{ "model": { "rank": 17606, "code": "thing-q583760", "model_id": "vr.tr.antisymmetric-relation", "name": "antisymmetric relation", "purpose": "Let an agent explain antisymmetric relations, relay definitions, examples and connections to order theory from mathematics sources, describe the named relation types and flag the lower bound alias, and distinguish antisymmetry from asymmetry, symmetry, non-symmetry and total orders.", "family": "Thing Registry", "category": "Cross-cutting context", "status": "research-draft", "kind": "thing", "plane": "XCT", "domain": "XCT.QLT", "industry": "", "version": "", "url": "/models/thing/q583760/", "tier": 2, "score": 30, "payload": { "layer": "wikidata", "aliases": [ "asymmetric relation", "asymmetric property", "partial order", "lexicographical order", "pointwise order", "lower bound", "Stratification (mathematics)", "inclusion", "dense order", "Loewner order", "complete partial order", "happened-before", "total order", "upper bound", "Stochastic ordering", "Bruhat order", "well-founded order", "evidence lower bound", "perfect elimination ordering", "well-order", "shortlex order", "monomial order", "minimal upper bound" ], "aliasCount": 23, "merged": 23, "knownIn": 30, "facets": null, "markers": [], "lexicalClass": "", "senseRank": null, "alsoRegisteredAs": null, "source": { "dataset": "wikidata", "item": "Q583760", "url": "https://www.wikidata.org/wiki/Q583760", "license": "CC0 1.0" } }, "research": { "vercy": "1.0-draft", "publication": { "status": "research-draft", "adjudicationStatus": "unreviewed", "publishableCanonical": false, "generatedAt": "2026-09-13T20:55:37Z", "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-Q583760", "registryId": "vr.tr.antisymmetric-relation", "name": "antisymmetric relation", "version": "0.2.0-wave.4", "entryKind": "thing", "family": "Thing Registry", "domain": [ "XCT.QLT" ], "status": "research-draft" }, "canonicalUrl": "https://ver.cy/models/thing/q583760/", "model": { "registry_id": "vr.tr.antisymmetric-relation", "name": "antisymmetric relation", "purpose": "Let an agent explain antisymmetric relations, relay definitions, examples and connections to order theory from mathematics sources, describe the named relation types and flag the lower bound alias, and distinguish antisymmetry from asymmetry, symmetry, non-symmetry and total orders.", "definition": "A binary relation R on a set such that whenever a R b and b R a, then a equals b, meaning no two distinct elements are related in both directions, as with less than or equal to and divisibility on the natural numbers; asymmetric relations, where a R b excludes b R a, are exactly the antisymmetric and irreflexive ones, and antisymmetry together with reflexivity and transitivity defines partial orders such as lexicographical and pointwise orders, while the registry alias lower bound is an element-level concept in ordered sets rather than a relation type.", "what_it_is_for": "Not applicable; a mathematical property.", "affordances": [ "explain the property", "relay examples", "describe named order types", "distinguish related properties" ], "distinguishing_features": [ "No distinct mutual pairs", "Basis of partial orders", "Compatible with reflexivity", "Differs from asymmetry" ], "appearance": "Not a visible object; seen in diagrams without two-way arrows between distinct points.", "visual_identification": [ "Relation with no distinct two-way pairs", "Asymmetric relation, asymmetric property, partial order, lexicographical order, pointwise order, lower bound", "Asymmetric relations are also irreflexive; symmetric relations go both ways; non-symmetric only means not symmetric; total orders compare all pairs" ], "physical_properties": [ { "quantity": "definition", "typical_range": "aRb and bRa imply a = b", "unit": "formula", "note": "" }, { "quantity": "partial order", "typical_range": "reflexive, antisymmetric, transitive", "unit": "list", "note": "" }, { "quantity": "registry parent", "typical_range": "endorelation", "unit": "note", "note": "" } ], "families_and_kinds": [ "partial orders", "total orders", "lexicographical orders", "pointwise orders", "asymmetric relations as a subclass" ], "related_models": [ { "relation": "is a kind of", "target": "endorelation", "why": "in registry terms" }, { "relation": "underlies", "target": "partial order", "why": "" }, { "relation": "includes", "target": "asymmetric relation", "why": "as irreflexive case" }, { "relation": "is contrasted with", "target": "symmetric relation", "why": "" } ], "identifiers": [], "standards_and_regulation": [ "No regulation" ], "failure_modes_and_hazards": [ "Confusing antisymmetric and asymmetric", "Treating non-symmetric as antisymmetric", "Registry alias for an element concept" ], "in_scope": [], "out_of_scope": [], "characteristics": [] }, "sources": [], "structure": { "bundles": [ { "id": "understand", "name": "Understand", "description": "What an antisymmetric relation is.", "rationale": "Science.", "layers": [ { "id": "definition", "name": "Definition", "description": "Definition.", "findings": [ { "id": "definition-finding", "name": "Definition", "description": "Definition.", "questions": [ { "text": "What is an antisymmetric relation, and how does it differ from asymmetric, symmetric and non-symmetric relations?", "kind": "definition" }, { "text": "Is the question about maths, databases or logic?", "kind": "boundary" } ] } ] }, { "id": "named", "name": "Named", "description": "Named concepts.", "findings": [ { "id": "named-finding", "name": "Named", "description": "Named.", "questions": [ { "text": "What are asymmetric relations, partial orders, lexicographical and pointwise orders, and lower bounds?", "kind": "definition" }, { "text": "Which entry fits the specific concept?", "kind": "action" } ] } ] } ] }, { "id": "orders", "name": "Order theory", "description": "Order theory.", "rationale": "Science.", "layers": [ { "id": "partial", "name": "Partial orders", "description": "Partial orders.", "findings": [ { "id": "partial-finding", "name": "Partial orders", "description": "Partial orders.", "questions": [ { "text": "How does antisymmetry help define partial orders?", "kind": "provenance" }, { "text": "Which references are standard?", "kind": "provenance" } ] } ] }, { "id": "bounds", "name": "Bounds", "description": "Bounds.", "findings": [ { "id": "bounds-finding", "name": "Bounds", "description": "Bounds.", "questions": [ { "text": "What are lower and upper bounds in ordered sets?", "kind": "provenance" }, { "text": "Which sources are cited?", "kind": "provenance" } ] } ] } ] }, { "id": "examples", "name": "Examples", "description": "Examples.", "rationale": "Application.", "layers": [ { "id": "numbers", "name": "Numbers", "description": "Number relations.", "findings": [ { "id": "numbers-finding", "name": "Numbers", "description": "Numbers.", "questions": [ { "text": "Why is divisibility on natural numbers antisymmetric but not on integers?", "kind": "provenance" }, { "text": "Which entry fits divisibility?", "kind": "action" } ] } ] }, { "id": "orders", "name": "Orders", "description": "Lexicographic order.", "findings": [ { "id": "orders-finding", "name": "Orders", "description": "Orders.", "questions": [ { "text": "How does lexicographic ordering sort words?", "kind": "provenance" }, { "text": "Which entry fits lexicographic order?", "kind": "action" } ] } ] } ] }, { "id": "context", "name": "Context", "description": "Related properties.", "rationale": "Context.", "layers": [ { "id": "properties", "name": "Properties", "description": "Relation properties.", "findings": [ { "id": "properties-finding", "name": "Properties", "description": "Properties.", "questions": [ { "text": "How do reflexive, symmetric, antisymmetric and transitive properties combine?", "kind": "provenance" }, { "text": "Which entry fits binary relation?", "kind": "action" } ] } ] }, { "id": "graphs", "name": "Graphs", "description": "Graphs.", "findings": [ { "id": "graphs-finding", "name": "Graphs", "description": "Graphs.", "questions": [ { "text": "How are antisymmetric relations drawn as directed graphs and Hasse diagrams?", "kind": "provenance" }, { "text": "Which entry fits Hasse diagram?", "kind": "action" } ] } ] } ] } ] }, "openQuestions": [ "Should asymmetric relation be a separate primary entry?", "How should mathematics sources be linked?", "The registry alias lower bound should be moved to order theory element concepts" ], "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 antisymmetric relation, record what state it is in, and decide what may be done with it.", "whatItIs": "Let an agent explain antisymmetric relations, relay definitions, examples and connections to order theory from mathematics sources, describe the named relation types and flag the lower bound alias, and distinguish antisymmetry from asymmetry, symmetry, non-symmetry and total orders.", "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: asymmetric relation, asymmetric property, partial order, lexicographical order, pointwise order, lower bound, Stratification (mathematics), inclusion, dense order, Loewner order, complete partial order, happened-before.", "23 finer distinctions are held as aliases rather than separate entries, because telling them apart needs a task that asks for it.", "Described in 30 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 antisymmetric relation, 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": [ "asymmetric relation", "asymmetric property", "partial order", "lexicographical order", "pointwise order", "lower bound", "Stratification (mathematics)", "inclusion", "dense order", "Loewner order", "complete partial order", "happened-before" ] } ], "standing": "Described in 30 Wikipedia languages, which measures how widely it is written about rather than how important or how common it is. 23 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 antisymmetric relation from another, and a antisymmetric relation 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 antisymmetric relation, 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 antisymmetric relation, 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 antisymmetric relation 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 antisymmetric relation, 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 antisymmetric relation, 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 antisymmetric relation 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 antisymmetric relation 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 antisymmetric relation, 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 antisymmetric relation, 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 antisymmetric relation 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 antisymmetric relation from the things most often confused with it.", "questions": [ { "id": "distinguishing-features-q01", "text": "What identifies and describes what distinguishes a antisymmetric relation, 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 antisymmetric relation, 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 antisymmetric relation 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 antisymmetric relation 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 antisymmetric relation between them.", "questions": [ { "id": "stages-and-transitions-q01", "text": "What identifies and describes the lifecycle of a antisymmetric relation, 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 antisymmetric relation, 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 antisymmetric relation 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 antisymmetric relation, how often and by whom.", "findings": [ { "id": "observation-record", "name": "Observation record", "description": "How an observation of a antisymmetric relation 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 antisymmetric relation, 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 antisymmetric relation, 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 antisymmetric relation 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 antisymmetric relation 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 antisymmetric relation 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 antisymmetric relation 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 antisymmetric relation 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 antisymmetric relation?", "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 antisymmetric relation?", "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 antisymmetric relation 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 antisymmetric relation and how confident it is.", "questions": [ { "id": "claim-provenance-q01", "text": "What identifies and describes a claim about a antisymmetric relation, 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 antisymmetric relation, 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 antisymmetric relation 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 antisymmetric relation is retired without being erased.", "questions": [ { "id": "validity-and-supersession-q01", "text": "What identifies and describes the validity of a claim about a antisymmetric relation, 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 antisymmetric relation, 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 antisymmetric relation 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 } } } }