{ "model": { "rank": 14664, "code": "thing-q188211", "model_id": "vr.tr.invariant", "name": "invariant", "purpose": "Let an agent explain invariants by field, transformation, examples and use in proofs, classification and program correctness.", "family": "Thing Registry", "category": "Cross-cutting context", "status": "research-draft", "kind": "thing", "plane": "XCT", "domain": "XCT.QLT", "industry": "", "version": "", "url": "/models/thing/q188211/", "tier": 2, "score": 35, "payload": { "layer": "wikidata", "aliases": [ "adiabatic invariant", "focal parameter", "p-quantile", "homology", "link invariant", "de Rham cohomology", "tree property", "Dolbeault cohomology", "invariant of geometric transformation", "irregularity of a surface", "Gromov–Witten invariant", "cohomological invariant", "Invariant of a binary form", "j-multiplicity", "weak dimension", "Gopakumar-Vafa invariant", "knot invariant", "Griffiths group", "systole", "6-j symbol", "general covariance", "étale fundamental group", "degree of a continuous mapping", "exponent of a group", "Berezinian", "Carminati–McLenaghan invariants", "cardinal function", "Bass number", "birational invariant", "Chow ring", "cohomological dimension", "cohomotopy set", "Complex dimension", "covering number", "Deligne cohomology", "Deviation of a local ring", "differential invariant", "Donaldson–Thomas theory", "Fitting ideal", "Hilbert–Samuel function" ], "aliasCount": 64, "merged": 66, "knownIn": 35, "facets": null, "markers": [], "lexicalClass": "", "senseRank": null, "alsoRegisteredAs": null, "source": { "dataset": "wikidata", "item": "Q188211", "url": "https://www.wikidata.org/wiki/Q188211", "license": "CC0 1.0" } }, "research": { "vercy": "1.0-draft", "publication": { "status": "research-draft", "adjudicationStatus": "unreviewed", "publishableCanonical": false, "generatedAt": "2026-09-11T12:12:49Z", "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": 1, "engine": "claude" }, "metaModel": { "id": "THING-Q188211", "registryId": "vr.tr.invariant", "name": "invariant", "version": "0.2.0-wave.1", "entryKind": "thing", "family": "Thing Registry", "domain": [ "XCT.QLT" ], "status": "research-draft" }, "canonicalUrl": "https://ver.cy/models/thing/q188211/", "model": { "registry_id": "vr.tr.invariant", "name": "invariant", "purpose": "Let an agent explain invariants by field, transformation, examples and use in proofs, classification and program correctness.", "definition": "A property, quantity or object that remains unchanged when a specified transformation or operation is applied, used throughout mathematics, physics and computer science; examples include the determinant under similarity, the Euler characteristic, knot invariants, conserved quantities and loop invariants.", "what_it_is_for": "Classifying objects, proving results and checking correctness.", "affordances": [ "identify invariants under a transformation", "use invariants to show two objects differ", "explain loop invariants in algorithms", "relate invariants to conservation laws" ], "distinguishing_features": [ "Defined relative to transformations", "Used to distinguish objects", "Complete invariants classify fully", "Links to symmetry" ], "appearance": "Not physical; formulas, numbers or structures in mathematics and code.", "visual_identification": [ "Unchanged under a stated transformation", "Euler characteristic and knot polynomials", "A constant is not necessarily an invariant of anything" ], "physical_properties": [], "families_and_kinds": [ "algebraic invariants", "topological invariants", "knot and link invariants", "physical invariants and conserved quantities", "loop and class invariants in programming" ], "related_models": [ { "relation": "is a kind of", "target": "mathematical property", "why": "category" }, { "relation": "is defined by", "target": "transformation group", "why": "context" }, { "relation": "includes", "target": "Euler characteristic", "why": "example" }, { "relation": "is related to", "target": "symmetry", "why": "concept" } ], "identifiers": [], "standards_and_regulation": [ "No specific regulation; formal verification standards use invariants" ], "failure_modes_and_hazards": [ "Not stating the transformation", "Treating an incomplete invariant as a classifier" ], "in_scope": [], "out_of_scope": [], "characteristics": [] }, "sources": [], "structure": { "bundles": [ { "id": "concept", "name": "Concept", "description": "What it means.", "rationale": "Transformations matter.", "layers": [ { "id": "transformation", "name": "Transformation", "description": "Under what.", "findings": [ { "id": "transformation-finding", "name": "Transformation", "description": "Transformation.", "questions": [ { "text": "Under which transformations is this quantity invariant?", "kind": "definition" }, { "text": "Is it invariant under all of them?", "kind": "boundary" } ] } ] }, { "id": "completeness", "name": "Completeness", "description": "Classification.", "findings": [ { "id": "completeness-finding", "name": "Completeness", "description": "Completeness.", "questions": [ { "text": "Is the invariant complete, so that equal values imply equivalence?", "kind": "boundary" }, { "text": "Which counterexamples exist?", "kind": "provenance" } ] } ] } ] }, { "id": "examples", "name": "Examples", "description": "Fields.", "rationale": "Invariants appear widely.", "layers": [ { "id": "topology", "name": "Topology", "description": "Shapes.", "findings": [ { "id": "topology-finding", "name": "Topology", "description": "Topological invariants.", "questions": [ { "text": "How does the Euler characteristic distinguish surfaces?", "kind": "definition" }, { "text": "How is it computed?", "kind": "measurement" } ] } ] }, { "id": "knots", "name": "Knots", "description": "Knot theory.", "findings": [ { "id": "knots-finding", "name": "Knots", "description": "Knot invariants.", "questions": [ { "text": "Which knot invariants can show two knots are different?", "kind": "definition" }, { "text": "How are they calculated?", "kind": "measurement" } ] } ] } ] }, { "id": "physics", "name": "Physics", "description": "Conservation.", "rationale": "Symmetry gives invariants.", "layers": [ { "id": "conservation", "name": "Conservation", "description": "Conserved quantities.", "findings": [ { "id": "conservation-finding", "name": "Conservation", "description": "Conserved quantities.", "questions": [ { "text": "How does Noether theorem link symmetries to conserved quantities?", "kind": "definition" }, { "text": "Which quantity corresponds to which symmetry?", "kind": "definition" } ] } ] }, { "id": "adiabatic", "name": "Adiabatic", "description": "Adiabatic invariants.", "findings": [ { "id": "adiabatic-finding", "name": "Adiabatic", "description": "Adiabatic invariants.", "questions": [ { "text": "What is an adiabatic invariant, and where is it used?", "kind": "definition" }, { "text": "How approximate is it?", "kind": "boundary" } ] } ] } ] }, { "id": "computing", "name": "Computing", "description": "Programs.", "rationale": "Invariants prove correctness.", "layers": [ { "id": "loop", "name": "Loop", "description": "Loop invariants.", "findings": [ { "id": "loop-finding", "name": "Loop", "description": "Loop invariants.", "questions": [ { "text": "What loop invariant proves this algorithm correct?", "kind": "definition" }, { "text": "Does it hold at initialisation, maintenance and termination?", "kind": "boundary" } ] } ] }, { "id": "verification", "name": "Verification", "description": "Formal methods.", "findings": [ { "id": "verification-finding", "name": "Verification", "description": "Formal verification.", "questions": [ { "text": "Which tools check invariants in code?", "kind": "provenance" }, { "text": "How are they specified?", "kind": "definition" } ] } ] } ] } ] }, "openQuestions": [ "Should each invariant be a separate entry?", "How should fields be linked?", "How should programming invariants 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 invariant, record what state it is in, and decide what may be done with it.", "whatItIs": "Let an agent explain invariants by field, transformation, examples and use in proofs, classification and program correctness.", "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: adiabatic invariant, focal parameter, p-quantile, homology, link invariant, de Rham cohomology, tree property, Dolbeault cohomology, invariant of geometric transformation, irregularity of a surface, Gromov–Witten invariant, cohomological invariant.", "66 finer distinctions are held as aliases rather than separate entries, because telling them apart needs a task that asks for it.", "Described in 35 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 invariant, 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": [ "adiabatic invariant", "focal parameter", "p-quantile", "homology", "link invariant", "de Rham cohomology", "tree property", "Dolbeault cohomology", "invariant of geometric transformation", "irregularity of a surface", "Gromov–Witten invariant", "cohomological invariant" ] } ], "standing": "Described in 35 Wikipedia languages, which measures how widely it is written about rather than how important or how common it is. 66 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 invariant from another, and a invariant 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 invariant, 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 invariant, 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 invariant 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 invariant, 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 invariant, 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 invariant 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 invariant 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 invariant, 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 invariant, 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 invariant 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 invariant from the things most often confused with it.", "questions": [ { "id": "distinguishing-features-q01", "text": "What identifies and describes what distinguishes a invariant, 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 invariant, 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 invariant 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 invariant 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 invariant between them.", "questions": [ { "id": "stages-and-transitions-q01", "text": "What identifies and describes the lifecycle of a invariant, 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 invariant, 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 invariant 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 invariant, how often and by whom.", "findings": [ { "id": "observation-record", "name": "Observation record", "description": "How an observation of a invariant 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 invariant, 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 invariant, 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 invariant 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 invariant 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 invariant 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 invariant 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 invariant 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 invariant?", "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 invariant?", "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 invariant 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 invariant and how confident it is.", "questions": [ { "id": "claim-provenance-q01", "text": "What identifies and describes a claim about a invariant, 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 invariant, 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 invariant 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 invariant is retired without being erased.", "questions": [ { "id": "validity-and-supersession-q01", "text": "What identifies and describes the validity of a claim about a invariant, 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 invariant, 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 invariant 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 } } } }