{ "model": { "rank": 4403, "code": "thing-q170008", "model_id": "vr.tr.arithmetic-progression", "name": "arithmetic progression", "purpose": "Enable an agent to recognize arithmetic progressions, establish their parameters and validity, and determine which computations and transformations are justified.", "family": "Thing Registry", "category": "Cross-cutting context", "status": "research-draft", "kind": "thing", "plane": "XCT", "domain": "XCT.QLT", "industry": "", "version": "", "url": "/models/thing/q170008/", "tier": 2, "score": 75, "payload": { "layer": "wikidata", "aliases": [ "regularly spaced time" ], "aliasCount": 1, "merged": 1, "knownIn": 75, "facets": null, "markers": [], "lexicalClass": "", "senseRank": null, "alsoRegisteredAs": null, "source": { "dataset": "wikidata", "item": "Q170008", "url": "https://www.wikidata.org/wiki/Q170008", "license": "CC0 1.0" } }, "research": { "vercy": "1.0-draft", "publication": { "status": "research-draft", "adjudicationStatus": "unreviewed", "publishableCanonical": false, "generatedAt": "2026-09-09T20:08:25Z", "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: 01a087c8-5ce0-7291-be93-a3c5ea4254cd\n--------\nuser\nDescribe what is already known about one registered thing. Answer as JSON only, no prose around it.\n\nThing: arithmetic progression\nSense to describe: (none recorded)\nDomain code: XCT.REL\nAlso known as: (none)\n\n\nContext for this batch of 695 things:\n# Batch 004", "usd": 0, "recall": true }, "codex": { "seconds": 56, "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: 01a087c8-5cd2-77c3-9776-5c000b9911ec\n--------\nuser\nYou are drafting a Vercy meta-model for one registered thing. Answer as JSON only, no prose around it.\n\nThing: arithmetic progression\nRegistry id: vr.tr.arithmetic-progression\nPlane / domain: XCT / XCT.REL\nRegistry definition: (none recorded)\nNames folded into" } } }, "metaModel": { "id": "THING-Q170008", "registryId": "vr.tr.arithmetic-progression", "name": "arithmetic progression", "version": "0.1.0-research.1", "entryKind": "thing", "family": "Thing Registry", "domain": [ "XCT.REL" ], "status": "research-draft" }, "canonicalUrl": "https://ver.cy/models/thing/q170008/", "model": { "registry_id": "vr.tr.arithmetic-progression", "name": "arithmetic progression", "purpose": "Enable an agent to recognize arithmetic progressions, establish their parameters and validity, and determine which computations and transformations are justified.", "definition": "An arithmetic progression is a finite or infinite sequence of numbers in which the difference between each term and its predecessor is constant, so that a_n = a_1 + (n − 1)d for a fixed common difference d.", "scope_statement": "This model owns finite and infinite ordered numerical sequences with a constant difference between consecutive terms, including their representations, identification conditions, derived quantities, and arithmetic-preserving transformations; the default setting is exact real-valued terms indexed by consecutive integers.", "in_scope": [ "Constant-difference identity, including increasing, decreasing, and constant progressions", "First term, common difference, index origin, and finite or infinite extent", "Explicit, recursive, and partially observed representations", "Recovery and consistency checking of parameters from indexed terms or constraints", "Term membership, finite sums, and justified transformations" ], "out_of_scope": [ "General sequences whose consecutive differences are not constant", "Geometric progressions defined by a constant ratio", "Arithmetic series as independently studied summation objects, especially convergence theory", "Arithmetic functions and number-theoretic properties not implied by constant spacing", "Empirical trend models and statistical estimation beyond assessing compatibility with an arithmetic progression", "Continuous affine functions except as representations restricted to integer indices" ], "distinguishing_features": [ "For every adjacent pair in the stated index range, a_(n+1) - a_n equals the same value d; a constant ratio alone does not establish this condition.", "The explicit term rule is a_n = a_k + (n-k)d for integer indices in the progression's domain, distinguishing the sequence from a continuous line.", "Where triples exist, a_(n+2) - 2a_(n+1) + a_n = 0; nonlinear polynomial sequences generally fail this test.", "Ordering and index gaps matter: unequal differences between observations may still fit a progression when the observations are not consecutive.", "A constant sequence qualifies with d = 0 and can also qualify as geometric, so these classes are not disjoint." ], "characteristics": [ { "name": "Value domain", "kind": "category", "unit_or_values": "Integers, rationals, or reals in the default model; other domains require explicit conventions", "why_it_matters": "Determines which terms, differences, divisions, and comparisons are admissible." }, { "name": "Anchor term", "kind": "measurement", "unit_or_values": "Value a_k at a recorded integer index k; dimensionless or in the terms' stated unit", "why_it_matters": "Together with the common difference and index domain, fixes the progression." }, { "name": "Common difference", "kind": "measurement", "unit_or_values": "Exact value d in term units per index increment", "why_it_matters": "Controls spacing, direction, term generation, and arithmetic identity." }, { "name": "Index domain", "kind": "category", "unit_or_values": "Finite consecutive integer interval, one-sided infinite interval, or explicitly supported two-sided interval", "why_it_matters": "Determines which terms exist and whether an endpoint or finite total is available." }, { "name": "Term count", "kind": "measurement", "unit_or_values": "Nonnegative integer N for a finite representation, or infinite; short-sequence conventions must be stated", "why_it_matters": "Determines how strongly observations constrain the difference and which finite-sum operations apply." }, { "name": "Verification state", "kind": "state", "unit_or_values": "Proved on the declared domain, compatible with observed terms, contradicted, or underdetermined", "why_it_matters": "Prevents a finite pattern from being treated as proof of an unrestricted continuation." }, { "name": "Representation", "kind": "category", "unit_or_values": "Explicit rule, recurrence with initial condition, complete finite list, or partial indexed observations", "why_it_matters": "Determines how the progression can be evaluated and what evidence supports its identity." }, { "name": "Observation indexing", "kind": "relation", "unit_or_values": "Mapping from each observed value to its sequence index, including known or unknown gaps", "why_it_matters": "Supports correct parameter recovery when observed terms are not consecutive." } ], "affordances": [ "Verify constant differences over a complete finite sequence or prove them from a defining rule.", "Recover an anchor and common difference from sufficient indexed information, reporting ambiguity or inconsistency.", "Generate terms, interpolate missing indexed terms, and extrapolate when the defining rule is established or explicitly assumed.", "Determine whether a candidate value occurs and identify its admissible indices.", "Compute finite block sums and solve endpoint or term-count constraints.", "Apply affine value transformations, contiguous restrictions, or regularly spaced index sampling and determine the resulting progression." ] }, "sources": [], "structure": { "bundles": [ { "id": "arithmetic-identity", "name": "Arithmetic identity", "description": "Establishes what constant difference means for the declared values and index domain.", "rationale": "An agent must distinguish a valid progression from a suggestive list and handle degenerate cases explicitly.", "layers": [ { "id": "constant-difference-condition", "name": "Constant-difference condition", "description": "Connects the adjacent-difference invariant with explicit and recursive definitions.", "findings": [ { "id": "equivalent-term-rules", "name": "Equivalent term rules", "description": "On a consecutive integer index domain, a_(n+1) = a_n + d and a_n = a_k + (n-k)d describe the same progression when an anchor is fixed.", "questions": [ { "text": "What anchor, common difference, and index domain define this progression?", "kind": "definition", "id": "equivalent-term-rules-q01" }, { "text": "Does the supplied rule establish the same adjacent difference at every admissible step?", "kind": "measurement", "id": "equivalent-term-rules-q02" } ] } ] }, { "id": "domain-and-degenerate-cases", "name": "Domain and degenerate cases", "description": "Records the numerical setting and cases in which familiar tests become insufficient.", "findings": [ { "id": "constant-and-short-sequences", "name": "Constant and short sequences", "description": "Zero difference gives a constant progression. Two real-valued terms determine a difference, while a singleton does not determine one; acceptance of empty or singleton progressions requires a stated convention.", "questions": [ { "text": "Which convention governs empty and singleton sequences, and is the common difference supplied or recoverable?", "kind": "boundary", "id": "constant-and-short-sequences-q01" }, { "text": "Is d zero, and which operations therefore need a separate constant-sequence case?", "kind": "action", "id": "constant-and-short-sequences-q02" } ] } ] } ] }, { "id": "representation-and-evidence", "name": "Representation and evidence", "description": "Records how terms are specified and the strength of the evidence for arithmetic structure.", "rationale": "Correct calculations depend on index interpretation, while justified continuation depends on evidence beyond a short prefix.", "layers": [ { "id": "index-aware-representation", "name": "Index-aware representation", "description": "Makes index origin, extent, and observation gaps explicit.", "findings": [ { "id": "indexed-observations", "name": "Indexed observations", "description": "Values must be attached to their actual indices; a gap of h indices implies a value difference of hd, not necessarily d.", "questions": [ { "text": "Are the listed terms consecutive, regularly sampled, or attached to irregularly spaced known indices?", "kind": "definition", "id": "indexed-observations-q01" }, { "text": "What source establishes the index origin, omitted positions, and final index if one exists?", "kind": "provenance", "id": "indexed-observations-q02" } ] } ] }, { "id": "proof-and-observation", "name": "Proof and observation", "description": "Separates exact arithmetic identity from compatibility with limited or rounded data.", "findings": [ { "id": "verification-strength", "name": "Verification strength", "description": "A complete finite list can be checked exhaustively, but a finite prefix alone does not prove an infinite continuation. Rounded observations require an explicit error model before arithmetic compatibility can be assessed.", "questions": [ { "text": "Is arithmetic structure established by a definition or proof, by a complete finite check, or only suggested by observations?", "kind": "provenance", "id": "verification-strength-q01" }, { "text": "Are values exact, and if they are rounded or measured, what uncertainty bounds govern the compatibility test?", "kind": "measurement", "id": "verification-strength-q02" } ] } ] } ] }, { "id": "parameter-recovery-and-membership", "name": "Parameter recovery and membership", "description": "Determines which progression fits the available constraints and which values belong to it.", "rationale": "Agents need to resolve missing terms and candidate membership without silently assuming uniqueness or valid indices.", "layers": [ { "id": "constraint-identifiability", "name": "Constraint identifiability", "description": "Uses indexed values and additional conditions to recover or reject parameters.", "findings": [ { "id": "recovering-the-difference", "name": "Recovering the difference", "description": "For distinct known indices i and j over the reals, d = (a_j-a_i)/(j-i). Further observations must satisfy that same rule, and integer-valued progressions impose additional integrality constraints.", "questions": [ { "text": "Do the available indexed terms determine a unique d, or do unknown index gaps leave multiple possibilities?", "kind": "measurement", "id": "recovering-the-difference-q01" }, { "text": "Do all remaining observations and value-domain restrictions agree with the recovered anchor and difference?", "kind": "boundary", "id": "recovering-the-difference-q02" } ] } ] }, { "id": "candidate-term-membership", "name": "Candidate-term membership", "description": "Tests values against both the term equation and the allowed index range.", "findings": [ { "id": "admissible-index-test", "name": "Admissible index test", "description": "For d ≠ 0, a candidate x belongs exactly when n = k + (x-a_k)/d is an integer in the index domain. For d = 0, every existing term equals the anchor.", "questions": [ { "text": "Does the candidate produce an integer index inside the declared finite or infinite index domain?", "kind": "measurement", "id": "admissible-index-test-q01" }, { "text": "If d is zero, does the candidate equal the anchor, and which existing indices should be returned?", "kind": "action", "id": "admissible-index-test-q02" } ] } ] } ] }, { "id": "derived-operations-and-preservation", "name": "Derived operations and preservation", "description": "Governs finite aggregation and transformations that retain constant spacing.", "rationale": "Recognizing a progression should enable reliable operations while exposing their preconditions and scope.", "layers": [ { "id": "finite-block-aggregation", "name": "Finite block aggregation", "description": "Computes sums using the correct endpoints and number of terms.", "findings": [ { "id": "finite-sum-and-endpoints", "name": "Finite sum and endpoints", "description": "A nonempty block of N consecutive terms has sum N(first + last)/2, with last = first + (N-1)d. The formula describes a finite block and does not supply a total for an infinite progression.", "questions": [ { "text": "What are the inclusive starting and ending indices, and does N equal their difference plus one?", "kind": "measurement", "id": "finite-sum-and-endpoints-q01" }, { "text": "When solving from a sum or endpoint, do the resulting term counts and indices satisfy the required integer and range constraints?", "kind": "action", "id": "finite-sum-and-endpoints-q02" } ] } ] }, { "id": "arithmetic-preserving-transformations", "name": "Arithmetic-preserving transformations", "description": "Tracks how affine value changes and regular index selection alter the parameters.", "findings": [ { "id": "transformed-spacing", "name": "Transformed spacing", "description": "An affine value map b_n = αa_n + β gives difference αd. Sampling a_(r+hm) gives difference hd wherever the sampled indices exist; reversing a finite progression changes the difference to -d.", "questions": [ { "text": "What anchor, difference, and valid index domain result from the proposed transformation?", "kind": "action", "id": "transformed-spacing-q01" }, { "text": "Is the selected index spacing constant, or does preservation require a special case such as d = 0?", "kind": "boundary", "id": "transformed-spacing-q02" } ] } ] } ] }, { "id": "evidence-and-external-alignment", "name": "Evidence and external alignment", "description": "What the world already says about this thing, gathered so the model can be checked against it.", "rationale": "A model that cannot be lined up against existing standards, identifiers and practice cannot be adopted by anyone who already uses them.", "layers": [ { "id": "reported-evidence", "name": "Reported evidence", "description": "Findings from the breadth pass, kept separate from the structural claims.", "findings": [ { "id": "evidence-confidence-notes", "name": "Check these first", "description": "Recalled without web access and unsourced; every item is a lead to verify.", "evidence": [ "This describes the standard numerical sense; the core definition is broadly settled.", "Some number-theoretic contexts require a nonzero or positive common difference to exclude trivial progressions.", "The definition permits real or complex terms; increasing and decreasing classifications apply to real-valued progressions." ], "questions": [ { "id": "evidence-confidence-notes-q01", "text": "Which of these check these first hold for the sense of arithmetic 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 arithmetic progression", "Infinite arithmetic progression", "Increasing real arithmetic progression (d > 0)", "Decreasing real arithmetic progression (d < 0)", "Constant arithmetic progression (d = 0)" ], "questions": [ { "id": "evidence-kinds-q01", "text": "Which of these kinds and varieties hold for the sense of arithmetic 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": [ "Representing equally spaced sampling times or measurement positions.", "Calculating totals when successive payments or deposits increase by a fixed amount.", "Describing regularly spaced seats, objects or construction elements.", "Studying patterns among integers and primes in number theory.", "Generating evenly spaced numerical grids." ], "questions": [ { "id": "evidence-real-world-use-q01", "text": "Which of these real-world use hold for the sense of arithmetic 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 difference d", "typical_range": "Any real number for a real-valued progression; no universal typical range", "unit": "Same unit as the terms, or dimensionless" }, { "quantity": "Number of terms N", "typical_range": "Any positive integer for a nonempty finite progression; infinite progressions have no finite term count", "unit": "Dimensionless count" } ], "questions": [ { "id": "evidence-measurements-q01", "text": "Which of these typical measurements hold for the sense of arithmetic 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 constant additive difference with the constant multiplicative ratio of a geometric progression.", "Introducing an indexing error by mixing a_0-based and a_1-based formulas.", "Confusing the sequence with its arithmetic series, which is a sum of terms.", "Assuming that a few equally spaced observations establish an arithmetic pattern for all later terms.", "Using exact equality of floating-point differences to test approximately measured or computed data." ], "questions": [ { "id": "evidence-failure-modes-and-hazards-q01", "text": "Which of these failure modes and hazards hold for the sense of arithmetic 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 sequence", "difference": "Usually a synonym for arithmetic progression, with no mathematical distinction." }, { "name": "Arithmetic series", "difference": "A series sums the terms of an arithmetic progression; the progression is the sequence itself." }, { "name": "Geometric progression", "difference": "Successive terms are related by a fixed multiplicative factor rather than a fixed additive difference." }, { "name": "Affine function", "difference": "An arithmetic progression is an affine function of an integer index; an affine function can have a broader domain." }, { "name": "Polynomial sequence", "difference": "An arithmetic progression has constant first differences; sequences generated by higher-degree polynomials generally require higher-order differences to become constant." } ], "questions": [ { "id": "evidence-neighbours-q01", "text": "Which of these neighbouring kinds and how to tell them apart hold for the sense of arithmetic progression this model covers, and on what evidence?", "kind": "provenance" } ] } ] } ] } ] }, "openQuestions": [ "Which registry or world-model entry already owns the broader sequence concept, and does an existing publication already cover arithmetic progression?", "Which reference convention should govern empty and singleton progressions and the distinction between a finite arithmetic sequence and a finite segment of an infinite progression?", "Should complex-valued, modular, or abstract additive-group progressions be supported here, and which domain-specific tests would replace real-valued division and order?", "Should two-sided infinite progressions be first-class instances or explicitly declared extensions of the default indexing convention?", "What evidence and uncertainty conventions should govern recognition from rounded observations without treating approximate agreement as exact arithmetic identity?" ], "statistics": { "bundles": 5, "layers": 9, "findings": 14, "questions": 22 } }, "draft": { "generator": "vr.draft.v3", "status": "draft-generated", "researched": false, "archetype": "abstract concept", "method": "Written from the archetype playbook - what this kind of thing needs beyond identity and provenance - and from the structure that recurred across 6,333 models already researched by two engines. Applied to this entry by rule. No source was read for this thing and no claim here is researched. This entry carries no facets of its own, so they were inferred from its domain - a guess about a whole domain applied to one thing.", "facetsInferred": true, "nextPass": "A researcher replaces this draft with a sourced specification. Treat every sentence below as a proposal to argue with.", "purpose": "Give an agent a durable, checkable way to recognise a arithmetic progression, record what state it is in, and decide what may be done with it.", "whatItIs": "Enable an agent to recognize arithmetic progressions, establish their parameters and validity, and determine which computations and transformations are justified.", "characteristics": { "substance": "abstract", "origin": "conceptual", "agency": "inert" }, "whatYouCanDoWithIt": [ "observed and measured" ], "distinguishingFeatures": [ "Names folded into this entry, which a task may need to split apart again: regularly spaced time.", "1 finer distinctions are held as aliases rather than separate entries, because telling them apart needs a task that asks for it.", "Described in 75 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 arithmetic 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": [ "regularly spaced time" ] } ], "standing": "Described in 75 Wikipedia languages, which measures how widely it is written about rather than how important or how common it is. 1 finer distinctions are held inside this entry as names rather than as separate models.", "structure": { "bundles": [ { "id": "identity-and-classification", "name": "Identity, naming and classification", "description": "How an agent tells one arithmetic progression from another, and a arithmetic 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 arithmetic 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 arithmetic 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 arithmetic 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 arithmetic 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 arithmetic 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 arithmetic 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 arithmetic 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 arithmetic 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 arithmetic 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 arithmetic 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 arithmetic progression from the things most often confused with it.", "questions": [ { "id": "distinguishing-features-q01", "text": "What identifies and describes what distinguishes a arithmetic 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 arithmetic 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 arithmetic 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 arithmetic 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 arithmetic progression between them.", "questions": [ { "id": "stages-and-transitions-q01", "text": "What identifies and describes the lifecycle of a arithmetic 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 arithmetic 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 arithmetic 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 arithmetic progression, how often and by whom.", "findings": [ { "id": "observation-record", "name": "Observation record", "description": "How an observation of a arithmetic 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 arithmetic 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 arithmetic 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 arithmetic 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 arithmetic 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 arithmetic 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 arithmetic 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 arithmetic 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 arithmetic 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 arithmetic 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 arithmetic 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 arithmetic progression and how confident it is.", "questions": [ { "id": "claim-provenance-q01", "text": "What identifies and describes a claim about a arithmetic 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 arithmetic 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 arithmetic 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 arithmetic progression is retired without being erased.", "questions": [ { "id": "validity-and-supersession-q01", "text": "What identifies and describes the validity of a claim about a arithmetic 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 arithmetic 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 arithmetic 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 } } } }