{ "model": { "rank": 5196, "code": "thing-q199691", "model_id": "vr.tr.laplace-transform", "name": "Laplace transform", "purpose": "Enable an agent to recognise a Laplace-transform representation, assess its mathematical validity, and choose justified transformation, inversion, or application steps.", "family": "Thing Registry", "category": "Cross-cutting context", "status": "research-draft", "kind": "thing", "plane": "XCT", "domain": "XCT.QLT", "industry": "", "version": "", "url": "/models/thing/q199691/", "tier": 2, "score": 69, "payload": { "layer": "wikidata", "aliases": [], "aliasCount": 0, "merged": 0, "knownIn": 69, "facets": null, "markers": [], "lexicalClass": "", "senseRank": null, "alsoRegisteredAs": null, "source": { "dataset": "wikidata", "item": "Q199691", "url": "https://www.wikidata.org/wiki/Q199691", "license": "CC0 1.0" } }, "research": { "vercy": "1.0-draft", "publication": { "status": "research-draft", "adjudicationStatus": "unreviewed", "publishableCanonical": false, "generatedAt": "2026-09-09T21:52:21Z", "providers": [ "Codex" ], "breadth": "recalled by Codex without web access - no source was read", "missingProviders": [], "pass": 2, "cost": { "grok": { "seconds": 16.5, "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: 01a08827-65b1-7903-8da7-2bf0c9ecf71c\n--------\nuser\nDescribe what is already known about one registered thing. Answer as JSON only, no prose around it.\n\nThing: Laplace transform\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": 63.4, "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: 01a08827-65a0-7190-9ec2-a387e2dec25e\n--------\nuser\nYou are drafting a Vercy meta-model for one registered thing. Answer as JSON only, no prose around it.\n\nThing: Laplace transform\nRegistry id: vr.tr.laplace-transform\nPlane / domain: XCT / XCT.REL\nRegistry definition: (none recorded)\nNames folded into this entr" } } }, "metaModel": { "id": "THING-Q199691", "registryId": "vr.tr.laplace-transform", "name": "Laplace transform", "version": "0.1.0-research.1", "entryKind": "thing", "family": "Thing Registry", "domain": [ "XCT.REL" ], "status": "research-draft" }, "canonicalUrl": "https://ver.cy/models/thing/q199691/", "model": { "registry_id": "vr.tr.laplace-transform", "name": "Laplace transform", "purpose": "Enable an agent to recognise a Laplace-transform representation, assess its mathematical validity, and choose justified transformation, inversion, or application steps.", "definition": "The Laplace transform is an integral transform that maps a function or suitable generalized function of a real variable t to a function of a complex variable s using the kernel exp(-st), with its domain determined by convergence and by whether integration is unilateral or bilateral.", "scope_statement": "This model owns the Laplace transform as an integral-transform concept and its concrete uses, including unilateral and bilateral conventions, admissible inputs, convergence, operational identities, inversion, and interpretation.", "in_scope": [ "Unilateral and bilateral definitions using an exponential kernel and a complex transform variable", "Input functions or distributions, their support, and assumptions governing transform existence", "Transform expressions together with their regions of convergence and singularity information", "Conditions for applying transform identities, inversion procedures, and asymptotic theorems", "Use of Laplace transforms in differential equations, convolution, and continuous-time system analysis" ], "out_of_scope": [ "Fourier, Mellin, and Z transforms as independently modelled transform families", "General complex analysis and distribution theory beyond requirements of Laplace-transform operations", "Physical systems and differential equations independently of their transform representations", "Numerical integration and symbolic algebra software as tools in their own right", "The Laplace differential operator, Laplace equation, and Laplace probability distribution" ], "distinguishing_features": [ "Its defining kernel is e^(-st), with s generally complex; it is not the spatial differential operator called the Laplacian.", "A unilateral transform integrates over a specified nonnegative-time domain, while a bilateral transform integrates over the whole real line.", "A bilateral transform is identified by both its expression and its region of convergence; the same rational expression can represent different time-domain signals.", "Its relationship to a Fourier transform requires appropriate convergence or boundary-value assumptions, rather than unconditional substitution of s = iω.", "It maps continuous-time differentiation to algebraic expressions in s under stated hypotheses, with boundary or initial terms determined by the convention." ], "characteristics": [ { "name": "Transform convention", "kind": "category", "unit_or_values": "Unilateral or bilateral; kernel sign, integration limits, and inverse normalization recorded", "why_it_matters": "Determines which input information is represented and which formulas apply." }, { "name": "Origin treatment", "kind": "category", "unit_or_values": "Ordinary-function endpoint convention; 0− or 0+ distributional convention; explicitly specified alternative", "why_it_matters": "Controls treatment of impulses and initial data at t = 0." }, { "name": "Input class and support", "kind": "category", "unit_or_values": "Ordinary function or specified distribution class; right-sided, left-sided, two-sided, or compact support", "why_it_matters": "Constrains existence, convergence, and permissible operations." }, { "name": "Transform-variable dimensions", "kind": "measurement", "unit_or_values": "s has reciprocal units of t; for time in seconds, s is measured in s^-1", "why_it_matters": "Makes the exponent dimensionless and exposes inconsistent scaling." }, { "name": "Region of convergence", "kind": "state", "unit_or_values": "Specified subset of the complex s-plane, with boundary inclusion and convergence sense; unknown or empty where applicable", "why_it_matters": "Determines where the integral represents the expression and helps disambiguate inversion." }, { "name": "Existence justification", "kind": "state", "unit_or_values": "Established under recorded assumptions; conditional; distributional; formal only; unverified; disproved", "why_it_matters": "Separates justified transforms from manipulations that have not established existence." }, { "name": "Singularity structure", "kind": "category", "unit_or_values": "Locations and orders of poles, branch points and cuts, or other identified singularities", "why_it_matters": "Informs inversion contours and time-domain interpretation." }, { "name": "Transform pair", "kind": "relation", "unit_or_values": "Input linked to expression, convention, convergence region, parameter restrictions, and derivation", "why_it_matters": "Preserves the conditions that make a tabulated or computed pair usable." }, { "name": "Inversion reliability", "kind": "state", "unit_or_values": "Analytically justified; numerically checked with stated error evidence; formal; unresolved", "why_it_matters": "Determines whether reconstructed values support subsequent decisions." } ], "affordances": [ "Construct a transform pair while recording its convention, input assumptions, and convergence region.", "Determine where a defining integral converges and distinguish that domain from analytic continuation.", "Apply linearity, shifting, differentiation, integration, or convolution identities after checking their hypotheses.", "Translate an initial-value problem into the transform domain and reconstruct a candidate solution.", "Invert a transform analytically or numerically, then verify the result against the original representation.", "Assess asymptotic or system-behaviour claims using convergence, singularity, and theorem conditions." ] }, "sources": [], "structure": { "bundles": [ { "id": "definition-and-conventions", "name": "Definition and conventions", "description": "Identifies the precise Laplace-transform operation being represented.", "rationale": "Unilateral, bilateral, and distributional conventions can produce different interpretations of otherwise similar notation.", "layers": [ { "id": "integral-definition", "name": "Integral definition", "description": "Records the kernel, integration domain, and variable interpretation.", "findings": [ { "id": "transform-variant", "name": "Transform variant", "description": "An identifiable transform specifies whether it integrates f(t)e^(-st) over nonnegative time or the whole real line.", "questions": [ { "text": "Is the defining integral unilateral or bilateral, and what exact integration limits and kernel are used?", "kind": "definition", "id": "transform-variant-q01" }, { "text": "What are the dimensions of t, s, and the transformed quantity?", "kind": "measurement", "id": "transform-variant-q02" } ] } ] }, { "id": "origin-and-generalisation", "name": "Origin and generalisation", "description": "Separates ordinary-function definitions from conventions needed for impulses and generalised inputs.", "findings": [ { "id": "endpoint-semantics", "name": "Endpoint semantics", "description": "Changing a function at a single endpoint does not change its ordinary integral, but distributional contributions at the origin require an explicit convention.", "questions": [ { "text": "Does the input contain an impulse or another distribution supported at t = 0, and how is it included?", "kind": "boundary", "id": "endpoint-semantics-q01" }, { "text": "Which reference or derivation establishes the chosen origin convention and its initial-value notation?", "kind": "provenance", "id": "endpoint-semantics-q02" } ] } ] } ] }, { "id": "existence-and-convergence", "name": "Existence and convergence", "description": "Determines whether and where the transform represents its input.", "rationale": "An algebraic expression alone does not establish that a Laplace integral exists or identifies the intended input.", "layers": [ { "id": "input-admissibility", "name": "Input admissibility", "description": "Records local behaviour, growth, and the mathematical sense of convergence.", "findings": [ { "id": "existence-conditions", "name": "Existence conditions", "description": "Existence must be assessed using input-specific hypotheses; familiar exponential-order criteria are sufficient conditions in their stated setting, not universal necessities.", "questions": [ { "text": "What local integrability, growth, or distributional assumptions justify the transform?", "kind": "boundary", "id": "existence-conditions-q01" }, { "text": "Is convergence absolute, conditional, or defined through a specified generalised framework?", "kind": "definition", "id": "existence-conditions-q02" } ] } ] }, { "id": "convergence-domain", "name": "Convergence domain", "description": "Links the expression to its valid complex domain and support interpretation.", "findings": [ { "id": "expression-with-region", "name": "Expression with region", "description": "A transform record retains its convergence region and distinguishes integral-defined values from any analytic continuation.", "questions": [ { "text": "What half-plane, strip, or other explicitly justified set is the region of convergence, including its boundary behaviour?", "kind": "measurement", "id": "expression-with-region-q01" }, { "text": "Could the same expression correspond to another bilateral input under a different convergence region?", "kind": "boundary", "id": "expression-with-region-q02" }, { "text": "Which values belong only to an analytic continuation beyond the integral's convergence region?", "kind": "boundary", "id": "expression-with-region-q03" } ] } ] } ] }, { "id": "operational-identities", "name": "Operational identities", "description": "Governs valid movement between time-domain operations and transform-domain expressions.", "rationale": "Useful symbolic rules can fail or lose information when support, boundary terms, or convergence conditions are omitted.", "layers": [ { "id": "differentiation-and-initial-data", "name": "Differentiation and initial data", "description": "Tracks the assumptions and boundary terms introduced by differentiation and integration.", "findings": [ { "id": "boundary-term-accounting", "name": "Boundary-term accounting", "description": "Derivative identities require regularity or distributional justification and boundary terms consistent with the selected transform convention.", "questions": [ { "text": "Which initial or boundary terms appear when transforming the specified derivative?", "kind": "definition", "id": "boundary-term-accounting-q01" }, { "text": "Are jumps and impulses handled consistently with the recorded input class and origin convention?", "kind": "boundary", "id": "boundary-term-accounting-q02" }, { "text": "What conditions justify integration by parts or the corresponding distributional identity?", "kind": "action", "id": "boundary-term-accounting-q03" } ] } ] }, { "id": "shifts-products-and-convolution", "name": "Shifts, products, and convolution", "description": "Records support and convergence changes caused by standard transform operations.", "findings": [ { "id": "identity-applicability", "name": "Identity applicability", "description": "Time shifts, exponential weighting, scaling, and convolution must carry their support and convergence qualifications.", "questions": [ { "text": "Does the proposed time shift require a step factor or an additional term under the unilateral convention?", "kind": "boundary", "id": "identity-applicability-q01" }, { "text": "What convergence region is justified after the operation, and can cancellations enlarge it?", "kind": "measurement", "id": "identity-applicability-q02" }, { "text": "What hypotheses permit replacing the relevant time-domain convolution by a product of transforms?", "kind": "action", "id": "identity-applicability-q03" } ] } ] } ] }, { "id": "inversion-and-verification", "name": "Inversion and verification", "description": "Supports recovery of the input and assessment of the recovered result.", "rationale": "Inversion depends on the function class, convergence region, analytic structure, and numerical reliability.", "layers": [ { "id": "analytic-reconstruction", "name": "Analytic reconstruction", "description": "Specifies uniqueness conditions and an appropriate analytic inversion method.", "findings": [ { "id": "inverse-identification", "name": "Inverse identification", "description": "An inverse is interpreted within a stated function or distribution class, including the equivalence and discontinuity conventions supplied by the inversion theorem.", "questions": [ { "text": "Under what hypotheses is the inverse unique, and is equality pointwise, almost everywhere, or distributional?", "kind": "boundary", "id": "inverse-identification-q01" }, { "text": "If using a Bromwich integral, where may the vertical contour lie relative to the convergence region and singularities?", "kind": "action", "id": "inverse-identification-q02" }, { "text": "How are branch cuts or discontinuity values treated by the chosen inversion method?", "kind": "definition", "id": "inverse-identification-q03" } ] } ] }, { "id": "numerical-reconstruction", "name": "Numerical reconstruction", "description": "Assesses finite-precision inversion and independent checks.", "findings": [ { "id": "reconstruction-confidence", "name": "Reconstruction confidence", "description": "Numerical inversion records the method, evaluation range, sensitivity, and evidence supporting accuracy.", "questions": [ { "text": "How sensitive is the inverse to transform-evaluation error, working precision, and algorithm parameters over the requested time range?", "kind": "measurement", "id": "reconstruction-confidence-q01" }, { "text": "Does forward transformation, a known transform pair, or an independent governing-equation check corroborate the reconstruction?", "kind": "action", "id": "reconstruction-confidence-q02" } ] } ] } ] }, { "id": "application-and-interpretation", "name": "Application and interpretation", "description": "Connects transform calculations to equations, systems, and asymptotic claims.", "rationale": "Successful algebra does not by itself justify a physical interpretation, stability conclusion, or limiting value.", "layers": [ { "id": "equations-and-system-representations", "name": "Equations and system representations", "description": "Distinguishes transformed solutions from system properties and preserves initial conditions.", "findings": [ { "id": "representation-role", "name": "Representation role", "description": "A transformed trajectory, forcing term, impulse response, and transfer function have different roles; transfer-function interpretations require explicit system assumptions.", "questions": [ { "text": "Does the expression represent a particular solution, an input, an impulse response, or a transfer function under zero initial conditions?", "kind": "definition", "id": "representation-role-q01" }, { "text": "Which initial conditions and system assumptions are needed to recover a solution to the original problem?", "kind": "action", "id": "representation-role-q02" }, { "text": "What support and convergence evidence justifies any claimed causality or stability property?", "kind": "boundary", "id": "representation-role-q03" } ] } ] }, { "id": "limits-and-frequency-boundaries", "name": "Limits and frequency boundaries", "description": "Checks conditions for extracting initial values, final values, or frequency-domain information.", "findings": [ { "id": "theorem-qualified-interpretation", "name": "Theorem-qualified interpretation", "description": "Initial-value, final-value, and Fourier-boundary interpretations require their own hypotheses and cannot be inferred from substitution alone.", "questions": [ { "text": "Which precise initial-value or final-value theorem applies, and are its regularity, limit, or pole conditions satisfied?", "kind": "boundary", "id": "theorem-qualified-interpretation-q01" }, { "text": "Does the imaginary axis support an ordinary Fourier integral, or is a separately justified boundary-value interpretation required?", "kind": "boundary", "id": "theorem-qualified-interpretation-q02" }, { "text": "What additional analysis is required if a formal transform-domain limit exists but the relevant theorem's hypotheses fail?", "kind": "action", "id": "theorem-qualified-interpretation-q03" } ] } ] } ] }, { "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 mathematical integral transform; no narrower registry sense was supplied.", "Unilateral versus bilateral integration and treatment of the origin are consequential conventions, rather than competing definitions of an unsettled concept.", "These statements are recalled knowledge, not source-verified findings; no dedicated identifier or governing standard is asserted." ], "questions": [ { "id": "evidence-confidence-notes-q01", "text": "Which of these check these first hold for the sense of Laplace transform 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": [ "Unilateral (one-sided) Laplace transform", "Bilateral (two-sided) Laplace transform", "Laplace-Stieltjes transform", "Distributional Laplace transform" ], "questions": [ { "id": "evidence-kinds-q01", "text": "Which of these kinds and varieties hold for the sense of Laplace transform 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": [ "Solving linear ordinary differential equations with initial conditions.", "Representing continuous-time linear time-invariant systems through transfer functions.", "Analyzing electrical circuits and their transient responses.", "Studying distributions of nonnegative random variables and sums of independent random variables.", "Solving some partial differential equations by transforming one independent variable." ], "questions": [ { "id": "evidence-real-world-use-q01", "text": "Which of these real-world use hold for the sense of Laplace transform 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": "Complex transform variable s", "typical_range": "Complex values within a region of convergence; no universal numerical range.", "unit": "Reciprocal of the unit of t; s^-1 when t is measured in seconds." } ], "questions": [ { "id": "evidence-measurements-q01", "text": "Which of these typical measurements hold for the sense of Laplace transform 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": [ "Ignoring the region of convergence can make inversion ambiguous: the same bilateral transform expression can represent different functions with different convergence regions.", "Confusing unilateral and bilateral conventions can produce incorrect treatment of negative-time behavior and initial conditions.", "Mishandling impulses at the integration boundary can change results; the convention at t = 0 must be specified.", "Applying transform identities without their convergence or regularity conditions can yield invalid conclusions.", "Numerical inverse Laplace transformation can be ill-conditioned and sensitive to roundoff, noise, and algorithm choice." ], "questions": [ { "id": "evidence-failure-modes-and-hazards-q01", "text": "Which of these failure modes and hazards hold for the sense of Laplace transform 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": "Fourier transform", "difference": "Uses an oscillatory kernel with a real frequency variable; identification with the Laplace transform on the imaginary axis requires appropriate convergence or a justified boundary-value interpretation." }, { "name": "Z-transform", "difference": "Transforms discrete sequences using a sum, whereas the ordinary Laplace transform integrates a continuous-variable function." }, { "name": "Mellin transform", "difference": "Uses a power kernel t^(s-1) on positive arguments rather than the exponential kernel exp(-st)." }, { "name": "Transfer function", "difference": "Describes a system's input-output relation, typically in the Laplace domain under zero initial conditions; it is not the transform operation itself." } ], "questions": [ { "id": "evidence-neighbours-q01", "text": "Which of these neighbouring kinds and how to tell them apart hold for the sense of Laplace transform this model covers, and on what evidence?", "kind": "provenance" } ] } ] } ] } ] }, "openQuestions": [ "Which authoritative mathematical, engineering, and distribution-theoretic references should anchor the model's convention-specific definitions and theorem statements?", "Should unilateral and bilateral variants receive equal default prominence, or should intended registry use determine a preferred presentation?", "How far should the model extend into distributional Laplace transforms and analytic boundary values without duplicating neighbouring mathematical models?", "What evidence and error criteria should qualify numerical inversion as reliable for different application classes?" ], "statistics": { "bundles": 6, "layers": 11, "findings": 16, "questions": 32 } }, "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 Laplace transform, record what state it is in, and decide what may be done with it.", "whatItIs": "Enable an agent to recognise a Laplace-transform representation, assess its mathematical validity, and choose justified transformation, inversion, or application steps.", "characteristics": { "substance": "abstract", "origin": "conceptual", "agency": "inert" }, "whatYouCanDoWithIt": [ "observed and measured" ], "distinguishingFeatures": [ "Described in 69 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 Laplace transform, 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": [], "standing": "Described in 69 Wikipedia languages, which measures how widely it is written about rather than how important or how common it is.", "structure": { "bundles": [ { "id": "identity-and-classification", "name": "Identity, naming and classification", "description": "How an agent tells one Laplace transform from another, and a Laplace transform 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 Laplace transform, 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 Laplace transform, 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 Laplace transform 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 Laplace transform, 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 Laplace transform, 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 Laplace transform 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 Laplace transform 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 Laplace transform, 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 Laplace transform, 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 Laplace transform 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 Laplace transform from the things most often confused with it.", "questions": [ { "id": "distinguishing-features-q01", "text": "What identifies and describes what distinguishes a Laplace transform, 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 Laplace transform, 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 Laplace transform 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 Laplace transform 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 Laplace transform between them.", "questions": [ { "id": "stages-and-transitions-q01", "text": "What identifies and describes the lifecycle of a Laplace transform, 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 Laplace transform, 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 Laplace transform 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 Laplace transform, how often and by whom.", "findings": [ { "id": "observation-record", "name": "Observation record", "description": "How an observation of a Laplace transform 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 Laplace transform, 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 Laplace transform, 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 Laplace transform 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 Laplace transform 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 Laplace transform 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 Laplace transform 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 Laplace transform 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 Laplace transform?", "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 Laplace transform?", "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 Laplace transform 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 Laplace transform and how confident it is.", "questions": [ { "id": "claim-provenance-q01", "text": "What identifies and describes a claim about a Laplace transform, 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 Laplace transform, 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 Laplace transform 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 Laplace transform is retired without being erased.", "questions": [ { "id": "validity-and-supersession-q01", "text": "What identifies and describes the validity of a claim about a Laplace transform, 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 Laplace transform, 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 Laplace transform 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 } } } }