{ "model": { "rank": 5291, "code": "thing-q173523", "model_id": "vr.tr.geometric-progression", "name": "geometric progression", "purpose": "Enable an agent to recognise a geometric progression, establish its parameters and conventions, assess its behaviour, and perform justified calculations or applications.", "family": "Thing Registry", "category": "Cross-cutting context", "status": "research-draft", "kind": "thing", "plane": "XCT", "domain": "XCT.QLT", "industry": "", "version": "", "url": "/models/thing/q173523/", "tier": 2, "score": 68, "payload": { "layer": "wikidata", "aliases": [ "convergent infinite geometric sequence", "infinite descending geometric progression", "power sequence" ], "aliasCount": 3, "merged": 3, "knownIn": 68, "facets": null, "markers": [], "lexicalClass": "", "senseRank": null, "alsoRegisteredAs": null, "source": { "dataset": "wikidata", "item": "Q173523", "url": "https://www.wikidata.org/wiki/Q173523", "license": "CC0 1.0" } }, "research": { "vercy": "1.0-draft", "publication": { "status": "research-draft", "adjudicationStatus": "unreviewed", "publishableCanonical": false, "generatedAt": "2026-09-09T22:04:18Z", "providers": [ "Codex" ], "breadth": "recalled by Codex without web access - no source was read", "missingProviders": [], "pass": 2, "cost": { "grok": { "seconds": 18.2, "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: 01a08832-4c48-7180-aebf-f026a66da304\n--------\nuser\nDescribe what is already known about one registered thing. Answer as JSON only, no prose around it.\n\nThing: geometric progression\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", "usd": 0, "recall": true }, "codex": { "seconds": 66, "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: 01a08832-4c43-7d00-a98d-f728cf4defd0\n--------\nuser\nYou are drafting a Vercy meta-model for one registered thing. Answer as JSON only, no prose around it.\n\nThing: geometric progression\nRegistry id: vr.tr.geometric-progression\nPlane / domain: XCT / XCT.REL\nRegistry definition: (none recorded)\nNames folded into t" } } }, "metaModel": { "id": "THING-Q173523", "registryId": "vr.tr.geometric-progression", "name": "geometric progression", "version": "0.1.0-research.1", "entryKind": "thing", "family": "Thing Registry", "domain": [ "XCT.REL" ], "status": "research-draft" }, "canonicalUrl": "https://ver.cy/models/thing/q173523/", "model": { "registry_id": "vr.tr.geometric-progression", "name": "geometric progression", "purpose": "Enable an agent to recognise a geometric progression, establish its parameters and conventions, assess its behaviour, and perform justified calculations or applications.", "definition": "A geometric progression is a finite or infinite sequence whose successive terms satisfy a_{n+1} = r a_n for a fixed common ratio r, so that a_n = a_1 r^{n-1} for n ≥ 1, with the first term specified separately when r = 0.", "scope_statement": "This model owns geometric progression as an indexed numerical sequence generated by repeated multiplication by a fixed common ratio, including finite and infinite cases, parameter identification, behaviour, and associated sum calculations.", "in_scope": [ "The recurrence a_(n+1) = r a_n and its relationship to a constant quotient of consecutive terms", "Initial term, common ratio, index origin, numerical domain, and finite or infinite extent", "Exact recognition, parameter recovery, and assessment of approximately geometric observations", "Sign patterns, magnitude changes, term limits, and exceptional zero cases", "Finite sums and conditions for convergence of the associated infinite series", "Interpretation as a discrete constant-factor model with explicit assumptions" ], "out_of_scope": [ "Arithmetic progressions governed by a constant additive difference", "General recurrences with varying multipliers or additive forcing", "Continuous exponential functions except where sampled to produce a progression", "Geometric probability distributions and their statistical interpretation", "General series theory beyond sums associated with a geometric progression", "Domain-specific mechanisms of interest, population change, depreciation, or physical attenuation" ], "distinguishing_features": [ "A single multiplier r must satisfy every defined adjacent transition; visually exponential growth alone is insufficient.", "Constant consecutive quotients identify the multiplier only where the preceding term is nonzero; the recurrence can remain meaningful when quotient tests fail.", "Under zero-based indexing, terms satisfy a_n = a_0 r^n for n ≥ 1, with a_0 specified separately to avoid ambiguity when r = 0.", "A constant additive difference identifies an arithmetic progression; constant sequences can satisfy both definitions.", "The progression is the sequence of terms, whereas its associated geometric series is a sum of those terms and has separate convergence conditions." ], "characteristics": [ { "name": "Initial term", "kind": "measurement", "unit_or_values": "Real or complex value a_0; carries the units of the represented quantity when applicable", "why_it_matters": "Sets the scale and determines whether the sequence is identically zero." }, { "name": "Common ratio", "kind": "measurement", "unit_or_values": "Fixed real or complex multiplier r; dimensionless for terms representing the same quantity", "why_it_matters": "Determines multiplicative change, sign or phase behaviour, and convergence." }, { "name": "Indexing and extent", "kind": "category", "unit_or_values": "Index origin; consecutive index set; positive integer term count N or infinite extent", "why_it_matters": "Prevents off-by-one errors and distinguishes finite calculations from limit questions." }, { "name": "Numerical and zero conventions", "kind": "category", "unit_or_values": "Real or complex terms; recurrence or quotient definition; inclusion or exclusion of zero terms and zero ratio", "why_it_matters": "Makes recognition consistent in degenerate cases where common definitions can differ." }, { "name": "Geometric fit status", "kind": "state", "unit_or_values": "Exact, approximate under a specified tolerance, contradicted, or insufficient evidence", "why_it_matters": "Separates a proved sequence rule from a model inferred from limited observations." }, { "name": "Parameter identifiability", "kind": "state", "unit_or_values": "Unique, multiple compatible values, inconsistent, or undetermined", "why_it_matters": "Prevents an agent from reporting a unique ratio when zeros, missing terms, or sparse sampling leave ambiguity." }, { "name": "Magnitude and sign or phase pattern", "kind": "state", "unit_or_values": "Magnitude decreasing, constant, or increasing; fixed sign, alternating sign, complex phase evolution, or zero", "why_it_matters": "Supports correct behavioural descriptions without confusing magnitude growth with numerical monotonicity." }, { "name": "Term and series convergence", "kind": "state", "unit_or_values": "Recorded separately: convergent with limit or sum, divergent, or not applicable to finite extent", "why_it_matters": "A convergent sequence does not necessarily have a convergent associated series." }, { "name": "Index-to-application mapping", "kind": "relation", "unit_or_values": "One index step corresponds to a declared period, distance increment, iteration, or other repeatable step", "why_it_matters": "Connects the multiplier to the actual spacing and conditions of an application." } ], "affordances": [ "Test whether specified terms satisfy a fixed multiplicative recurrence and identify the transitions that fail.", "Recover compatible initial terms and ratios while reporting ambiguity or inconsistency.", "Generate terms, fill justified gaps, and solve threshold questions within a declared index range.", "Classify magnitude, sign or phase behaviour, and sequence limits.", "Calculate finite sums and justified infinite sums or truncation bounds.", "Fit and assess a constant-factor approximation, then restrict extrapolation to its supported assumptions." ] }, "sources": [], "structure": { "bundles": [ { "id": "definition-and-sequence-boundary", "name": "Definition and sequence boundary", "description": "Establishes exactly which sequence and definition the agent is using.", "rationale": "Zero cases, indexing, and confusion between a sequence and a sum can change whether an operation is valid.", "layers": [ { "id": "multiplicative-membership", "name": "Multiplicative membership", "description": "Tests membership through a fixed multiplier while exposing definition-dependent cases.", "findings": [ { "id": "fixed-ratio-recurrence", "name": "Fixed-ratio recurrence", "description": "The recurrence a_(n+1) = r a_n gives a direct membership test; quotient-based recognition additionally requires nonzero denominators.", "questions": [ { "text": "Does one fixed value of r satisfy every adjacent transition in the stated sequence?", "kind": "definition", "id": "fixed-ratio-recurrence-q01" }, { "text": "Does the adopted definition admit r = 0 and the all-zero sequence, and which reference establishes that convention?", "kind": "boundary", "id": "fixed-ratio-recurrence-q02" } ] } ] }, { "id": "index-domain-and-extent", "name": "Index domain and extent", "description": "Records the first index, available transitions, and finite or infinite interpretation.", "findings": [ { "id": "declared-sequence-object", "name": "Declared sequence object", "description": "An ordered sequence with a declared index set must be distinguished from an unordered collection, a sampled subsequence, and an associated sum.", "questions": [ { "text": "What is the first index, how many terms are included, and are supplied terms consecutive?", "kind": "definition", "id": "declared-sequence-object-q01" }, { "text": "Is the object being assessed the progression itself, a finite sum, or an infinite series?", "kind": "boundary", "id": "declared-sequence-object-q02" } ] } ] } ] }, { "id": "parameter-recovery-and-evidence", "name": "Parameter recovery and evidence", "description": "Determines which parameters the available terms actually support.", "rationale": "Sparse terms and zeros can leave several compatible ratios, while noisy measurements require a different standard from exact identities.", "layers": [ { "id": "exact-parameter-identification", "name": "Exact parameter identification", "description": "Recovers parameters from indexed values without assuming uniqueness.", "findings": [ { "id": "ratio-identifiability", "name": "Ratio identifiability", "description": "A nonzero term followed by its successor fixes r; separated nonzero terms instead constrain a power of r and can leave root ambiguities.", "questions": [ { "text": "Which observed adjacent pair with a nonzero first term fixes the candidate ratio?", "kind": "measurement", "id": "ratio-identifiability-q01" }, { "text": "If only terms k steps apart are known, which solutions of r^k = a_(n+k)/a_n are permitted by the numerical domain?", "kind": "measurement", "id": "ratio-identifiability-q02" }, { "text": "Do all remaining terms support those candidates, including transitions into or out of zero?", "kind": "boundary", "id": "ratio-identifiability-q03" } ] } ] }, { "id": "observational-support", "name": "Observational support", "description": "Separates a stipulated or proved rule from a fitted pattern.", "findings": [ { "id": "exact-versus-approximate-geometricity", "name": "Exact versus approximate geometricity", "description": "A finite observed prefix can support a geometric fit but does not establish that unobserved terms follow the same rule.", "questions": [ { "text": "Is the fixed multiplier supplied by a definition, derived from a mechanism, or estimated from observations?", "kind": "provenance", "id": "exact-versus-approximate-geometricity-q01" }, { "text": "What measurement error, rounding rule, and residual tolerance justify calling the observations approximately geometric?", "kind": "measurement", "id": "exact-versus-approximate-geometricity-q02" }, { "text": "What evidence supports extending the fitted rule beyond the observed indices?", "kind": "action", "id": "exact-versus-approximate-geometricity-q03" } ] } ] } ] }, { "id": "term-behaviour-and-limits", "name": "Term behaviour and limits", "description": "Characterises individual terms across the admissible range of ratios.", "rationale": "Positive growth, alternating signs, complex phase changes, and degenerate constants require different interpretations.", "layers": [ { "id": "magnitude-sign-and-phase", "name": "Magnitude, sign, and phase", "description": "Separates magnitude change from order and direction.", "findings": [ { "id": "ratio-regimes", "name": "Ratio regimes", "description": "For nonzero terms, |r| governs magnitude change; negative real r alternates signs, while complex r also changes phase.", "questions": [ { "text": "Is |r| below, equal to, or above one, and is the initial term zero?", "kind": "measurement", "id": "ratio-regimes-q01" }, { "text": "For real terms, how do the signs of a_0 and r affect sign alternation and monotonicity?", "kind": "measurement", "id": "ratio-regimes-q02" }, { "text": "For complex terms, what phase increment replaces a real-valued increasing or decreasing description?", "kind": "boundary", "id": "ratio-regimes-q03" } ] } ] }, { "id": "infinite-term-limits", "name": "Infinite term limits", "description": "Evaluates sequence convergence separately from summability.", "findings": [ { "id": "sequence-limit-classification", "name": "Sequence limit classification", "description": "In real or complex arithmetic, a zero initial term gives the zero sequence; otherwise |r| < 1 gives limit zero, r = 1 gives a constant limit, and other ratios do not give a finite term limit.", "questions": [ { "text": "Which parameter case establishes a finite limit, unbounded magnitude, or bounded nonconvergence?", "kind": "measurement", "id": "sequence-limit-classification-q01" }, { "text": "If terms tend to zero, has convergence of their sum been assessed independently?", "kind": "boundary", "id": "sequence-limit-classification-q02" } ] } ] } ] }, { "id": "sums-and-computation", "name": "Sums and computation", "description": "Supports aggregation and numerically reliable evaluation.", "rationale": "Finite sums, infinite sums, and floating-point calculations have distinct validity conditions.", "layers": [ { "id": "finite-aggregation", "name": "Finite aggregation", "description": "Computes totals over a specified finite run of terms.", "findings": [ { "id": "finite-sum-cases", "name": "Finite sum cases", "description": "For N terms starting at a_0, S_N = a_0(1-r^N)/(1-r) when r ≠ 1, and S_N = N a_0 when r = 1.", "questions": [ { "text": "Which first term and term count define the requested sum, including both endpoint conventions?", "kind": "measurement", "id": "finite-sum-cases-q01" }, { "text": "Does r = 1 require the constant-sequence formula, or does r near one require a more stable numerical evaluation?", "kind": "action", "id": "finite-sum-cases-q02" } ] } ] }, { "id": "infinite-sums-and-tail-control", "name": "Infinite sums and tail control", "description": "Checks convergence before assigning an infinite total or truncation guarantee.", "findings": [ { "id": "convergent-sum-and-remainder", "name": "Convergent sum and remainder", "description": "For a nonzero initial term, the infinite geometric series converges exactly when |r| < 1, with sum a_0/(1-r); after N terms its remainder is a_0 r^N/(1-r). The all-zero sequence sums to zero separately.", "questions": [ { "text": "Do the parameters justify an ordinary convergent infinite sum?", "kind": "boundary", "id": "convergent-sum-and-remainder-q01" }, { "text": "How many terms make the remainder magnitude no greater than the required error tolerance?", "kind": "action", "id": "convergent-sum-and-remainder-q02" }, { "text": "Could overflow, underflow, or cancellation materially affect the computed terms or total?", "kind": "measurement", "id": "convergent-sum-and-remainder-q03" } ] } ] } ] }, { "id": "discrete-modelling-and-permitted-inference", "name": "Discrete modelling and permitted inference", "description": "Connects geometric structure to applications and decisions.", "rationale": "A ratio only has an operational meaning relative to a step size and assumptions that sustain repeated multiplication.", "layers": [ { "id": "constant-factor-interpretation", "name": "Constant-factor interpretation", "description": "Records what one multiplication represents in the application.", "findings": [ { "id": "step-and-rate-assumptions", "name": "Step and rate assumptions", "description": "For a positive real multiplier, r = 1 + g represents a fractional change g per declared step; unequal spacing or additive inputs require separate justification.", "questions": [ { "text": "What does one index increment represent, and are the relevant intervals or repeated operations comparable?", "kind": "definition", "id": "step-and-rate-assumptions-q01" }, { "text": "What assumptions keep the multiplier fixed, and could additive inputs or changing conditions break the recurrence?", "kind": "boundary", "id": "step-and-rate-assumptions-q02" } ] } ] }, { "id": "prediction-and-threshold-actions", "name": "Prediction and threshold actions", "description": "Restricts extrapolation and inverse calculations to supported parameter regimes.", "findings": [ { "id": "admissible-term-and-index-solutions", "name": "Admissible term and index solutions", "description": "Predicted terms and threshold indices must respect integer indexing, sequence extent, parameter uncertainty, and the relevant sign or magnitude behaviour.", "questions": [ { "text": "Is the requested threshold about signed value or magnitude, and does the progression move toward it?", "kind": "action", "id": "admissible-term-and-index-solutions-q01" }, { "text": "Which admissible integer index first satisfies the threshold, verified directly in the original recurrence or term formula?", "kind": "action", "id": "admissible-term-and-index-solutions-q02" }, { "text": "How sensitive is the prediction to uncertainty in the initial term and common ratio over the proposed horizon?", "kind": "measurement", "id": "admissible-term-and-index-solutions-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": [ "Definitions differ on whether zero initial terms and a zero common ratio are admitted; specify the convention before handling degenerate cases.", "For a nonzero initial term, an infinite geometric series converges exactly when |r| < 1; convergence of the progression itself is a separate question.", "This account uses recalled mathematical knowledge and does not represent source-verified research." ], "questions": [ { "id": "evidence-confidence-notes-q01", "text": "Which of these check these first hold for the sense of geometric progression 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": [ "Finite geometric progression", "Infinite geometric progression", "Constant progression with common ratio 1", "Alternating-sign progression with negative real common ratio", "Geometrically decaying progression with 0 < |r| < 1", "Progression with complex terms and common ratio" ], "questions": [ { "id": "evidence-kinds-q01", "text": "Which of these kinds and varieties hold for the sense of geometric progression 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": [ "Modelling balances under a constant compound interest rate without deposits or withdrawals", "Modelling quantities that grow or decay by a fixed factor over equal time steps", "Constructing logarithmically spaced frequency bands and numerical grids", "Calculating repeated percentage reductions", "Analysing algorithms whose work or problem size changes by a fixed multiplicative factor" ], "questions": [ { "id": "evidence-real-world-use-q01", "text": "Which of these real-world use hold for the sense of geometric progression 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": "Common ratio r", "typical_range": "No universal typical range; commonly real, and possibly complex", "unit": "Dimensionless" }, { "quantity": "Initial term a_1", "typical_range": "Unrestricted by the recurrence; some definitions exclude zero", "unit": "Same as the modelled quantity, or dimensionless" }, { "quantity": "Number of terms in a finite progression", "typical_range": "Positive integer", "unit": "Count" } ], "questions": [ { "id": "evidence-measurements-q01", "text": "Which of these typical measurements hold for the sense of geometric progression this model covers, and on what evidence?", "kind": "provenance" } ] }, { "id": "evidence-failure-modes-and-hazards", "name": "Failure modes and hazards", "description": "Recalled without web access and unsourced; every item is a lead to verify.", "evidence": [ "Confusing a geometric progression, which is a sequence, with a geometric series, which sums its terms.", "Using the infinite-sum formula a_1/(1-r) for a nonzero initial term when |r| ≥ 1.", "Applying the finite-sum formula a_1(1-r^N)/(1-r) at r = 1; the sum is then N a_1.", "Computing a common ratio by division when a preceding term is zero; the recurrence and quotient definitions need explicit conventions in this case.", "Assuming a constant growth factor remains valid indefinitely in empirical systems with changing rates or resource constraints." ], "questions": [ { "id": "evidence-failure-modes-and-hazards-q01", "text": "Which of these failure modes and hazards hold for the sense of geometric progression 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": "Arithmetic progression", "difference": "Successive terms have a constant additive difference rather than a constant multiplicative factor; constant sequences can satisfy both definitions." }, { "name": "Geometric series", "difference": "A geometric series is the sum of terms of a geometric progression, rather than the sequence itself." }, { "name": "Exponential function", "difference": "A geometric progression has a discrete index; an exponential function can have a continuous argument and yields a geometric progression when sampled at equal intervals." }, { "name": "Harmonic progression", "difference": "The reciprocals of its nonzero terms form an arithmetic progression, rather than its terms necessarily sharing a constant ratio." } ], "questions": [ { "id": "evidence-neighbours-q01", "text": "Which of these neighbouring kinds and how to tell them apart hold for the sense of geometric progression this model covers, and on what evidence?", "kind": "provenance" } ] } ] } ] } ] }, "openQuestions": [ "Which reference convention should the registry adopt for zero ratios, all-zero sequences, and single-term progressions?", "Should the registered concept include complex-valued progressions directly, or use a real-valued default with an explicit extension?", "Does an existing Vercy world model already own this concept or the sequence-versus-series boundary?", "Which application-specific error models and tolerances should govern claims that measured data are approximately geometric?", "Which reference sources should establish the model's definitions, exceptional cases, and numerical evaluation guidance?" ], "statistics": { "bundles": 6, "layers": 11, "findings": 16, "questions": 31 } }, "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 geometric progression, record what state it is in, and decide what may be done with it.", "whatItIs": "Enable an agent to recognise a geometric progression, establish its parameters and conventions, assess its behaviour, and perform justified calculations 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: convergent infinite geometric sequence, infinite descending geometric progression, power sequence.", "3 finer distinctions are held as aliases rather than separate entries, because telling them apart needs a task that asks for it.", "Described in 68 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 geometric progression, 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": [ "convergent infinite geometric sequence", "infinite descending geometric progression", "power sequence" ] } ], "standing": "Described in 68 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 geometric progression from another, and a geometric progression 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 geometric progression, 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 geometric progression, 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 geometric progression 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 geometric progression, 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 geometric progression, 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 geometric progression 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 geometric progression 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 geometric progression, 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 geometric progression, 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 geometric progression 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 geometric progression from the things most often confused with it.", "questions": [ { "id": "distinguishing-features-q01", "text": "What identifies and describes what distinguishes a geometric progression, 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 geometric progression, 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 geometric progression 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 geometric progression 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 geometric progression between them.", "questions": [ { "id": "stages-and-transitions-q01", "text": "What identifies and describes the lifecycle of a geometric progression, 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 geometric progression, 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 geometric progression 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 geometric progression, how often and by whom.", "findings": [ { "id": "observation-record", "name": "Observation record", "description": "How an observation of a geometric progression 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 geometric progression, 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 geometric progression, 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 geometric progression 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 geometric progression 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 geometric progression 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 geometric progression 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 geometric progression 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 geometric progression?", "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 geometric progression?", "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 geometric progression 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 geometric progression and how confident it is.", "questions": [ { "id": "claim-provenance-q01", "text": "What identifies and describes a claim about a geometric progression, 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 geometric progression, 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 geometric progression 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 geometric progression is retired without being erased.", "questions": [ { "id": "validity-and-supersession-q01", "text": "What identifies and describes the validity of a claim about a geometric progression, 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 geometric progression, 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 geometric progression 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 } } } }