{ "model": { "rank": 4342, "code": "thing-q102761", "model_id": "vr.tr.least-common-multiple", "name": "least common multiple", "purpose": "Enable an agent to recognise, compute and verify a least common multiple and judge when it correctly represents a shared divisibility or alignment requirement.", "family": "Thing Registry", "category": "Cross-cutting context", "status": "research-draft", "kind": "thing", "plane": "XCT", "domain": "XCT.QLT", "industry": "", "version": "", "url": "/models/thing/q102761/", "tier": 2, "score": 76, "payload": { "layer": "wikidata", "aliases": [ "lowest common denominator" ], "aliasCount": 1, "merged": 1, "knownIn": 76, "facets": null, "markers": [], "lexicalClass": "", "senseRank": null, "alsoRegisteredAs": null, "source": { "dataset": "wikidata", "item": "Q102761", "url": "https://www.wikidata.org/wiki/Q102761", "license": "CC0 1.0" } }, "research": { "vercy": "1.0-draft", "publication": { "status": "research-draft", "adjudicationStatus": "unreviewed", "publishableCanonical": false, "generatedAt": "2026-09-09T20:00:08Z", "providers": [ "Codex" ], "breadth": "recalled by Codex without web access - no source was read", "missingProviders": [], "pass": 2, "cost": { "grok": { "seconds": 19.4, "error": "Reading additional input from stdin...\nOpenAI Codex v0.153.4\n--------\nworkdir: R:\\02_PROJECTS\\02_Meta_Models_Platforms\\Ver.cy\\current\\thing-registry-backlog\nmodel: gpt-6-astra\nprovider: openai\napproval: never\nsandbox: read-only\nreasoning effort: none\nreasoning summaries: none\nsession id: 01a087c0-ccad-7113-b832-a24b6b9ddde8\n--------\nuser\nDescribe what is already known about one registered thing. Answer as JSON only, no prose around it.\n\nThing: least common multiple\nSense to describe: (none recorded)\nDomain code: XCT.QLT\nAlso known as: (none)\n\n\nContext for this batch of 695 things:\n# Batch 004:", "usd": 0, "recall": true }, "codex": { "seconds": 54.6, "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: 01a087c0-ccb8-7f82-b9c8-b6371afb9978\n--------\nuser\nYou are drafting a Vercy meta-model for one registered thing. Answer as JSON only, no prose around it.\n\nThing: least common multiple\nRegistry id: vr.tr.least-common-multiple\nPlane / domain: XCT / XCT.QLT\nRegistry definition: (none recorded)\nNames folded into t" } } }, "metaModel": { "id": "THING-Q102761", "registryId": "vr.tr.least-common-multiple", "name": "least common multiple", "version": "0.1.0-research.1", "entryKind": "thing", "family": "Thing Registry", "domain": [ "XCT.QLT" ], "status": "research-draft" }, "canonicalUrl": "https://ver.cy/models/thing/q102761/", "model": { "registry_id": "vr.tr.least-common-multiple", "name": "least common multiple", "purpose": "Enable an agent to recognise, compute and verify a least common multiple and judge when it correctly represents a shared divisibility or alignment requirement.", "definition": "The least common multiple of a nonempty finite collection of positive integers is the smallest positive integer divisible by every integer in that collection.", "scope_statement": "This model owns the least common multiple of a finite, nonempty collection of integers, including input conventions, defining divisibility conditions, computation, verification and justified applications; it distinguishes the standard positive-integer definition from explicitly declared extensions involving zero.", "in_scope": [ "The least positive integer divisible by every input when all inputs are nonzero", "Normalisation of negative integer inputs to their absolute values", "The convention that a collection containing zero has least common multiple zero", "Exact computation and verification using greatest common divisors or prime exponents", "Finite collections, repeated inputs and incremental accumulation", "Use in common denominators and compatible periodic alignment problems" ], "out_of_scope": [ "Greatest common divisor as a separately modelled concept", "General prime factorisation methods beyond their role in computing or verifying an LCM", "Complete fraction arithmetic and fraction simplification", "General scheduling with offsets, constraints or uncertain durations", "Least common multiples of polynomials or elements of other algebraic structures", "Extensions to rational inputs, empty collections or infinite collections" ], "distinguishing_features": [ "For nonzero integer inputs, the result is positive and every input divides it; this separates an LCM from a greatest common divisor, which divides every input.", "Every common multiple is divisible by the LCM; merely being a common multiple is insufficient.", "For positive inputs, the LCM equals their product only when those inputs are pairwise coprime; shared prime factors generally make the LCM smaller.", "Each prime exponent in a nonzero LCM is the maximum exponent appearing among the absolute input values, whereas a GCD uses the minimum.", "When an input is zero, a result of zero uses an explicit extension of the definition because no positive integer is divisible by zero." ], "characteristics": [ { "name": "Input integers", "kind": "relation", "unit_or_values": "Finite, nonempty collection of integers", "why_it_matters": "An LCM is relative to its inputs; its numeric value alone does not identify the divisibility problem." }, { "name": "Input domain", "kind": "category", "unit_or_values": "Positive integers; nonzero signed integers; integers including zero", "why_it_matters": "Determines whether sign normalisation or an explicit zero convention is required." }, { "name": "Zero convention", "kind": "category", "unit_or_values": "Zero inputs excluded; LCM defined as zero whenever an input is zero", "why_it_matters": "Prevents an implementation convention from being confused with the least-positive-common-multiple definition." }, { "name": "LCM value", "kind": "measurement", "unit_or_values": "Exact nonnegative integer; dimensionless", "why_it_matters": "Records the candidate or verified result without rounding or machine overflow." }, { "name": "Verification state", "kind": "state", "unit_or_values": "Uncomputed; candidate; common-multiple condition verified; leastness verified; rejected", "why_it_matters": "Distinguishes finding any common multiple from establishing the least common multiple." }, { "name": "Computation method", "kind": "category", "unit_or_values": "GCD reduction; prime-exponent maxima; bounded enumeration; other documented exact method", "why_it_matters": "Makes the result reproducible and exposes method-specific failure conditions." }, { "name": "Application scale", "kind": "relation", "unit_or_values": "Optional mapping from integer inputs to counts of a shared exact unit", "why_it_matters": "Allows an integer LCM to represent a duration or length only when all inputs use a justified common scale." } ], "affordances": [ "Validate integer inputs and apply declared sign and zero conventions.", "Compute an exact LCM for two or more inputs using GCD reduction or prime-exponent maxima.", "Verify both common divisibility and leastness of a proposed result.", "Update an existing LCM when an additional integer constraint is introduced.", "Construct a least common denominator for specified positive integer denominators.", "Determine a shared repeat interval for exact integer periods after checking scale and phase assumptions." ] }, "sources": [], "structure": { "bundles": [ { "id": "definition-and-divisibility", "name": "Definition and divisibility", "description": "Establishes what makes a candidate the least common multiple of the supplied integers.", "rationale": "Common divisibility alone does not establish leastness, and zero requires a distinct definitional convention.", "layers": [ { "id": "common-multiple-condition", "name": "Common multiple condition", "description": "Checks the direction and completeness of the required divisibility relations.", "findings": [ { "id": "every-input-divides-result", "name": "Every input divides the result", "description": "A common multiple must be an integer multiple of each input; reversing this relation tests for a common divisor instead.", "questions": [ { "text": "For every input a, is there an integer k such that the candidate m equals a times k?", "kind": "definition", "id": "every-input-divides-result-q01" }, { "text": "Have all supplied inputs been checked, including any zero input through the divisibility definition rather than a remainder operation?", "kind": "measurement", "id": "every-input-divides-result-q02" } ] } ] }, { "id": "leastness-and-zero", "name": "Leastness and zero", "description": "Separates the least positive common multiple from other common multiples and records the zero extension.", "findings": [ { "id": "leastness-certificate", "name": "Leastness certificate", "description": "For nonzero inputs, the LCM is the smallest positive common multiple and divides every common multiple. Under the zero extension, a collection containing zero has LCM zero.", "questions": [ { "text": "What establishes that every common multiple of these inputs is divisible by the proposed LCM?", "kind": "definition", "id": "leastness-certificate-q01" }, { "text": "If an input is zero, is the zero extension declared instead of claiming that zero is a positive common multiple?", "kind": "boundary", "id": "leastness-certificate-q02" } ] } ] } ] }, { "id": "input-domain-and-normalisation", "name": "Input domain and normalisation", "description": "Identifies admissible collections and transformations that preserve their LCM.", "rationale": "Signs, zero, repeated values and unsupported domains can change how a request must be interpreted before computation.", "layers": [ { "id": "integer-domain", "name": "Integer domain", "description": "Ensures the request belongs to the finite integer interpretation owned by this model.", "findings": [ { "id": "admissible-input-collection", "name": "Admissible input collection", "description": "The owned domain is a finite, nonempty integer collection. Negative values can be replaced by absolute values; zero requires the selected convention.", "questions": [ { "text": "Is the collection finite and nonempty, and is every value an exact integer?", "kind": "boundary", "id": "admissible-input-collection-q01" }, { "text": "Which sign normalisation and zero policy govern these inputs?", "kind": "definition", "id": "admissible-input-collection-q02" } ] } ] }, { "id": "redundant-inputs", "name": "Redundant inputs", "description": "Recognises input constraints that do not alter the result.", "findings": [ { "id": "divisibility-preserving-reduction", "name": "Divisibility-preserving reduction", "description": "Order and duplicate inputs do not affect the LCM. Among positive inputs, an input that divides another imposes no additional constraint.", "questions": [ { "text": "Which positive inputs divide another supplied input and can be removed without changing the LCM?", "kind": "measurement", "id": "divisibility-preserving-reduction-q01" }, { "text": "Can duplicates and redundant divisors be removed while retaining the original collection for explanation?", "kind": "action", "id": "divisibility-preserving-reduction-q02" } ] } ] } ] }, { "id": "exact-computation-and-verification", "name": "Exact computation and verification", "description": "Connects executable calculation methods to evidence that the result is correct.", "rationale": "An agent must distinguish an exact verified result from a plausible value produced by rounding, overflow or incomplete factorisation.", "layers": [ { "id": "gcd-reduction", "name": "GCD reduction", "description": "Computes pairwise LCMs and extends them across a finite collection.", "findings": [ { "id": "gcd-based-accumulation", "name": "GCD-based accumulation", "description": "For nonzero a and b, lcm(a,b) equals abs((a/gcd(a,b)) times b). Repeated pairwise application handles a finite collection; a zero input is handled explicitly under the zero extension.", "questions": [ { "text": "Does the computation use exact division by the GCD before multiplication and handle zero before any undefined division?", "kind": "action", "id": "gcd-based-accumulation-q01" }, { "text": "Can the numeric representation hold every intermediate value and the final LCM exactly?", "kind": "measurement", "id": "gcd-based-accumulation-q02" } ] } ] }, { "id": "prime-exponent-verification", "name": "Prime-exponent verification", "description": "Uses prime factors to explain both common divisibility and leastness for nonzero inputs.", "findings": [ { "id": "maximum-prime-exponents", "name": "Maximum prime exponents", "description": "For each prime appearing in the absolute inputs, the LCM contains exactly the largest input exponent of that prime. The LCM of inputs all equal to one is one.", "questions": [ { "text": "Does the candidate contain every required prime with exactly its maximum input exponent and no additional prime factors?", "kind": "measurement", "id": "maximum-prime-exponents-q01" }, { "text": "What calculation record or independently checked factorisation supports the claimed exponent maxima?", "kind": "provenance", "id": "maximum-prime-exponents-q02" } ] } ] } ] }, { "id": "application-fit", "name": "Application fit", "description": "Determines when a divisibility result answers the practical question being asked.", "rationale": "Correct LCM arithmetic can still give the wrong answer when denominator representation, period units or starting phases are misunderstood.", "layers": [ { "id": "common-denominators", "name": "Common denominators", "description": "Applies the LCM to specified positive integer denominators while distinguishing representation choices.", "findings": [ { "id": "denominator-selection", "name": "Denominator selection", "description": "The LCM of specified denominators is their least common multiple. Reducing fractions first can produce a smaller common denominator sufficient to represent the same rational values.", "questions": [ { "text": "Is the task to find the LCM of the written denominators or the smallest common denominator after reducing the fractions?", "kind": "boundary", "id": "denominator-selection-q01" }, { "text": "Are all denominators positive integers, and what exact multiplier converts each selected denominator to the computed LCM?", "kind": "action", "id": "denominator-selection-q02" } ] } ] }, { "id": "periodic-alignment", "name": "Periodic alignment", "description": "Applies integer LCMs to exact repeat intervals with compatible starting conditions.", "findings": [ { "id": "period-and-phase-conditions", "name": "Period and phase conditions", "description": "For processes aligned at a shared origin with positive integer periods in a common unit, the LCM gives the first positive return to joint alignment. Different phases require additional congruence checks.", "questions": [ { "text": "Are all periods exact positive integer counts of the same unit, and were the processes aligned at the stated origin?", "kind": "boundary", "id": "period-and-phase-conditions-q01" }, { "text": "If starting phases differ, must simultaneous congruences be solved before an alignment time can be asserted?", "kind": "action", "id": "period-and-phase-conditions-q02" } ] } ] } ] }, { "id": "evidence-and-external-alignment", "name": "Evidence and external alignment", "description": "What the world already says about this thing, gathered so the model can be checked against it.", "rationale": "A model that cannot be lined up against existing standards, identifiers and practice cannot be adopted by anyone who already uses them.", "layers": [ { "id": "reported-evidence", "name": "Reported evidence", "description": "Findings from the breadth pass, kept separate from the structural claims.", "findings": [ { "id": "evidence-confidence-notes", "name": "Check these first", "description": "Recalled without web access and unsourced; every item is a lead to verify.", "evidence": [ "The sense described is the standard integer-arithmetic concept; polynomial least common multiples are an established extension.", "When extending to arbitrary integers, a common convention uses absolute values and sets lcm(a, 0) = 0, including lcm(0, 0); this requires extending the smallest-positive-common-multiple definition.", "The arithmetic definition is settled; conventions for zero inputs, empty collections, and algebraic normalization should be checked for the intended implementation." ], "questions": [ { "id": "evidence-confidence-notes-q01", "text": "Which of these check these first hold for the sense of least common multiple 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": [ "Least common multiple of two positive integers", "Least common multiple of a finite collection of positive integers", "Polynomial least common multiple, defined up to multiplication by a unit and commonly normalized to be monic over a field" ], "questions": [ { "id": "evidence-kinds-q01", "text": "Which of these kinds and varieties hold for the sense of least common multiple this model covers, and on what evidence?", "kind": "provenance" } ] }, { "id": "evidence-identifiers", "name": "Identifiers and schemes", "description": "Recalled without web access and unsourced; every item is a lead to verify.", "evidence": [ { "scheme": "Mathematical notation", "value_or_pattern": "lcm(a, b) or LCM(a, b)", "note": "Conventional notation for the operation, rather than a registry identifier." } ], "questions": [ { "id": "evidence-identifiers-q01", "text": "Which of these identifiers and schemes hold for the sense of least common multiple 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": [ "Finding the least common denominator when adding or comparing fractions.", "Determining when periodic events with commensurable periods and a shared starting point next coincide.", "Finding the smallest quantity divisible into each of several specified integer group sizes.", "Computing the order of a permutation as the least common multiple of its disjoint cycle lengths." ], "questions": [ { "id": "evidence-real-world-use-q01", "text": "Which of these real-world use hold for the sense of least common multiple 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": "Least common multiple of positive integers a and b", "typical_range": "No universal typical range; max(a, b) ≤ lcm(a, b) ≤ ab.", "unit": "Dimensionless" } ], "questions": [ { "id": "evidence-measurements-q01", "text": "Which of these typical measurements hold for the sense of least common multiple 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 the least common multiple with the greatest common divisor.", "Using the product of the inputs as their least common multiple when the inputs are not coprime.", "Taking minimum rather than maximum prime-factor exponents when constructing the least common multiple.", "Overflowing fixed-width integer arithmetic when computing ab/gcd(a, b); dividing before multiplying reduces intermediate overflow risk.", "Applying the shared-start recurrence rule to events with different phase offsets, whose coincidence requires solving additional congruence conditions." ], "questions": [ { "id": "evidence-failure-modes-and-hazards-q01", "text": "Which of these failure modes and hazards hold for the sense of least common multiple 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": "greatest common divisor", "difference": "The greatest common divisor divides every input; the least common multiple is divisible by every input." }, { "name": "common multiple", "difference": "A common multiple is divisible by every input but need not be the smallest positive one." }, { "name": "least common denominator", "difference": "The least common denominator applies the least common multiple specifically to the denominators in a collection of fractions." }, { "name": "product", "difference": "For two positive integers, their product equals their least common multiple exactly when they are coprime." } ], "questions": [ { "id": "evidence-neighbours-q01", "text": "Which of these neighbouring kinds and how to tell them apart hold for the sense of least common multiple this model covers, and on what evidence?", "kind": "provenance" } ] } ] } ] } ] }, "openQuestions": [ "Which authoritative reference should anchor the registry definition, given that none is recorded?", "Should the published model accept zero inputs by default or require an explicit declaration of the zero extension?", "Does the registry intend this entry to cover algebraic generalisations, or should those be linked as separate neighbouring concepts?", "Which consuming applications require exact unit conversion and phase information alongside the integer LCM?", "What verification evidence should consuming agents retain: reproducible GCD steps, prime-exponent certificates or another exact proof?" ], "statistics": { "bundles": 5, "layers": 9, "findings": 15, "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 least common multiple, record what state it is in, and decide what may be done with it.", "whatItIs": "Enable an agent to recognise, compute and verify a least common multiple and judge when it correctly represents a shared divisibility or alignment requirement.", "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: lowest common denominator.", "1 finer distinctions are held as aliases rather than separate entries, because telling them apart needs a task that asks for it.", "Described in 76 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 least common multiple, 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": [ "lowest common denominator" ] } ], "standing": "Described in 76 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 least common multiple from another, and a least common multiple 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 least common multiple, 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 least common multiple, 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 least common multiple 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 least common multiple, 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 least common multiple, 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 least common multiple 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 least common multiple 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 least common multiple, 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 least common multiple, 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 least common multiple 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 least common multiple from the things most often confused with it.", "questions": [ { "id": "distinguishing-features-q01", "text": "What identifies and describes what distinguishes a least common multiple, 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 least common multiple, 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 least common multiple 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 least common multiple 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 least common multiple between them.", "questions": [ { "id": "stages-and-transitions-q01", "text": "What identifies and describes the lifecycle of a least common multiple, 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 least common multiple, 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 least common multiple 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 least common multiple, how often and by whom.", "findings": [ { "id": "observation-record", "name": "Observation record", "description": "How an observation of a least common multiple 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 least common multiple, 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 least common multiple, 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 least common multiple 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 least common multiple 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 least common multiple 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 least common multiple 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 least common multiple 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 least common multiple?", "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 least common multiple?", "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 least common multiple 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 least common multiple and how confident it is.", "questions": [ { "id": "claim-provenance-q01", "text": "What identifies and describes a claim about a least common multiple, 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 least common multiple, 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 least common multiple 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 least common multiple is retired without being erased.", "questions": [ { "id": "validity-and-supersession-q01", "text": "What identifies and describes the validity of a claim about a least common multiple, 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 least common multiple, 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 least common multiple 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 } } } }