{ "model": { "rank": 5025, "code": "thing-q173740", "model_id": "vr.tr.cartesian-product", "name": "Cartesian product", "purpose": "Enable an agent to recognise a Cartesian product, verify its members and projections, and determine which constructions or computations its factors permit.", "family": "Thing Registry", "category": "Cross-cutting context", "status": "research-draft", "kind": "thing", "plane": "XCT", "domain": "XCT.QLT", "industry": "", "version": "", "url": "/models/thing/q173740/", "tier": 2, "score": 70, "payload": { "layer": "wikidata", "aliases": [ "trivial fiber bundle", "Cartesian power" ], "aliasCount": 2, "merged": 2, "knownIn": 70, "facets": null, "markers": [], "lexicalClass": "", "senseRank": null, "alsoRegisteredAs": null, "source": { "dataset": "wikidata", "item": "Q173740", "url": "https://www.wikidata.org/wiki/Q173740", "license": "CC0 1.0" } }, "research": { "vercy": "1.0-draft", "publication": { "status": "research-draft", "adjudicationStatus": "unreviewed", "publishableCanonical": false, "generatedAt": "2026-09-09T21:29:55Z", "providers": [ "Codex" ], "breadth": "recalled by Codex without web access - no source was read", "missingProviders": [], "pass": 2, "cost": { "grok": { "seconds": 18.3, "error": "Reading additional input from stdin...\nOpenAI Codex v0.153.4\n--------\nworkdir: R:\\02_PROJECTS\\02_Meta_Models_Platforms\\Ver.cy\\current\\thing-registry-backlog\nmodel: gpt-6-astra\nprovider: openai\napproval: never\nsandbox: read-only\nreasoning effort: none\nreasoning summaries: none\nsession id: 01a08812-faff-72b1-ba15-b20a6d6c7ce6\n--------\nuser\nDescribe what is already known about one registered thing. Answer as JSON only, no prose around it.\n\nThing: Cartesian product\nSense to describe: (none recorded)\nDomain code: XCT.REL\nAlso known as: (none)\n\n\nContext for this batch of 1001 things:\n# Batch 005: 10", "usd": 0, "recall": true }, "codex": { "seconds": 55.4, "error": "Reading additional input from stdin...\nOpenAI Codex v0.153.4\n--------\nworkdir: R:\\02_PROJECTS\\02_Meta_Models_Platforms\\Ver.cy\\current\\thing-registry-backlog\nmodel: gpt-6-astra\nprovider: openai\napproval: never\nsandbox: read-only\nreasoning effort: none\nreasoning summaries: none\nsession id: 01a08812-faef-7a70-a6e2-38d6babf14cc\n--------\nuser\nYou are drafting a Vercy meta-model for one registered thing. Answer as JSON only, no prose around it.\n\nThing: Cartesian product\nRegistry id: vr.tr.cartesian-product\nPlane / domain: XCT / XCT.REL\nRegistry definition: (none recorded)\nNames folded into this entr" } } }, "metaModel": { "id": "THING-Q173740", "registryId": "vr.tr.cartesian-product", "name": "Cartesian product", "version": "0.1.0-research.1", "entryKind": "thing", "family": "Thing Registry", "domain": [ "XCT.REL" ], "status": "research-draft" }, "canonicalUrl": "https://ver.cy/models/thing/q173740/", "model": { "registry_id": "vr.tr.cartesian-product", "name": "Cartesian product", "purpose": "Enable an agent to recognise a Cartesian product, verify its members and projections, and determine which constructions or computations its factors permit.", "definition": "The Cartesian product of an indexed family of sets is the set of all functions that assign to each index an element of its corresponding set; for two sets A and B, it is represented as the set A × B of all ordered pairs (a, b) with a ∈ A and b ∈ B.", "scope_statement": "This model owns the set-theoretic Cartesian product of two sets or an indexed family of sets, including coordinate identity, membership, projections, cardinality, and the distinction between a full product and a constrained subset.", "in_scope": [ "Binary products consisting of all ordered pairs drawn from two specified factors", "Finite and infinite indexed products represented by coordinate assignments", "Factor order, index sets, repeated factors, and tuple representation conventions", "Membership, equality, projections, and coordinatewise construction of functions", "Emptiness, cardinality, and the feasibility of enumeration" ], "out_of_scope": [ "Relations and constraint sets that select only some tuples from a product", "Disjoint unions, tensor products, and other distinct mathematical constructions", "Abstract categorical products outside the category of sets", "Topology, algebraic operations, or measures added to an underlying product set", "Database-specific treatment of duplicate rows, nulls, and query execution" ], "distinguishing_features": [ "A binary product contains exactly every ordered pair (a, b) with a in its first factor and b in its second; an additional cross-coordinate restriction defines a subset instead.", "Coordinates retain their positions or index labels: swapping factors gives a canonical bijection, but does not generally give the same set of ordered pairs.", "An indexed-product member supplies exactly one admissible value at every index, including when different indices have the same factor set.", "Union membership requires belonging to at least one constituent set; product membership requires a complete assignment across all coordinates.", "The set-theoretic product supports a unique function from any common domain for each compatible family of coordinate functions." ], "characteristics": [ { "name": "Factor family", "kind": "relation", "unit_or_values": "An assignment i ↦ A_i of a set to each index i", "why_it_matters": "Determines the admissible values at each coordinate." }, { "name": "Indexing and arity", "kind": "category", "unit_or_values": "Specified index set I; empty, finite, or infinite", "why_it_matters": "Determines which coordinates a member must supply and whether finite-tuple reasoning applies." }, { "name": "Representation convention", "kind": "category", "unit_or_values": "Ordered pairs, nested pairs, finite tuples, or functions with domain I", "why_it_matters": "Separates literal equality of representations from canonical correspondence." }, { "name": "Coordinate projections", "kind": "relation", "unit_or_values": "Maps π_i: ∏ A_i → A_i", "why_it_matters": "Connects each product member to its component values and supports coordinatewise reasoning." }, { "name": "Inhabitation status", "kind": "state", "unit_or_values": "Empty, proven nonempty, or unresolved under the stated assumptions", "why_it_matters": "Controls whether an agent may construct or assume the existence of a member." }, { "name": "Cardinality", "kind": "measurement", "unit_or_values": "Nonnegative integer or infinite cardinal; unknown when undetermined", "why_it_matters": "Supports size calculations and prevents infeasible enumeration." }, { "name": "Foundational assumptions", "kind": "category", "unit_or_values": "Stated set theory and any choice principle invoked", "why_it_matters": "Nonemptiness of arbitrary products of nonempty sets cannot be assumed independently of foundational commitments." } ], "affordances": [ "Construct a member by assigning an admissible value to every coordinate.", "Check membership and compare members coordinate by coordinate.", "Project members or functions into individual factors.", "Calculate finite product sizes and enumerate finite products when feasible.", "Build canonical coordinate permutations and reassociation bijections.", "Identify when filtering or coupling coordinates has produced a relation or another subset of the original product." ] }, "sources": [], "structure": { "bundles": [ { "id": "factors-and-coordinate-identity", "name": "Factors and coordinate identity", "description": "Records which sets supply values and how their coordinates are distinguished.", "rationale": "The factors alone do not identify a product unless their positions or indices and representation conventions are known.", "layers": [ { "id": "factor-indexing", "name": "Factor indexing", "description": "Identifies the index set and the factor assigned to each index.", "findings": [ { "id": "indexed-factor-family", "name": "Indexed factor family", "description": "A product is determined by an indexed family of factor sets; repeated occurrences of the same set remain separate coordinates.", "questions": [ { "text": "What is the index set, and which factor set is assigned to each index?", "kind": "definition", "id": "indexed-factor-family-q01" }, { "text": "Are repeated factors distinguished by positions or explicit labels?", "kind": "boundary", "id": "indexed-factor-family-q02" } ] } ] }, { "id": "tuple-conventions", "name": "Tuple conventions", "description": "Separates the mathematical coordinate assignment from its chosen encoding.", "findings": [ { "id": "representation-and-reindexing", "name": "Representation and reindexing", "description": "Ordered pairs, nested pairs, and indexed functions require explicit correspondence rules; reassociation and permutation usually provide bijections rather than literal equality.", "questions": [ { "text": "How are pairs or tuples represented, and what makes two represented members equal?", "kind": "definition", "id": "representation-and-reindexing-q01" }, { "text": "Does a proposed coordinate permutation or reassociation preserve literal equality, or require a specified bijection?", "kind": "action", "id": "representation-and-reindexing-q02" } ] } ] } ] }, { "id": "membership-and-product-boundaries", "name": "Membership and product boundaries", "description": "Defines valid coordinate assignments and distinguishes the full product from restrictions on it.", "rationale": "An agent must not confuse possible coordinate combinations with combinations admitted by an additional relation or constraint.", "layers": [ { "id": "complete-coordinate-assignments", "name": "Complete coordinate assignments", "description": "Tests whether a candidate supplies exactly the required coordinates with admissible values.", "findings": [ { "id": "coordinatewise-membership", "name": "Coordinatewise membership", "description": "An indexed member is a function with domain I whose value at each i belongs to A_i; binary membership specialises this condition to two coordinates.", "questions": [ { "text": "Does the candidate supply a value at every required index without introducing extra indices?", "kind": "boundary", "id": "coordinatewise-membership-q01" }, { "text": "What membership test establishes that each supplied value belongs to its corresponding factor?", "kind": "action", "id": "coordinatewise-membership-q02" } ] } ] }, { "id": "unrestricted-combinations", "name": "Unrestricted combinations", "description": "Checks whether all combinations admitted by the factors are retained.", "findings": [ { "id": "product-versus-restricted-subset", "name": "Product versus restricted subset", "description": "The full product imposes no cross-coordinate condition beyond factor membership; a restriction that excludes otherwise admissible combinations yields a proper subset.", "questions": [ { "text": "Does the construction retain every combination allowed by the stated factors?", "kind": "boundary", "id": "product-versus-restricted-subset-q01" }, { "text": "Can a stated restriction be absorbed into individual factors, or does it couple coordinates and require a separate relation model?", "kind": "boundary", "id": "product-versus-restricted-subset-q02" } ] } ] } ] }, { "id": "existence-size-and-enumeration", "name": "Existence, size, and enumeration", "description": "Records whether members exist, how many there are, and what can be computed explicitly.", "rationale": "Empty factors, empty index sets, and infinite families produce materially different existence and computation conditions.", "layers": [ { "id": "inhabitation-and-choice", "name": "Inhabitation and choice", "description": "Handles empty factors, zero coordinates, and assumptions needed for infinite selections.", "findings": [ { "id": "empty-and-nonempty-products", "name": "Empty and nonempty products", "description": "An empty factor makes a product empty. Under the indexed-function convention the empty-index product contains the empty function. Finite families of nonempty sets have nonempty products; the assertion for every arbitrary family is equivalent to the axiom of choice.", "questions": [ { "text": "Is the index set empty, or is any factor known to be empty?", "kind": "definition", "id": "empty-and-nonempty-products-q01" }, { "text": "If nonemptiness is asserted, is there an explicit member, a finite construction, or an identified choice principle supporting it?", "kind": "provenance", "id": "empty-and-nonempty-products-q02" } ] } ] }, { "id": "cardinality-and-effective-access", "name": "Cardinality and effective access", "description": "Distinguishes mathematical size from the availability and cost of generating members.", "findings": [ { "id": "product-size-and-enumeration", "name": "Product size and enumeration", "description": "A finite family of finite factors has size equal to the product of their sizes. Infinite products require cardinal reasoning, and even countably many finite nontrivial factors can produce an uncountable set.", "questions": [ { "text": "What factor cardinalities are established, and what product cardinality follows under the stated assumptions?", "kind": "measurement", "id": "product-size-and-enumeration-q01" }, { "text": "Are factor enumerators available, and is complete enumeration of the product possible within the intended resource limits?", "kind": "action", "id": "product-size-and-enumeration-q02" } ] } ] } ] }, { "id": "projections-and-coordinatewise-maps", "name": "Projections and coordinatewise maps", "description": "Captures the maps that extract coordinates and assemble product-valued functions.", "rationale": "Projections explain how a product is used and provide a structural test beyond its tuple encoding.", "layers": [ { "id": "coordinate-projections", "name": "Coordinate projections", "description": "Records each projection and the conditions under which coordinate values have preimages.", "findings": [ { "id": "projection-images-and-fibres", "name": "Projection images and fibres", "description": "A projection returns one coordinate. The fibre over an admissible value corresponds to the product of the remaining factors, so surjectivity requires checking whether those assignments exist, with empty codomains handled explicitly.", "questions": [ { "text": "What are the domain, codomain, and coordinate rule of each projection used?", "kind": "definition", "id": "projection-images-and-fibres-q01" }, { "text": "For a specified value in a factor, can the remaining coordinates be filled to produce a preimage?", "kind": "action", "id": "projection-images-and-fibres-q02" } ] } ] }, { "id": "assembling-product-valued-functions", "name": "Assembling product-valued functions", "description": "Uses coordinate functions to construct and verify a unique map into the product.", "findings": [ { "id": "set-product-universal-property", "name": "Set-product universal property", "description": "Given functions f_i from one set X into each factor A_i, there is a unique function f from X into the product whose composition with every projection is f_i.", "questions": [ { "text": "Do all supplied coordinate functions have the same domain and the required factor codomains?", "kind": "boundary", "id": "set-product-universal-property-q01" }, { "text": "Does the assembled function satisfy every projection equation, and does coordinatewise equality establish its uniqueness?", "kind": "action", "id": "set-product-universal-property-q02" } ] } ] } ] }, { "id": "evidence-and-external-alignment", "name": "Evidence and external alignment", "description": "What the world already says about this thing, gathered so the model can be checked against it.", "rationale": "A model that cannot be lined up against existing standards, identifiers and practice cannot be adopted by anyone who already uses them.", "layers": [ { "id": "reported-evidence", "name": "Reported evidence", "description": "Findings from the breadth pass, kept separate from the structural claims.", "findings": [ { "id": "evidence-confidence-notes", "name": "Check these first", "description": "Recalled without web access and unsourced; every item is a lead to verify.", "evidence": [ "This describes the standard set-theoretic sense; products of topological spaces or algebraic structures add structure to an underlying Cartesian product.", "Ordered pairs and tuples admit different set-theoretic encodings, so literal equality should be distinguished from canonical identification.", "These statements are recalled mathematical knowledge; no sources were consulted." ], "questions": [ { "id": "evidence-confidence-notes-q01", "text": "Which of these check these first hold for the sense of Cartesian product this model covers, and on what evidence?", "kind": "provenance" } ] }, { "id": "evidence-kinds", "name": "Kinds and varieties", "description": "Recalled without web access and unsourced; every item is a lead to verify.", "evidence": [ "Binary Cartesian product", "Finite Cartesian product", "Infinite indexed Cartesian product", "Cartesian power of a set", "Empty indexed Cartesian product" ], "questions": [ { "id": "evidence-kinds-q01", "text": "Which of these kinds and varieties hold for the sense of Cartesian product this model covers, and on what evidence?", "kind": "provenance" } ] }, { "id": "evidence-real-world-use", "name": "Real-world use", "description": "Recalled without web access and unsourced; every item is a lead to verify.", "evidence": [ "Defining binary relations as subsets of Cartesian products.", "Constructing coordinate spaces, including real coordinate spaces ℝⁿ.", "Enumerating combinations of parameter choices in exhaustive search and experimental design.", "Expressing database cross joins, with SQL duplicate and null semantics requiring additional interpretation.", "Constructing joint state spaces for systems with multiple components." ], "questions": [ { "id": "evidence-real-world-use-q01", "text": "Which of these real-world use hold for the sense of Cartesian product this model covers, and on what evidence?", "kind": "provenance" } ] }, { "id": "evidence-measurements", "name": "Typical measurements", "description": "Recalled without web access and unsourced; every item is a lead to verify.", "evidence": [ { "quantity": "Cardinality of a finite Cartesian product", "typical_range": "For finite sets A₁ through Aₙ, the number of tuples is |A₁| × ⋯ × |Aₙ|; any nonnegative integer is possible.", "unit": "elements" }, { "quantity": "Tuple arity", "typical_range": "Any nonnegative integer for finite products; general indexed products can have infinitely many coordinates.", "unit": "coordinates" } ], "questions": [ { "id": "evidence-measurements-q01", "text": "Which of these typical measurements hold for the sense of Cartesian product this model covers, and on what evidence?", "kind": "provenance" } ] }, { "id": "evidence-failure-modes-and-hazards", "name": "Failure modes and hazards", "description": "Recalled without web access and unsourced; every item is a lead to verify.", "evidence": [ "Confusing ordered pairs with unordered pairs: coordinate positions matter.", "Treating A × B and B × A as literally equal; swapping coordinates gives a canonical bijection, not equality in general.", "Enumerating a product can cause combinatorial explosion as factor sizes or the number of factors grow.", "Assuming every product of nonempty sets is nonempty without acknowledging that the assertion for arbitrary indexed families is equivalent to the axiom of choice.", "Confusing a product with an empty factor, which is empty, with a product indexed by the empty set, which contains exactly one element." ], "questions": [ { "id": "evidence-failure-modes-and-hazards-q01", "text": "Which of these failure modes and hazards hold for the sense of Cartesian product this model covers, and on what evidence?", "kind": "provenance" } ] }, { "id": "evidence-neighbours", "name": "Neighbouring kinds and how to tell them apart", "description": "Recalled without web access and unsourced; every item is a lead to verify.", "evidence": [ { "name": "Binary relation", "difference": "A binary relation from A to B is any subset of A × B; the Cartesian product includes every permitted ordered pair." }, { "name": "Union", "difference": "A union collects elements from its member sets; a Cartesian product forms tuples choosing one element from each factor." }, { "name": "Power set", "difference": "The power set of A contains all subsets of A; a Cartesian power of A contains indexed tuples of elements of A." }, { "name": "Categorical product", "difference": "A categorical product is specified by a universal property involving projections; in the category of sets, Cartesian products realize that property." }, { "name": "Tensor product", "difference": "A tensor product represents bilinear or multilinear maps between algebraic structures; a Cartesian product collects coordinate choices." } ], "questions": [ { "id": "evidence-neighbours-q01", "text": "Which of these neighbouring kinds and how to tell them apart hold for the sense of Cartesian product this model covers, and on what evidence?", "kind": "provenance" } ] } ] } ] } ] }, "openQuestions": [ "Which tuple encoding and equality conventions should Vercy adopt when exchanging products between implementations?", "Should this entry own variable-factor indexed products directly, or link their dependent-type interpretation to a neighbouring model?", "Which foundational assumptions should be recorded by default when an application asserts that an infinite product is nonempty?", "Which authoritative references should support the published treatment of empty products, choice, cardinality, and the set-product universal property?" ], "statistics": { "bundles": 5, "layers": 9, "findings": 14, "questions": 22 } }, "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 Cartesian product, record what state it is in, and decide what may be done with it.", "whatItIs": "Enable an agent to recognise a Cartesian product, verify its members and projections, and determine which constructions or computations its factors permit.", "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: trivial fiber bundle, Cartesian power.", "2 finer distinctions are held as aliases rather than separate entries, because telling them apart needs a task that asks for it.", "Described in 70 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 Cartesian product, 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": [ "trivial fiber bundle", "Cartesian power" ] } ], "standing": "Described in 70 Wikipedia languages, which measures how widely it is written about rather than how important or how common it is. 2 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 Cartesian product from another, and a Cartesian product 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 Cartesian product, 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 Cartesian product, 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 Cartesian product 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 Cartesian product, 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 Cartesian product, 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 Cartesian product 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 Cartesian product 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 Cartesian product, 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 Cartesian product, 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 Cartesian product 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 Cartesian product from the things most often confused with it.", "questions": [ { "id": "distinguishing-features-q01", "text": "What identifies and describes what distinguishes a Cartesian product, 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 Cartesian product, 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 Cartesian product 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 Cartesian product 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 Cartesian product between them.", "questions": [ { "id": "stages-and-transitions-q01", "text": "What identifies and describes the lifecycle of a Cartesian product, 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 Cartesian product, 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 Cartesian product 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 Cartesian product, how often and by whom.", "findings": [ { "id": "observation-record", "name": "Observation record", "description": "How an observation of a Cartesian product 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 Cartesian product, 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 Cartesian product, 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 Cartesian product 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 Cartesian product 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 Cartesian product 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 Cartesian product 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 Cartesian product 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 Cartesian product?", "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 Cartesian product?", "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 Cartesian product 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 Cartesian product and how confident it is.", "questions": [ { "id": "claim-provenance-q01", "text": "What identifies and describes a claim about a Cartesian product, 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 Cartesian product, 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 Cartesian product 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 Cartesian product is retired without being erased.", "questions": [ { "id": "validity-and-supersession-q01", "text": "What identifies and describes the validity of a claim about a Cartesian product, 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 Cartesian product, 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 Cartesian product 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 } } } }