Registry", "category": "Cross-cutting context", "status": "research-draft", "kind": "thing", "plane": "XCT", "domain": "XCT.QLT", "industry": "", "version": "", "url": "/models/thing/q192089/", "tier": 2, "score": 55, "payload": { "layer": "wikidata", "aliases": [ "prime magic square", "multimagic square", "Magic square of squares", "frame magic square", "kamea", "HSA magic square", "magic square of Franklin", "bimagic square", "addition-multiplication magic square", "pandiagonal magic square", "trimagic square", "alphamagic square", "associative magic square", "most-perfect magic square" ], "aliasCount": 14, "merged": 14, "knownIn": 55, "facets": null, "markers": [], "lexicalClass": "", "senseRank": null, "alsoRegisteredAs": null, "source": { "dataset": "wikidata", "item": "Q192089", "url": "https://www.wikidata.org/wiki/Q192089", "license": "CC0 1.0" } }, "research": { "vercy": "1.0-draft", "publication": { "status": "research-draft", "adjudicationStatus": "unreviewed", "publishableCanonical": false, "generatedAt": "2026-09-13T03:46:20Z", "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-Q192089", "registryId": "vr.tr.magic-square", "name": "magic square", "version": "0.2.0-wave.3", "entryKind": "thing", "family": "Thing Registry", "domain": [ "XCT.QLT" ], "status": "research-draft" }, "canonicalUrl": "https://ver.cy/models/thing/q192089/", "model": { "registry_id": "vr.tr.magic-square", "name": "magic square", "purpose": "Let an agent explain magic squares and their varieties, relay construction methods, properties and open problems from mathematical references, describe their cultural history, and distinguish magic squares from Latin squares and sudoku.", "definition": "A square grid of distinct numbers, usually the integers from 1 to n squared, arranged so that every row, column and main diagonal sums to the same magic constant, known since ancient China as the Lo Shu square, studied in Islamic and medieval mathematics, and elaborated into prime magic squares, multimagic squares whose entries remain magic when raised to powers, bordered or frame magic squares, geometric magic squares, and the still open problem of a magic square of squares; magic squares also appear as kameas in Western occult tradition and in art such as Durer Melencolia I.", "what_it_is_for": "Not applicable; a mathematical object.", "affordances": [ "explain the definition and varieties", "relay construction methods", "describe open problems", "distinguish from related grids" ], "distinguishing_features": [ "Constant line sums", "Order-dependent constructions", "Rich variants", "Cultural history" ], "appearance": "A square grid of numbers with equal row, column and diagonal sums.", "visual_identification": [ "Grid with constant line sums", "Lo Shu, Durer square, prime, multimagic, frame, geometric magic squares, kameas", "Latin squares repeat symbols without sums; sudoku is a Latin square puzzle" ], "physical_properties": [ { "quantity": "magic constant for order n", "typical_range": "n(n^2 + 1)/2", "unit": "formula", "note": "normal squares" }, { "quantity": "order 3 normal squares", "typical_range": "1", "unit": "count", "note": "up to symmetry" }, { "quantity": "order 4 normal squares", "typical_range": "880", "unit": "count", "note": "up to symmetry" } ], "families_and_kinds": [ "normal magic squares by order", "odd, doubly even and singly even construction classes", "prime magic squares", "multimagic squares such as bimagic and trimagic", "bordered or frame magic squares", "geometric magic squares", "magic squares of squares as an open problem", "kameas in occult tradition" ], "related_models": [ { "relation": "is a kind of", "target": "magic figure", "why": "in registry terms" }, { "relation": "is a kind of", "target": "magic hypercube", "why": "in registry terms, in two dimensions" }, { "relation": "is a kind of", "target": "geometric magic square", "why": "in registry terms, as a special case" }, { "relation": "is contrasted with", "target": "Latin square", "why": "which has no sum condition" } ], "identifiers": [ { "scheme": "OEIS", "value_or_pattern": "A006052", "note": "number of magic squares of order n" } ], "standards_and_regulation": [ "No regulation; standard mathematical definitions" ], "failure_modes_and_hazards": [ "Confusing magic squares with sudoku or Latin squares", "Overstating what is known about magic squares of squares", "Presenting occult uses as mathematics" ], "in_scope": [], "out_of_scope": [], "characteristics": [] }, "sources": [], "structure": { "bundles": [ { "id": "understand", "name": "Understand", "description": "What a magic square is.", "rationale": "Mathematics.", "layers": [ { "id": "definition", "name": "Definition", "description": "Definition.", "findings": [ { "id": "definition-finding", "name": "Definition", "description": "Definition.", "questions": [ { "text": "What is a magic square, and what is the magic constant?", "kind": "definition" }, { "text": "Is the question about magic squares, Latin squares, sudoku or kameas?", "kind": "boundary" } ] } ] }, { "id": "varieties", "name": "Varieties", "description": "Varieties.", "findings": [ { "id": "varieties-finding", "name": "Varieties", "description": "Varieties.", "questions": [ { "text": "What are prime, multimagic, frame, geometric and other magic squares?", "kind": "definition" }, { "text": "Which entry fits the specific variety?", "kind": "action" } ] } ] } ] }, { "id": "construct", "name": "Construct", "description": "Construction.", "rationale": "Mathematics.", "layers": [ { "id": "methods", "name": "Methods", "description": "Construction methods.", "findings": [ { "id": "methods-finding", "name": "Methods", "description": "Methods.", "questions": [ { "text": "How are odd, doubly even and singly even magic squares constructed, for example by the Siamese and LUX methods?", "kind": "action" }, { "text": "Which references are standard?", "kind": "provenance" } ] } ] }, { "id": "counting", "name": "Counting", "description": "Counting and properties.", "findings": [ { "id": "counting-finding", "name": "Counting", "description": "Counting.", "questions": [ { "text": "How many magic squares exist for each order, and what algebraic properties do they have?", "kind": "provenance" }, { "text": "Which sources are cited?", "kind": "provenance" } ] } ] } ] }, { "id": "problems", "name": "Problems", "description": "Open problems.", "rationale": "Mathematics.", "layers": [ { "id": "squares", "name": "Squares", "description": "Magic squares of squares.", "findings": [ { "id": "squares-finding", "name": "Squares", "description": "Squares.", "questions": [ { "text": "What is the magic square of squares problem, and what is known about it?", "kind": "provenance" }, { "text": "Which entry fits magic square of squares?", "kind": "action" } ] } ] }, { "id": "multimagic", "name": "Multimagic", "description": "Multimagic records.", "findings": [ { "id": "multimagic-finding", "name": "Multimagic", "description": "Multimagic.", "questions": [ { "text": "What multimagic squares have been found, and what remains open?", "kind": "provenance" }, { "text": "Which entry fits multimagic square?", "kind": "action" } ] } ] } ] }, { "id": "context", "name": "Context", "description": "History and culture.", "rationale": "Context.", "layers": [ { "id": "history", "name": "History", "description": "History.", "findings": [ { "id": "history-finding", "name": "History", "description": "History.", "questions": [ { "text": "How did magic squares travel from the Lo Shu through Islamic and Indian mathematics to Europe?", "kind": "provenance" }, { "text": "Which entry fits the history of recreational mathematics?", "kind": "action" } ] } ] }, { "id": "culture", "name": "Culture", "description": "Art and occult.", "findings": [ { "id": "culture-finding", "name": "Culture", "description": "Culture.", "questions": [ { "text": "How do magic squares appear in Durer Melencolia I, the Sagrada Familia and kameas of occult tradition, described with attribution?", "kind": "provenance" }, { "text": "Which entry fits kamea?", "kind": "action" } ] } ] } ] } ] }, "openQuestions": [ "Should multimagic square and kamea be separate entries?", "How should mathematical references be linked?", "The registry entry has merged aliases naming varieties and occult uses; 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 magic square, record what state it is in, and decide what may be done with it.", "whatItIs": "Let an agent explain magic squares and their varieties, relay construction methods, properties and open problems from mathematical references, describe their cultural history, and distinguish magic squares from Latin squares and sudoku.", "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: prime magic square, multimagic square, Magic square of squares, frame magic square, kamea, HSA magic square, magic square of Franklin, bimagic square, addition-multiplication magic square, pandiagonal magic square, trimagic square, alphamagic square.", "14 finer distinctions are held as aliases rather than separate entries, because telling them apart needs a task that asks for it.", "Described in 55 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 magic square, 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": [ "prime magic square", "multimagic square", "Magic square of squares", "frame magic square", "kamea", "HSA magic square", "magic square of Franklin", "bimagic square", "addition-multiplication magic square", "pandiagonal magic square", "trimagic square", "alphamagic square" ] } ], "standing": "Described in 55 Wikipedia languages, which measures how widely it is written about rather than how important or how common it is. 14 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 magic square from another, and a magic square 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 magic square, 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 magic square, 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 magic square 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 magic square, 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 magic square, 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 magic square 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 magic square 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 magic square, 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 magic square, 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 magic square 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 magic square from the things most often confused with it.", "questions": [ { "id": "distinguishing-features-q01", "text": "What identifies and describes what distinguishes a magic square, 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 magic square, 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 magic square 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 magic square 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 magic square between them.", "questions": [ { "id": "stages-and-transitions-q01", "text": "What identifies and describes the lifecycle of a magic square, 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 magic square, 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 magic square 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 magic square, how often and by whom.", "findings": [ { "id": "observation-record", "name": "Observation record", "description": "How an observation of a magic square 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 magic square, 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 magic square, 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 magic square 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 magic square 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 magic square 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 magic square 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 magic square 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 magic square?", "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 magic square?", "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 magic square 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 magic square and how confident it is.", "questions": [ { "id": "claim-provenance-q01", "text": "What identifies and describes a claim about a magic square, 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 magic square, 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 magic square 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 magic square is retired without being erased.", "questions": [ { "id": "validity-and-supersession-q01", "text": "What identifies and describes the validity of a claim about a magic square, 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 magic square, 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 magic square 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 } } } }