{ "model": { "rank": 4603, "code": "thing-q181365", "model_id": "vr.tr.scalar-product", "name": "scalar product", "purpose": "Enable an agent to recognise a scalar product, verify its mathematical assumptions, interpret its values and determine which geometric or computational operations are justified.", "family": "Thing Registry", "category": "Cross-cutting context", "status": "research-draft", "kind": "thing", "plane": "XCT", "domain": "XCT.QLT", "industry": "", "version": "", "url": "/models/thing/q181365/", "tier": 2, "score": 74, "payload": { "layer": "wikidata", "aliases": [ "canonical inner product" ], "aliasCount": 1, "merged": 1, "knownIn": 74, "facets": null, "markers": [], "lexicalClass": "", "senseRank": null, "alsoRegisteredAs": "vr.tr.scalar-product", "source": { "dataset": "wikidata", "item": "Q181365", "url": "https://www.wikidata.org/wiki/Q181365", "license": "CC0 1.0" } }, "research": { "vercy": "1.0-draft", "publication": { "status": "research-draft", "adjudicationStatus": "unreviewed", "publishableCanonical": false, "generatedAt": "2026-09-09T20:35:58Z", "providers": [ "Codex" ], "breadth": "recalled by Codex without web access - no source was read", "missingProviders": [], "pass": 2, "cost": { "grok": { "seconds": 20.7, "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: 01a087e1-860f-7ba3-ad0e-ce23e7004621\n--------\nuser\nDescribe what is already known about one registered thing. Answer as JSON only, no prose around it.\n\nThing: scalar 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: 1001 ", "usd": 0, "recall": true }, "codex": { "seconds": 59.3, "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: 01a087e1-8605-71c1-85ba-338a3a0eb7dc\n--------\nuser\nYou are drafting a Vercy meta-model for one registered thing. Answer as JSON only, no prose around it.\n\nThing: scalar product\nRegistry id: vr.tr.scalar-product\nPlane / domain: XCT / XCT.REL\nRegistry definition: (none recorded)\nNames folded into this entry: (no" } } }, "metaModel": { "id": "THING-Q181365", "registryId": "vr.tr.scalar-product", "name": "scalar product", "version": "0.1.0-research.1", "entryKind": "thing", "family": "Thing Registry", "domain": [ "XCT.REL" ], "status": "research-draft" }, "canonicalUrl": "https://ver.cy/models/thing/q181365/", "model": { "registry_id": "vr.tr.scalar-product", "name": "scalar product", "purpose": "Enable an agent to recognise a scalar product, verify its mathematical assumptions, interpret its values and determine which geometric or computational operations are justified.", "definition": "A scalar product is a scalar-valued operation on pairs of vectors, usually meaning an inner product that is positive definite and symmetric bilinear over the real numbers or conjugate-symmetric sesquilinear over the complex numbers, with the Euclidean dot product as its standard finite-dimensional example.", "scope_statement": "This model owns scalar product as a positive-definite inner product on a real or complex vector space, including the Euclidean dot product, while recording terminology that extends the name to indefinite pairings without treating those pairings as inner products.", "in_scope": [ "The vector space, scalar field and admissible pairs of operands.", "Positive definiteness, symmetry or conjugate symmetry, and linearity conventions.", "Coordinate formulas, basis dependence and Gram matrices.", "Norms, orthogonality, angles and projections induced by the product.", "Evaluation methods, numerical reliability and application-specific interpretation." ], "out_of_scope": [ "Scalar multiplication of a vector, which returns a vector.", "Cross products and tensor products, whose outputs are not scalar inner-product values.", "General bilinear or sesquilinear forms except where needed to test the scalar-product boundary.", "The full theory of vector spaces, metric spaces and Hilbert spaces.", "Physical models such as mechanical work, which use a scalar product but supply their own quantities and laws." ], "distinguishing_features": [ "It takes two vectors from the same declared vector space and returns an element of its scalar field; scalar multiplication instead takes a scalar and a vector.", "For the adopted inner-product sense, the self-product is real and nonnegative and is zero exactly for the zero vector.", "Over the real numbers it is symmetric and bilinear; over the complex numbers it is conjugate symmetric and linear in one argument and conjugate-linear in the other.", "The sum of componentwise products represents the real Euclidean product in orthonormal coordinates; an arbitrary basis generally requires a Gram matrix.", "A scalar-valued pairing that permits a nonzero vector with zero or negative self-product falls outside the adopted positive-definite sense." ], "characteristics": [ { "name": "Scalar-product sense", "kind": "category", "unit_or_values": "Euclidean dot product; real inner product; complex inner product; explicitly distinguished indefinite pairing", "why_it_matters": "Determines which axioms and geometric consequences the name licenses." }, { "name": "Operand space", "kind": "relation", "unit_or_values": "Declared vector space over R or C, with dimension and domain restrictions", "why_it_matters": "Establishes whether the operands are compatible and whether evaluation is defined." }, { "name": "Complex linearity convention", "kind": "category", "unit_or_values": "Linear in the first argument; linear in the second argument; not applicable over R", "why_it_matters": "Controls conjugation in coordinate formulas and projection coefficients." }, { "name": "Axiom verification", "kind": "state", "unit_or_values": "Established; assumed; numerically supported; violated; unresolved, recorded separately for each axiom", "why_it_matters": "Separates a valid inner product from a proposed formula or limited numerical evidence." }, { "name": "Basis and Gram representation", "kind": "relation", "unit_or_values": "Ordered basis with its Gram matrix; implicit operator; integral representation", "why_it_matters": "Connects the abstract operation to an evaluable representation." }, { "name": "Evaluated product", "kind": "measurement", "unit_or_values": "Real or complex scalar; units determined by operands and weighting", "why_it_matters": "Records the result without assuming every scalar product is dimensionless or real." }, { "name": "Evaluation uncertainty", "kind": "measurement", "unit_or_values": "Absolute or relative error bound, tolerance, or unknown", "why_it_matters": "Determines whether near-zero products support an orthogonality decision." } ], "affordances": [ "Check whether a proposed scalar-valued operation satisfies the declared inner-product axioms.", "Evaluate a product using compatible coordinates, weights, conjugation and domain rules.", "Derive lengths and test orthogonality under the selected product.", "Compute justified projections, normalisations and orthogonal decompositions.", "Translate a product between bases while preserving its value.", "Identify invalid inferences caused by an indefinite form, a zero norm, an undefined integral or numerical error." ] }, "sources": [], "structure": { "bundles": [ { "id": "meaning-and-operands", "name": "Meaning and operands", "description": "Fix the mathematical sense of scalar product and the objects on which it acts.", "rationale": "The name alone does not distinguish a Euclidean dot product, a general inner product or an indefinite pairing.", "layers": [ { "id": "terminological-scope", "name": "Terminological scope", "description": "Record the intended meaning and its supporting definition.", "findings": [ { "id": "declared-product-sense", "name": "Declared product sense", "description": "Treat positive-definite inner products as the core sense and explicitly identify broader uses of the term.", "questions": [ { "text": "Does scalar product here mean the Euclidean dot product, an arbitrary positive-definite inner product or a broader pairing?", "kind": "definition", "id": "declared-product-sense-q01" }, { "text": "Which reference or application specification establishes this meaning?", "kind": "provenance", "id": "declared-product-sense-q02" } ] } ] }, { "id": "vector-space-domain", "name": "Vector-space domain", "description": "Identify the scalar field and admissible operands, including functional domains.", "findings": [ { "id": "compatible-admissible-vectors", "name": "Compatible admissible vectors", "description": "A product requires vectors in its declared space; function-space products may require integrability and equivalence-class conventions.", "questions": [ { "text": "What vector space and scalar field contain both operands?", "kind": "definition", "id": "compatible-admissible-vectors-q01" }, { "text": "For function operands, what integrability requirements and identifications up to equality almost everywhere make the product well-defined and positive definite?", "kind": "boundary", "id": "compatible-admissible-vectors-q02" } ] } ] } ] }, { "id": "axioms-and-conventions", "name": "Axioms and conventions", "description": "Establish the algebraic guarantees needed for inner-product reasoning.", "rationale": "Returning a scalar is insufficient to justify norms, orthogonality or projections.", "layers": [ { "id": "linearity-and-symmetry", "name": "Linearity and symmetry", "description": "Specify linearity, conjugation and argument order.", "findings": [ { "id": "field-sensitive-algebra", "name": "Field-sensitive algebra", "description": "Real products are symmetric bilinear forms; complex products are conjugate symmetric with opposite linearity behaviour in their two arguments.", "questions": [ { "text": "Which argument is linear, and where must scalar coefficients be conjugated?", "kind": "definition", "id": "field-sensitive-algebra-q01" }, { "text": "What proof or defining construction establishes additivity, scalar compatibility and the required symmetry?", "kind": "provenance", "id": "field-sensitive-algebra-q02" } ] } ] }, { "id": "positivity-and-degeneracy", "name": "Positivity and degeneracy", "description": "Separate positive-definite products from semidefinite and indefinite forms.", "findings": [ { "id": "self-product-test", "name": "Self-product test", "description": "An inner product has a real, strictly positive self-product for every nonzero vector; semidefinite forms may instead induce products on a quotient by their null space.", "questions": [ { "text": "Can any nonzero admissible vector have zero, negative or nonreal self-product?", "kind": "boundary", "id": "self-product-test-q01" }, { "text": "If a null space exists, is the intended object a semidefinite form or an inner product on an explicitly defined quotient space?", "kind": "definition", "id": "self-product-test-q02" } ] } ] } ] }, { "id": "representations-and-evaluation", "name": "Representations and evaluation", "description": "Connect the abstract product to coordinate, weighted and integral formulas.", "rationale": "A familiar componentwise formula can silently compute the wrong product when the basis, weights or conjugation differ.", "layers": [ { "id": "coordinate-representation", "name": "Coordinate representation", "description": "Record the basis and matrix that encode the product.", "findings": [ { "id": "gram-matrix-contract", "name": "Gram-matrix contract", "description": "For column coordinates and the complex convention linear in the second argument, the product is x*Gy, where G is Hermitian positive definite; real coordinates use xᵀGy.", "questions": [ { "text": "Which ordered basis and Gram matrix define the coordinate formula, and is that basis orthonormal for this product?", "kind": "definition", "id": "gram-matrix-contract-q01" }, { "text": "Under a change of basis, how are coordinates and the Gram matrix transformed to preserve the scalar value?", "kind": "action", "id": "gram-matrix-contract-q02" } ] } ] }, { "id": "weighted-and-functional-evaluation", "name": "Weighted and functional evaluation", "description": "Specify summation, integration and weighting beyond the ordinary finite-dimensional dot product.", "findings": [ { "id": "evaluation-rule-and-existence", "name": "Evaluation rule and existence", "description": "Weighted sums and integrals require explicit weights, conjugation, measures and existence conditions.", "questions": [ { "text": "What sum or integral computes the product, including its weights, measure and conjugated argument?", "kind": "definition", "id": "evaluation-rule-and-existence-q01" }, { "text": "What guarantees convergence and positive definiteness on the declared operand space?", "kind": "boundary", "id": "evaluation-rule-and-existence-q02" } ] } ] } ] }, { "id": "induced-geometry", "name": "Induced geometry", "description": "Record which geometric constructions follow from the chosen product.", "rationale": "Lengths, angles and orthogonal projections depend on the product and require specific operand or subspace conditions.", "layers": [ { "id": "norm-angle-and-orthogonality", "name": "Norm, angle and orthogonality", "description": "Derive geometric relations while respecting zero-vector and complex-space boundaries.", "findings": [ { "id": "geometric-interpretation", "name": "Geometric interpretation", "description": "The induced norm is the square root of the self-product and orthogonality means a zero product; the usual cosine angle formula applies directly to nonzero real vectors.", "questions": [ { "text": "What lengths and orthogonality relation does this product induce for the operands?", "kind": "measurement", "id": "geometric-interpretation-q01" }, { "text": "If an angle is requested, are both vectors nonzero, and what angle convention is declared for a complex space?", "kind": "boundary", "id": "geometric-interpretation-q02" } ] } ] }, { "id": "projection-and-decomposition", "name": "Projection and decomposition", "description": "Determine when normalisation and orthogonal projection are justified.", "findings": [ { "id": "projection-preconditions", "name": "Projection preconditions", "description": "Projection onto a nonzero vector uses its positive self-product as a denominator; projection onto general subspaces requires an existence argument, with closed subspaces of Hilbert spaces providing a standard guarantee.", "questions": [ { "text": "Which normalisation or projection formula matches the declared argument convention, and are its denominators nonzero?", "kind": "action", "id": "projection-preconditions-q01" }, { "text": "For a requested subspace projection, what establishes existence and uniqueness in the ambient space?", "kind": "boundary", "id": "projection-preconditions-q02" } ] } ] } ] }, { "id": "reliability-and-use", "name": "Reliability and use", "description": "Control numerical decisions and attach application meaning to the result.", "rationale": "Cancellation, scaling and chosen weights can change how an agent should interpret or act on a computed scalar.", "layers": [ { "id": "numerical-decisions", "name": "Numerical decisions", "description": "Distinguish exact algebraic properties from finite-precision evidence.", "findings": [ { "id": "near-zero-product", "name": "Near-zero product", "description": "A small computed value supports approximate orthogonality only relative to operand norms, product scaling and evaluation error.", "questions": [ { "text": "What precision, accumulation method and error estimate support the evaluated product?", "kind": "measurement", "id": "near-zero-product-q01" }, { "text": "What scale-aware tolerance justifies treating the operands as approximately orthogonal?", "kind": "action", "id": "near-zero-product-q02" } ] } ] }, { "id": "application-interpretation", "name": "Application interpretation", "description": "Record why this product was selected and what its magnitude represents.", "findings": [ { "id": "weighting-units-and-normalisation", "name": "Weighting, units and normalisation", "description": "A raw product combines magnitude with alignment; weights and units come from the application, while normalisation changes the quantity being interpreted.", "questions": [ { "text": "Why was this product or weighting selected, and what units does its output carry?", "kind": "provenance", "id": "weighting-units-and-normalisation-q01" }, { "text": "Does the intended decision require a raw product, a normalised similarity or a projection coefficient?", "kind": "action", "id": "weighting-units-and-normalisation-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": [ "The registry supplies no sense: check whether the intended scope is the Euclidean dot product, general inner products, or a broader usage that includes indefinite forms.", "Mathematical and physics sources use different conventions for which argument of a complex inner product is linear.", "This description is recalled knowledge; no sources or standards were consulted." ], "questions": [ { "id": "evidence-confidence-notes-q01", "text": "Which of these check these first hold for the sense of scalar 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": [ "Euclidean dot product", "Weighted inner product defined by a positive-definite matrix", "Complex Hermitian inner product", "Integral inner product on a space of functions" ], "questions": [ { "id": "evidence-kinds-q01", "text": "Which of these kinds and varieties hold for the sense of scalar 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": [ "Computing lengths, angles, orthogonality and projections in geometry.", "Expressing mechanical work as the dot product of a constant force and displacement.", "Constructing least-squares approximations and orthogonal decompositions.", "Comparing vector representations through cosine similarity.", "Calculating overlaps between quantum states using complex inner products." ], "questions": [ { "id": "evidence-real-world-use-q01", "text": "Which of these real-world use hold for the sense of scalar 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": "Euclidean dot product of vectors u and v", "typical_range": "Between -||u|| ||v|| and +||u|| ||v||; no universal numerical range", "unit": "Product of the units of the two vectors, when their components have compatible units" }, { "quantity": "Normalized real inner product for nonzero vectors", "typical_range": "[-1, 1]", "unit": "Dimensionless" } ], "questions": [ { "id": "evidence-measurements-q01", "text": "Which of these typical measurements hold for the sense of scalar 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": [ "Using the coordinate formula sum(u_i v_i) in a nonorthonormal basis without the required Gram matrix.", "Omitting complex conjugation for complex vectors, thereby losing positive definiteness.", "Mixing conventions about which argument of a complex inner product is linear.", "Normalizing a zero vector, for which cosine similarity is undefined.", "Treating an indefinite form as a positive-definite inner product, leading to invalid conclusions about lengths or angles." ], "questions": [ { "id": "evidence-failure-modes-and-hazards-q01", "text": "Which of these failure modes and hazards hold for the sense of scalar 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": "Scalar multiplication", "difference": "Combines a scalar and a vector to produce a vector; a scalar product combines two vectors to produce a scalar." }, { "name": "Dot product", "difference": "Usually denotes the standard Euclidean scalar product; an inner product can use other positive-definite forms or act on function spaces." }, { "name": "Bilinear form", "difference": "Is linear in each argument but need not be symmetric or positive definite." }, { "name": "Indefinite scalar product", "difference": "Allows nonzero vectors with zero or negative self-product, unlike a positive-definite inner product." }, { "name": "Cross product", "difference": "The ordinary three-dimensional cross product returns a vector perpendicular to its inputs rather than a scalar." }, { "name": "Norm", "difference": "Assigns a nonnegative size to one vector; a norm arises from an inner product exactly when it satisfies the parallelogram law." } ], "questions": [ { "id": "evidence-neighbours-q01", "text": "Which of these neighbouring kinds and how to tell them apart hold for the sense of scalar product this model covers, and on what evidence?", "kind": "provenance" } ] } ] } ] } ] }, "openQuestions": [ "Does the registry intend scalar product specifically as the Euclidean dot product or as the broader class of real and complex positive-definite inner products?", "Which authoritative references should establish the intended terminology and complex argument convention?", "Does an existing Vercy world model already own this concept, requiring a registry link instead of a separate publication?", "Should indefinite uses of scalar product be represented only as boundary references or included through an explicitly broader scope?", "Which applications and function spaces must the completed model support, and what evaluation tolerances do those uses require?" ], "statistics": { "bundles": 6, "layers": 11, "findings": 16, "questions": 26 } }, "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 scalar product, record what state it is in, and decide what may be done with it.", "whatItIs": "Enable an agent to recognise a scalar product, verify its mathematical assumptions, interpret its values and determine which geometric or computational operations are justified.", "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: canonical inner product.", "1 finer distinctions are held as aliases rather than separate entries, because telling them apart needs a task that asks for it.", "Described in 74 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 scalar 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": [ "canonical inner product" ] } ], "standing": "Described in 74 Wikipedia languages, which measures how widely it is written about rather than how important or how common it is. 1 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 scalar product from another, and a scalar 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 scalar 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 scalar 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 scalar 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 scalar 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 scalar 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 scalar 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 scalar 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 scalar 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 scalar 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 scalar 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 scalar product from the things most often confused with it.", "questions": [ { "id": "distinguishing-features-q01", "text": "What identifies and describes what distinguishes a scalar 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 scalar 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 scalar 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 scalar 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 scalar product between them.", "questions": [ { "id": "stages-and-transitions-q01", "text": "What identifies and describes the lifecycle of a scalar 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 scalar 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 scalar 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 scalar product, how often and by whom.", "findings": [ { "id": "observation-record", "name": "Observation record", "description": "How an observation of a scalar 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 scalar 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 scalar 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 scalar 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 scalar 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 scalar 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 scalar 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 scalar 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 scalar 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 scalar 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 scalar 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 scalar product and how confident it is.", "questions": [ { "id": "claim-provenance-q01", "text": "What identifies and describes a claim about a scalar 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 scalar 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 scalar 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 scalar product is retired without being erased.", "questions": [ { "id": "validity-and-supersession-q01", "text": "What identifies and describes the validity of a claim about a scalar 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 scalar 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 scalar 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 } } } }