{ "model": { "rank": 5719, "code": "thing-q204034", "model_id": "vr.tr.hyperbolic-function", "name": "hyperbolic function", "purpose": "Enable an AI agent to recognise a hyperbolic function, assess its mathematical and computational validity, and choose justified transformations, evaluations or applications.", "family": "Thing Registry", "category": "Cross-cutting context", "status": "research-draft", "kind": "thing", "plane": "XCT", "domain": "XCT.QLT", "industry": "", "version": "", "url": "/models/thing/q204034/", "tier": 2, "score": 65, "payload": { "layer": "wikidata", "aliases": [ "hyperbolic secant and hyperbolic cosecant", "hyperbolic sine and hyperbolic cosine", "hyperbolic tangent and hyperbolic cotangent" ], "aliasCount": 3, "merged": 3, "knownIn": 65, "facets": null, "markers": [], "lexicalClass": "", "senseRank": null, "alsoRegisteredAs": null, "source": { "dataset": "wikidata", "item": "Q204034", "url": "https://www.wikidata.org/wiki/Q204034", "license": "CC0 1.0" } }, "research": { "vercy": "1.0-draft", "publication": { "status": "research-draft", "adjudicationStatus": "unreviewed", "publishableCanonical": false, "generatedAt": "2026-09-07T09:06:46Z", "providers": [ "Codex" ], "missingProviders": [ "Grok" ], "pass": 2, "cost": { "grok": { "usd": null, "turns": null, "seconds": 9.7, "error": "Error: Internal error: {\n \"message\": \"API error (status 402 Payment Required): Grok Build usage balance exhausted\",\n \"http_status\": 402\n}", "retried": true }, "codex": { "seconds": 79.4, "error": "Reading additional input from stdin...\nOpenAI Codex v0.153.3\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: 01a07b1d-87a8-71c0-9358-54fb42653724\n--------\nuser\nYou are drafting a Vercy meta-model for one registered thing. Answer as JSON only, no prose around it.\n\nThing: hyperbolic function\nRegistry id: vr.tr.hyperbolic-function\nPlane / domain: XCT / XCT.REL\nRegistry definition: (none recorded)\nNames folded into this " } } }, "metaModel": { "id": "THING-Q204034", "registryId": "vr.tr.hyperbolic-function", "name": "hyperbolic function", "version": "0.1.0-research.1", "entryKind": "thing", "family": "Thing Registry", "domain": [ "XCT.REL" ], "status": "research-draft" }, "canonicalUrl": "https://ver.cy/models/thing/q204034/", "model": { "registry_id": "vr.tr.hyperbolic-function", "name": "hyperbolic function", "purpose": "Enable an AI agent to recognise a hyperbolic function, assess its mathematical and computational validity, and choose justified transformations, evaluations or applications.", "definition": "", "scope_statement": "This model owns the identity, argument conventions, domain, analytic behaviour, defining relations and permitted operations of a registered hyperbolic function, while recording inverse functions and application models as related objects.", "in_scope": [ "Identification of sinh, cosh, tanh, coth, sech and csch, including explicitly parameterised forms", "Real or complex argument domains, excluded points and output ranges", "Exponential definitions, hyperbolic identities and relationships among family members", "Zeros, poles, parity, periodicity, asymptotes and real monotonicity", "Conditions for differentiation, integration, inversion and stable numerical evaluation" ], "out_of_scope": [ "Circular trigonometric functions as independently modelled functions", "Inverse hyperbolic functions as independently modelled functions with their own branch conventions", "Hyperbolas and other conic sections as geometric objects", "Hyperbolic geometry, manifolds and curvature", "Physical systems or differential equations that use hyperbolic functions", "Software libraries and numerical algorithms as independently maintained implementations" ], "distinguishing_features": [ "A canonical member can be expressed using sinh(z) = (exp(z) - exp(-z))/2 and cosh(z) = (exp(z) + exp(-z))/2, or their specified quotients and reciprocals.", "The foundational identity is cosh(z)^2 - sinh(z)^2 = 1; confusing it with the circular identity changes the sign and invalidates deductions.", "Canonical hyperbolic functions have no nonzero real period; their complex extensions have imaginary periods, unlike the real periods of circular trigonometric functions.", "An inverse hyperbolic function solves for an argument of a hyperbolic function and requires inverse-domain or branch information; it is not a reciprocal family member.", "For real t, the pair (cosh(t), sinh(t)) lies on the right branch of the unit hyperbola; this interpretation applies to the pair and does not identify every hyperbolic function with a hyperbola." ], "characteristics": [ { "name": "Canonical family member", "kind": "category", "unit_or_values": "sinh | cosh | tanh | coth | sech | csch", "why_it_matters": "Determines the defining expression, singularities and applicable identities." }, { "name": "Argument setting", "kind": "category", "unit_or_values": "real scalar | complex scalar; other settings require an explicit extension", "why_it_matters": "Controls whether ordering, monotonicity, poles and imaginary periodicity are relevant." }, { "name": "Argument normalisation", "kind": "relation", "unit_or_values": "argument expression, parameter meanings and dimensionless normalisation", "why_it_matters": "Prevents treating hyperbolic arguments as degree-valued angles or applying identities to mismatched inputs." }, { "name": "Domain restrictions", "kind": "relation", "unit_or_values": "admissible set with excluded points and parameter-dependent restrictions", "why_it_matters": "Separates valid operations from evaluation at poles or outside a selected restriction." }, { "name": "Real output range", "kind": "relation", "unit_or_values": "subset of the real numbers for a stated real domain", "why_it_matters": "Supports equation feasibility checks and inverse selection." }, { "name": "Parity", "kind": "category", "unit_or_values": "even | odd | neither on the stated domain", "why_it_matters": "Supports symmetry checks and reductions while accounting for shifts or restrictions." }, { "name": "Singularity structure", "kind": "relation", "unit_or_values": "locations and orders of poles; entire when applicable", "why_it_matters": "Constrains continuation, simplification and numerical evaluation." }, { "name": "Injectivity on selected domain", "kind": "state", "unit_or_values": "injective | non-injective | not established", "why_it_matters": "Determines whether a single-valued inverse can be used without further restriction." }, { "name": "Evaluation error", "kind": "measurement", "unit_or_values": "absolute or relative error bound, with precision and argument region stated", "why_it_matters": "Determines whether a computed value is adequate for the intended decision." } ], "affordances": [ "Classify a function expression as a canonical hyperbolic member or a parameterised form.", "Evaluate values and limits using formulas appropriate to the argument magnitude and proximity to poles.", "Rewrite exponential and hyperbolic expressions while preserving domains and parameter assumptions.", "Differentiate or integrate expressions with the required chain factors and domain conditions.", "Solve equations or select an inverse after checking ranges, injectivity and complex branches.", "Check whether a proposed hyperbola parameterisation or differential-equation solution satisfies its defining conditions." ] }, "sources": [], "structure": { "bundles": [ { "id": "family-identity", "name": "Family identity", "description": "Establishes which hyperbolic function is represented and how its argument is formed.", "rationale": "Names and notation alone cannot distinguish reciprocals, inverses and transformed functions.", "layers": [ { "id": "canonical-definition", "name": "Canonical definition", "description": "Connects the named function to its exponential or quotient definition.", "findings": [ { "id": "member-identification", "name": "Member identification", "description": "Record the canonical family member and a defining expression that can be checked.", "questions": [ { "text": "Which of sinh, cosh, tanh, coth, sech or csch is represented, and what defining expression establishes that identity?", "kind": "definition", "id": "member-identification-q01" }, { "text": "Does any notation such as sinh^-1 mean a reciprocal, an inverse function or a power in this source?", "kind": "boundary", "id": "member-identification-q02" } ] } ] }, { "id": "argument-and-transformation", "name": "Argument and transformation", "description": "Separates the canonical function from scaling, translation and composition.", "findings": [ { "id": "normalised-argument", "name": "Normalised argument", "description": "Record the actual argument and external transformations before transferring canonical properties.", "questions": [ { "text": "For an expression such as A sinh(bx + c) + d, which symbols are variables and which are fixed parameters?", "kind": "definition", "id": "normalised-argument-q01" }, { "text": "If the input represents a physical quantity, what scale makes the exponential argument dimensionless?", "kind": "boundary", "id": "normalised-argument-q02" } ] } ] } ] }, { "id": "domain-and-singularities", "name": "Domain and singularities", "description": "Defines where the function exists and which outputs or inverses are admissible.", "rationale": "Quotient family members have excluded points, and real restrictions differ from complex analytic domains.", "layers": [ { "id": "admissible-inputs", "name": "Admissible inputs", "description": "Records the argument setting and exclusions induced by denominators or imposed restrictions.", "findings": [ { "id": "domain-and-poles", "name": "Domain and poles", "description": "Distinguish entire members from meromorphic members and identify restrictions on the represented expression.", "questions": [ { "text": "Is the function considered over the reals or complexes, and what additional domain restriction is imposed?", "kind": "boundary", "id": "domain-and-poles-q01" }, { "text": "Which zeros of sinh or cosh produce denominator zeros here, and are they poles or removable singularities of the full expression?", "kind": "definition", "id": "domain-and-poles-q02" } ] } ] }, { "id": "range-and-inversion", "name": "Range and inversion", "description": "Records attainable values and the restrictions needed to recover an argument.", "findings": [ { "id": "inverse-admissibility", "name": "Inverse admissibility", "description": "Make range and injectivity checks explicit before invoking an inverse hyperbolic function.", "questions": [ { "text": "What is the output range on the selected real domain, including whether limiting endpoints are attained?", "kind": "boundary", "id": "inverse-admissibility-q01" }, { "text": "What domain restriction or linked complex inverse branch makes solving for the argument single-valued?", "kind": "action", "id": "inverse-admissibility-q02" } ] } ] } ] }, { "id": "qualitative-behaviour", "name": "Qualitative behaviour", "description": "Captures symmetry, growth and local behaviour needed to recognise or assess the function.", "rationale": "These properties expose wrong family assignments and determine feasible bounds or solution intervals.", "layers": [ { "id": "real-behaviour", "name": "Real behaviour", "description": "Describes signs, extrema and trends on connected portions of the real domain.", "findings": [ { "id": "real-shape", "name": "Real shape", "description": "Record parity, zeros, monotonic intervals and asymptotic behaviour for the actual function form.", "questions": [ { "text": "What parity, real zeros, sign intervals and extrema hold after accounting for argument and output transformations?", "kind": "definition", "id": "real-shape-q01" }, { "text": "On each connected real-domain interval, where is the function increasing or decreasing, and what limits hold at its boundaries?", "kind": "boundary", "id": "real-shape-q02" } ] } ] }, { "id": "complex-behaviour", "name": "Complex behaviour", "description": "Describes imaginary periodicity and analytic features unavailable from a real graph.", "findings": [ { "id": "imaginary-periods-and-zeros", "name": "Imaginary periods and zeros", "description": "Record the complex zeros, periods and pole patterns relevant to continuation and equation solving.", "questions": [ { "text": "What imaginary periods or sign-changing imaginary shifts does this member have, and how does argument scaling alter them?", "kind": "definition", "id": "imaginary-periods-and-zeros-q01" }, { "text": "Which complex zeros and poles must be included when enumerating solutions or choosing a region of analysis?", "kind": "boundary", "id": "imaginary-periods-and-zeros-q02" } ] } ] } ] }, { "id": "identities-and-calculus", "name": "Identities and calculus", "description": "Specifies transformations and calculus operations that preserve mathematical meaning.", "rationale": "Hyperbolic identities have characteristic signs and domain conditions that are easily confused with circular analogues.", "layers": [ { "id": "algebraic-relations", "name": "Algebraic relations", "description": "Connects members through reciprocal, quotient, addition and exponential identities.", "findings": [ { "id": "domain-preserving-rewrites", "name": "Domain-preserving rewrites", "description": "Record applicable identities together with denominator exclusions and any continuation introduced by a rewrite.", "questions": [ { "text": "Which reciprocal, quotient, addition or double-argument identities justify the proposed rewrite?", "kind": "action", "id": "domain-preserving-rewrites-q01" }, { "text": "Does cancellation or conversion to exponentials change the apparent domain, requiring excluded inputs to remain recorded?", "kind": "boundary", "id": "domain-preserving-rewrites-q02" } ] } ] }, { "id": "differential-relations", "name": "Differential relations", "description": "Captures derivative, antiderivative and differential-equation relationships.", "findings": [ { "id": "calculus-preconditions", "name": "Calculus preconditions", "description": "Record derivative rules, chain factors and conditions on primitives or differential-equation claims.", "questions": [ { "text": "What derivative follows for the complete expression, including argument scaling and composition?", "kind": "action", "id": "calculus-preconditions-q01" }, { "text": "If an antiderivative uses a logarithm, what real interval or complex branch conditions make the expression valid?", "kind": "boundary", "id": "calculus-preconditions-q02" }, { "text": "If the function is used in a solution of y'' = y or a scaled variant, which coefficients and initial conditions establish the claimed solution?", "kind": "definition", "id": "calculus-preconditions-q03" } ] } ] } ] }, { "id": "evaluation-and-use", "name": "Evaluation and use", "description": "Connects mathematical properties to reliable computation and justified interpretation.", "rationale": "Correct symbolic definitions can still yield unreliable numerical values or unsupported application claims.", "layers": [ { "id": "numerical-evaluation", "name": "Numerical evaluation", "description": "Records accuracy needs and argument-dependent computational hazards.", "findings": [ { "id": "stable-value-computation", "name": "Stable value computation", "description": "Assess cancellation near zero, exponential overflow at large arguments and sensitivity near poles.", "questions": [ { "text": "What argument region and absolute or relative error tolerance must the computed values support?", "kind": "measurement", "id": "stable-value-computation-q01" }, { "text": "Does direct exponential evaluation risk cancellation, overflow or an indeterminate quotient, and which equivalent formula or series avoids it?", "kind": "action", "id": "stable-value-computation-q02" }, { "text": "Near a zero or pole, how does uncertainty in the argument affect the usefulness of the reported value?", "kind": "measurement", "id": "stable-value-computation-q03" } ] } ] }, { "id": "interpretation-and-checks", "name": "Interpretation and checks", "description": "Records the specific role played by the function and checks that can validate that role.", "findings": [ { "id": "application-contract", "name": "Application contract", "description": "Link the function to its application without treating mathematical availability as evidence of physical adequacy.", "questions": [ { "text": "Is the function being used as a hyperbola coordinate, a differential-equation solution, a bounded response or another explicitly stated construction?", "kind": "definition", "id": "application-contract-q01" }, { "text": "Which identity, boundary condition or independently computed value can check the proposed use?", "kind": "action", "id": "application-contract-q02" }, { "text": "Which source establishes the interpretation and normalisation of the argument in the linked application?", "kind": "provenance", "id": "application-contract-q03" } ] } ] } ] } ] }, "openQuestions": [ "Does this registry entry intend the six canonical direct functions only, or also inverse hyperbolic functions under one family-level model?", "Which authoritative references will support the definitions, complex pole patterns, identities and numerical evaluation guidance in a researched publication?", "Should matrix and operator hyperbolic functions be represented as extensions here or linked to separate functional-calculus models?", "What level of parameterised composition remains an instance of this model before ownership passes to a general function or expression model?", "Which numerical precision regimes and application contexts must a completed model support?" ], "statistics": { "bundles": 5, "layers": 10, "findings": 10, "questions": 23 } }, "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 hyperbolic function, record what state it is in, and decide what may be done with it.", "whatItIs": "Enable an AI agent to recognise a hyperbolic function, assess its mathematical and computational validity, and choose justified transformations, evaluations or applications.", "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: hyperbolic secant and hyperbolic cosecant, hyperbolic sine and hyperbolic cosine, hyperbolic tangent and hyperbolic cotangent.", "3 finer distinctions are held as aliases rather than separate entries, because telling them apart needs a task that asks for it.", "Described in 65 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 hyperbolic function, 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": [ "hyperbolic secant and hyperbolic cosecant", "hyperbolic sine and hyperbolic cosine", "hyperbolic tangent and hyperbolic cotangent" ] } ], "standing": "Described in 65 Wikipedia languages, which measures how widely it is written about rather than how important or how common it is. 3 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 hyperbolic function from another, and a hyperbolic function 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 hyperbolic function, 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 hyperbolic function, 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 hyperbolic function 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 hyperbolic function, 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 hyperbolic function, 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 hyperbolic function 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 hyperbolic function 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 hyperbolic function, 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 hyperbolic function, 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 hyperbolic function 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 hyperbolic function from the things most often confused with it.", "questions": [ { "id": "distinguishing-features-q01", "text": "What identifies and describes what distinguishes a hyperbolic function, 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 hyperbolic function, 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 hyperbolic function 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 hyperbolic function 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 hyperbolic function between them.", "questions": [ { "id": "stages-and-transitions-q01", "text": "What identifies and describes the lifecycle of a hyperbolic function, 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 hyperbolic function, 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 hyperbolic function 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 hyperbolic function, how often and by whom.", "findings": [ { "id": "observation-record", "name": "Observation record", "description": "How an observation of a hyperbolic function 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 hyperbolic function, 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 hyperbolic function, 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 hyperbolic function 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 hyperbolic function 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 hyperbolic function 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 hyperbolic function 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 hyperbolic function 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 hyperbolic function?", "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 hyperbolic function?", "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 hyperbolic function 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 hyperbolic function and how confident it is.", "questions": [ { "id": "claim-provenance-q01", "text": "What identifies and describes a claim about a hyperbolic function, 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 hyperbolic function, 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 hyperbolic function 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 hyperbolic function is retired without being erased.", "questions": [ { "id": "validity-and-supersession-q01", "text": "What identifies and describes the validity of a claim about a hyperbolic function, 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 hyperbolic function, 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 hyperbolic function 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 } } } }