{ "model": { "rank": 6796, "code": "thing-q905896", "model_id": "vr.tr.diophantine-equation", "name": "Diophantine equation", "purpose": "Enable an agent to identify a Diophantine equation, assess the evidence about its admissible solutions, and select justified transformations or solution methods.", "family": "Thing Registry", "category": "Information and virtual systems", "status": "research-draft", "kind": "thing", "plane": "INF", "domain": "INF.MED", "industry": "", "version": "", "url": "/models/thing/q905896/", "tier": 2, "score": 58, "payload": { "layer": "wikidata", "aliases": [ "polynomial–factorial diophantine equation", "Thue equation", "monkey and coconut problem", "Polynomial Diophantine equation", "Bachet's equation" ], "aliasCount": 5, "merged": 5, "knownIn": 58, "facets": null, "markers": [], "lexicalClass": "", "senseRank": null, "alsoRegisteredAs": null, "source": { "dataset": "wikidata", "item": "Q905896", "url": "https://www.wikidata.org/wiki/Q905896", "license": "CC0 1.0" } }, "research": { "vercy": "1.0-draft", "publication": { "status": "research-draft", "adjudicationStatus": "unreviewed", "publishableCanonical": false, "generatedAt": "2026-09-09T23:31:17Z", "providers": [ "Codex" ], "breadth": "recalled by Codex without web access - no source was read", "missingProviders": [], "pass": 2, "cost": { "grok": { "seconds": 17.5, "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: 01a08882-0ac6-7221-a6e3-3946bfc05a8a\n--------\nuser\nDescribe what is already known about one registered thing. Answer as JSON only, no prose around it.\n\nThing: Diophantine equation\nSense to describe: (none recorded)\nDomain code: INF.MED\nAlso known as: (none)\n\n\nContext for this batch of 1001 things:\n# Batch 007:", "usd": 0, "recall": true }, "codex": { "seconds": 58.9, "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: 01a08882-0ab7-7f13-b4bd-60987c075f3d\n--------\nuser\nYou are drafting a Vercy meta-model for one registered thing. Answer as JSON only, no prose around it.\n\nThing: Diophantine equation\nRegistry id: vr.tr.diophantine-equation\nPlane / domain: INF / INF.MED\nRegistry definition: (none recorded)\nNames folded into thi" } } }, "metaModel": { "id": "THING-Q905896", "registryId": "vr.tr.diophantine-equation", "name": "Diophantine equation", "version": "0.1.0-research.1", "entryKind": "thing", "family": "Thing Registry", "domain": [ "INF.MED" ], "status": "research-draft" }, "canonicalUrl": "https://ver.cy/models/thing/q905896/", "model": { "registry_id": "vr.tr.diophantine-equation", "name": "Diophantine equation", "purpose": "Enable an agent to identify a Diophantine equation, assess the evidence about its admissible solutions, and select justified transformations or solution methods.", "definition": "A Diophantine equation is a polynomial equation with integer coefficients whose solutions are required to be integers, with related formulations also studying rational solutions.", "scope_statement": "This model owns a polynomial equation with integer coefficients considered under explicitly stated arithmetic restrictions on its unknowns, together with its solution conditions, structural classification, and evidence of solvability; rational-point formulations and equation systems require explicit scope declarations.", "in_scope": [ "The defining polynomial equality, variables, coefficients, and parameters", "Admissible integer domains and additional solution restrictions", "Arithmetic structure relevant to classification and method selection", "Solution sets, equivalence conventions, and completeness claims", "Transformations, computational searches, and proof evidence" ], "out_of_scope": [ "Real or complex equations studied without arithmetic restrictions", "Diophantine approximation problems about closeness rather than exact equality", "Number theory as a discipline and its general research history", "Solver software implementation and computing infrastructure", "The full geometry of an associated variety beyond its role in the equation", "Application models that generate the equation, such as allocation or counting problems" ], "distinguishing_features": [ "Unknowns have explicit arithmetic domains, so a real-valued root alone does not establish an admissible solution.", "Satisfaction requires exact equality; a small numerical residual does not qualify.", "The core expression is polynomial with integer coefficients; exponential or other extended usages must be identified separately.", "The equation is distinct from its solution set: different presentations may define the same admissible tuples.", "An equation with fixed coefficients is distinguished from a parameterized family whose solvability depends on parameter values." ], "characteristics": [ { "name": "Defining equality", "kind": "category", "unit_or_values": "Exact symbolic equality, optionally normalized as P(x1,...,xn)=0", "why_it_matters": "Determines the mathematical constraint and enables exact substitution checks." }, { "name": "Number of unknowns", "kind": "measurement", "unit_or_values": "Nonnegative integer count, excluding fixed parameters", "why_it_matters": "Separates unknowns from family parameters and constrains applicable methods." }, { "name": "Polynomial degree", "kind": "measurement", "unit_or_values": "Total degree and degree in each unknown; undefined for the zero polynomial", "why_it_matters": "Supports structural classification while exposing exceptional parameter values that change degree." }, { "name": "Admissible domain", "kind": "category", "unit_or_values": "Integers, nonnegative integers, positive integers, or explicitly declared alternative arithmetic domains", "why_it_matters": "Changing the domain can change whether solutions exist and how many there are." }, { "name": "Additional restrictions", "kind": "category", "unit_or_values": "Unrestricted, primitive, nonzero, ordered, bounded, prescribed congruence classes, or explicit combinations", "why_it_matters": "Defines which exact roots count as solutions to the intended problem." }, { "name": "Parameter specification", "kind": "relation", "unit_or_values": "Parameter symbols linked to domains, fixed values, and quantifiers", "why_it_matters": "Prevents a result for one instance from being asserted for an entire family." }, { "name": "Established solution status", "kind": "state", "unit_or_values": "Unresolved, proven empty, proven nonempty with cardinality unresolved, proven finite nonempty, or proven infinite", "why_it_matters": "Separates mathematical conclusions from incomplete search outcomes." }, { "name": "Solution coverage", "kind": "state", "unit_or_values": "Unchecked candidates, verified examples, exhaustive within stated bounds, or globally complete description", "why_it_matters": "Prevents a list of discovered solutions from being mistaken for all solutions." }, { "name": "Solution identification convention", "kind": "category", "unit_or_values": "Literal tuples or equivalence under specified sign changes, permutations, or other justified actions", "why_it_matters": "Controls deduplication, representative selection, and solution counts." } ], "affordances": [ "Normalize and classify the equation while preserving its admissible solution conditions.", "Verify proposed solutions using exact arithmetic.", "Derive divisibility, parity, or congruence restrictions and test for obstructions.", "Choose a solution method whose hypotheses match the equation and domain.", "Enumerate solutions within explicit bounds and record the limits of the search.", "Attach proofs of existence, impossibility, finiteness, infinitude, or completeness to precisely scoped claims." ] }, "sources": [], "structure": { "bundles": [ { "id": "equation-and-domain", "name": "Equation and admissible domain", "description": "Establishes the exact equality and what counts as an admissible assignment.", "rationale": "The same symbolic equality can represent different Diophantine problems under different domains or restrictions.", "layers": [ { "id": "symbolic-definition", "name": "Symbolic definition", "description": "Separates the defining polynomial, unknowns, and parameters.", "findings": [ { "id": "exact-polynomial-presentation", "name": "Exact polynomial presentation", "description": "Record the equality without approximate coefficients or ambiguous symbol roles.", "questions": [ { "text": "What exact polynomial equality defines the equation, and which symbols are unknowns rather than fixed parameters?", "kind": "definition", "id": "exact-polynomial-presentation-q01" }, { "text": "Are all coefficients integers, or does the presentation require a justified conversion or an explicitly broader convention?", "kind": "boundary", "id": "exact-polynomial-presentation-q02" } ] } ] }, { "id": "admissibility-conditions", "name": "Admissibility conditions", "description": "Defines the arithmetic domain and any exclusions imposed on solutions.", "findings": [ { "id": "permitted-assignments", "name": "Permitted assignments", "description": "Make positivity, primitivity, nonzero requirements, and other restrictions explicit.", "questions": [ { "text": "Does each unknown range over all integers, nonnegative integers, positive integers, or another declared domain?", "kind": "definition", "id": "permitted-assignments-q01" }, { "text": "Must solutions satisfy coprimality, ordering, nonzero, or other conditions beyond the equality?", "kind": "boundary", "id": "permitted-assignments-q02" } ] } ] } ] }, { "id": "arithmetic-structure", "name": "Arithmetic structure", "description": "Records features of the polynomial that guide analysis.", "rationale": "Degree, factorization, homogeneity, and congruence behavior determine which deductions and methods are relevant.", "layers": [ { "id": "structural-classification", "name": "Structural classification", "description": "Identifies the equation's form and exceptional cases.", "findings": [ { "id": "method-relevant-form", "name": "Method-relevant form", "description": "Describe structural properties without assuming a named family guarantees a solution method.", "questions": [ { "text": "What are the total degree, degrees in individual unknowns, factorization, and homogeneity properties?", "kind": "measurement", "id": "method-relevant-form-q01" }, { "text": "Which parameter values make the polynomial vanish identically, become constant, factor further, or drop in degree?", "kind": "boundary", "id": "method-relevant-form-q02" } ] } ] }, { "id": "arithmetic-obstructions", "name": "Arithmetic obstructions", "description": "Tracks necessary restrictions obtained from divisibility and congruences.", "findings": [ { "id": "necessary-local-conditions", "name": "Necessary arithmetic conditions", "description": "Distinguish conditions that rule out solutions from tests that merely fail to rule them out.", "questions": [ { "text": "Which divisibility, parity, or residue-class conditions must every admissible solution satisfy?", "kind": "definition", "id": "necessary-local-conditions-q01" }, { "text": "Does a failed congruence test prove impossibility, and what remains unresolved when the tested congruences admit solutions?", "kind": "action", "id": "necessary-local-conditions-q02" } ] } ] } ] }, { "id": "solution-set-and-coverage", "name": "Solution set and coverage", "description": "Defines how solutions are represented, verified, counted, and described.", "rationale": "Finding a tuple, proving existence, and describing all solutions are different achievements.", "layers": [ { "id": "solution-representation", "name": "Solution representation", "description": "Sets exact validation and identification conventions.", "findings": [ { "id": "verified-solution-identity", "name": "Verified solution identity", "description": "Record exact tuples and any justified equivalence between them.", "questions": [ { "text": "Does exact substitution verify the equality and every additional admissibility condition for each reported tuple?", "kind": "action", "id": "verified-solution-identity-q01" }, { "text": "Are sign-related or permuted tuples counted separately, and which transformations actually preserve this equation and its domain?", "kind": "boundary", "id": "verified-solution-identity-q02" } ] } ] }, { "id": "global-solution-description", "name": "Global solution description", "description": "Separates examples, bounded enumerations, and complete characterizations.", "findings": [ { "id": "cardinality-and-completeness", "name": "Cardinality and completeness", "description": "Attach evidence to assertions about absence, number, or full coverage of solutions.", "questions": [ { "text": "What establishes that the admissible solution set is empty, nonempty, finite, or infinite?", "kind": "provenance", "id": "cardinality-and-completeness-q01" }, { "text": "If a list, recurrence, or parameterization is supplied, what proves it covers every admissible solution, including exceptional cases?", "kind": "provenance", "id": "cardinality-and-completeness-q02" } ] } ] } ] }, { "id": "transformations-and-methods", "name": "Transformations and methods", "description": "Connects the equation to justified reformulations and applicable techniques.", "rationale": "A transformation may lose solutions or introduce extraneous ones, and a method may require hypotheses that the equation does not satisfy.", "layers": [ { "id": "solution-preserving-reformulation", "name": "Solution-preserving reformulation", "description": "Records the correspondence between original and transformed problems.", "findings": [ { "id": "transformation-contract", "name": "Transformation contract", "description": "State the domain conditions and recovery rules for substitutions or algebraic reductions.", "questions": [ { "text": "How does each substitution, factorization step, or division map admissible solutions into the transformed problem?", "kind": "action", "id": "transformation-contract-q01" }, { "text": "Is the transformation reversible over the stated domain, and which zero cases, divisibility conditions, or extraneous candidates require separate treatment?", "kind": "boundary", "id": "transformation-contract-q02" } ] } ] }, { "id": "method-applicability", "name": "Method applicability", "description": "Matches techniques to proven structural conditions and intended outputs.", "findings": [ { "id": "justified-method-selection", "name": "Justified method selection", "description": "Choose techniques according to their hypotheses and the claim they can establish.", "questions": [ { "text": "Which hypotheses justify using a linear divisibility argument, factorization, descent, a Pell-type method, or an arithmetic-geometric method here?", "kind": "action", "id": "justified-method-selection-q01" }, { "text": "Will the selected method produce examples, an impossibility proof, a bound, or a complete solution description?", "kind": "action", "id": "justified-method-selection-q02" } ] } ] } ] }, { "id": "evidence-and-computation", "name": "Evidence and computation", "description": "Maintains the scope and reliability of mathematical and computational claims.", "rationale": "An unsuccessful search does not establish nonexistence, and a cited theorem supports only conclusions within its hypotheses.", "layers": [ { "id": "bounded-search", "name": "Bounded search", "description": "Makes finite exploration reproducible and its coverage explicit.", "findings": [ { "id": "search-coverage-record", "name": "Search coverage record", "description": "Record the enumerated region, arithmetic checks, pruning rules, and completion state.", "questions": [ { "text": "What coordinate bounds or height bound define the searched region, and was every admissible candidate in that region checked?", "kind": "measurement", "id": "search-coverage-record-q01" }, { "text": "What exact arithmetic and justified pruning rules were used, and is there a separate proof that every possible solution lies within the searched region?", "kind": "provenance", "id": "search-coverage-record-q02" } ] } ] }, { "id": "claim-validation", "name": "Claim validation", "description": "Links conclusions to proofs, sources, and unresolved assumptions.", "findings": [ { "id": "scoped-proof-evidence", "name": "Scoped proof evidence", "description": "Keep verified conclusions distinct from conjectures and conditional results.", "questions": [ { "text": "Which read source, inspectable proof, or checkable certificate supports each existence or completeness claim?", "kind": "provenance", "id": "scoped-proof-evidence-q01" }, { "text": "Does the evidence apply to this exact domain and parameter range, and does it depend on any unproved assumption?", "kind": "boundary", "id": "scoped-proof-evidence-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": [ "Terminology varies over whether rational solutions are included in the definition or treated as a related formulation; the solution domain should be explicit.", "The listed kinds overlap and do not form a mutually exclusive classification.", "The supplied domain code INF.MED should be checked against the registry taxonomy: this thing is a mathematical concept, independent of the medium in which an equation is written." ], "questions": [ { "id": "evidence-confidence-notes-q01", "text": "Which of these check these first hold for the sense of Diophantine equation 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": [ "Linear Diophantine equations", "Quadratic Diophantine equations", "Pell equations", "Thue equations", "Diophantine equations defining elliptic curves", "Homogeneous Diophantine equations" ], "questions": [ { "id": "evidence-kinds-q01", "text": "Which of these kinds and varieties hold for the sense of Diophantine equation 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": [ "Expressing exact counting, allocation and divisibility constraints in integers.", "Finding integer-sided geometric configurations, such as Pythagorean triples.", "Studying integer and rational points on algebraic curves.", "Representing computation in mathematical proofs about decidability." ], "questions": [ { "id": "evidence-real-world-use-q01", "text": "Which of these real-world use hold for the sense of Diophantine equation 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": "Total polynomial degree", "typical_range": "Positive integer for a nonconstant equation; no universal upper bound", "unit": "dimensionless" }, { "quantity": "Number of unknowns", "typical_range": "Positive integer; no universal upper bound", "unit": "count" }, { "quantity": "Number of integer solutions", "typical_range": "Zero, finitely many, or infinitely many", "unit": "count" } ], "questions": [ { "id": "evidence-measurements-q01", "text": "Which of these typical measurements hold for the sense of Diophantine equation 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": [ "Treating real or rational solutions as integer solutions without checking the required domain.", "Concluding that no solution exists because a bounded search found none.", "Assuming that solutions modulo every positive integer guarantee an integer solution.", "Expecting an algorithm that decides integer solvability for every polynomial equation; Hilbert's tenth problem establishes that no such general algorithm exists.", "Using transformations that introduce solutions or discard cases without checking their reversibility over integers." ], "questions": [ { "id": "evidence-failure-modes-and-hazards-q01", "text": "Which of these failure modes and hazards hold for the sense of Diophantine equation 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": "Polynomial equation", "difference": "A polynomial equation does not by itself require integer solutions; the arithmetic restriction distinguishes the Diophantine problem." }, { "name": "Congruence", "difference": "A congruence requires equality modulo a specified modulus, whereas a Diophantine equation requires exact equality." }, { "name": "Integer programming", "difference": "Integer programming typically optimizes an objective subject to integer constraints; a Diophantine equation specifies an equality whose integer solutions are sought." }, { "name": "Diophantine approximation", "difference": "Diophantine approximation studies how closely numbers can be approximated by rationals and related arithmetic bounds, rather than only exact polynomial equalities." }, { "name": "Exponential Diophantine equation", "difference": "An exponential Diophantine equation permits unknowns in exponents and therefore extends beyond the strict polynomial definition." } ], "questions": [ { "id": "evidence-neighbours-q01", "text": "Which of these neighbouring kinds and how to tell them apart hold for the sense of Diophantine equation this model covers, and on what evidence?", "kind": "provenance" } ] } ] } ] } ] }, "openQuestions": [ "Does the registry intend the strict polynomial-over-integers sense, or also exponential and other generalized Diophantine equations?", "Should rational solutions be owned by this model or represented as a related arithmetic-point problem with an explicit conversion?", "Are systems of Diophantine equations instances of this entry or a separately registered concept?", "Which existing Vercy world model, if any, already owns this concept and should serve as its single publication?", "Which authoritative sources and proof examples should anchor the researched publication's definitions and method boundaries?" ], "statistics": { "bundles": 6, "layers": 11, "findings": 16, "questions": 26 } }, "draft": { "generator": "vr.draft.v3", "status": "draft-generated", "researched": false, "archetype": "work, medium or creative form", "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 Diophantine equation, record what state it is in, and decide what may be done with it.", "whatItIs": "Enable an agent to identify a Diophantine equation, assess the evidence about its admissible solutions, and select justified transformations or solution methods.", "characteristics": { "substance": "information", "origin": "conceptual", "agency": "inert" }, "whatYouCanDoWithIt": [ "read and interpreted", "observed and measured" ], "distinguishingFeatures": [ "Names folded into this entry, which a task may need to split apart again: polynomial–factorial diophantine equation, Thue equation, monkey and coconut problem, Polynomial Diophantine equation, Bachet's equation.", "5 finer distinctions are held as aliases rather than separate entries, because telling them apart needs a task that asks for it.", "Described in 58 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 Diophantine equation, and on what evidence are they told apart?" ], "whatItIsMadeOf": "content that has to be carried by something else", "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": [ "read it and act on what it says", "observe it, measure it, record its state" ], "howItIsRecognised": [ "What is seen is a copy or a performance, not the work. Recognising the work means recognising the content through whatever is carrying it." ], "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": [ "polynomial–factorial diophantine equation", "Thue equation", "monkey and coconut problem", "Polynomial Diophantine equation", "Bachet's equation" ] } ], "standing": "Described in 58 Wikipedia languages, which measures how widely it is written about rather than how important or how common it is. 5 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 Diophantine equation from another, and a Diophantine equation 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 Diophantine equation, 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 Diophantine equation, 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 Diophantine equation 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 Diophantine equation, 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 Diophantine equation, 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 Diophantine equation 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 Diophantine equation 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 Diophantine equation, 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 Diophantine equation, 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 Diophantine equation 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 Diophantine equation from the things most often confused with it.", "questions": [ { "id": "distinguishing-features-q01", "text": "What identifies and describes what distinguishes a Diophantine equation, 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 Diophantine equation, 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 Diophantine equation 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 Diophantine equation 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 Diophantine equation between them.", "questions": [ { "id": "stages-and-transitions-q01", "text": "What identifies and describes the lifecycle of a Diophantine equation, 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 Diophantine equation, 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 Diophantine equation 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 Diophantine equation, how often and by whom.", "findings": [ { "id": "observation-record", "name": "Observation record", "description": "How an observation of a Diophantine equation 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 Diophantine equation, 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 Diophantine equation, 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 Diophantine equation is known, and what must it refuse?", "kind": "action", "answer_data": [ "permitted actions", "preconditions", "refusals", "escalation" ] } ] } ] } ] }, { "id": "content-and-access", "name": "Content, encoding and access", "description": "What a Diophantine equation says, how it is encoded and who may read it.", "rationale": "An informational thing carries content that can be copied, versioned and withheld, none of which its physical carrier explains.", "layers": [ { "id": "content-and-encoding", "name": "Content and encoding", "description": "The content itself, its format and its language.", "findings": [ { "id": "content-and-format", "name": "Content, format and language", "description": "What a Diophantine equation contains and in what form it is held.", "questions": [ { "id": "content-and-format-q01", "text": "What identifies and describes the content of a Diophantine equation, and in what units or vocabulary?", "kind": "definition", "answer_data": [ "identifiers", "types and classes", "values with units", "explicit unknowns" ] }, { "id": "content-and-format-q02", "text": "Who or what asserted this about the content of a Diophantine equation, by which method, and when was it true?", "kind": "provenance", "answer_data": [ "authority", "method", "evidence", "event time", "knowledge time" ] }, { "id": "content-and-format-q03", "text": "What may an agent decide or do once the content of a Diophantine equation is known, and what must it refuse?", "kind": "action", "answer_data": [ "permitted actions", "preconditions", "refusals", "escalation" ] } ] } ] }, { "id": "access-and-rights", "name": "Access, rights and retention", "description": "Who may read, copy or change it, and for how long it is kept.", "findings": [ { "id": "access-rules", "name": "Access rules and retention", "description": "The permissions attached to a Diophantine equation and the period it survives.", "questions": [ { "id": "access-rules-q01", "text": "What identifies and describes access to a Diophantine equation, and in what units or vocabulary?", "kind": "definition", "answer_data": [ "identifiers", "types and classes", "values with units", "explicit unknowns" ] }, { "id": "access-rules-q02", "text": "Who or what asserted this about access to a Diophantine equation, by which method, and when was it true?", "kind": "provenance", "answer_data": [ "authority", "method", "evidence", "event time", "knowledge time" ] }, { "id": "access-rules-q03", "text": "What may an agent decide or do once access to a Diophantine equation is known, and what must it refuse?", "kind": "action", "answer_data": [ "permitted actions", "preconditions", "refusals", "escalation" ] } ] } ] } ] }, { "id": "work-and-manifestation", "name": "Work, version and copy", "description": "Which level of Diophantine equation a statement is about.", "rationale": "The work, the edition, the file and the copy in hand are four things; rights and content attach to different ones.", "layers": [ { "id": "levels", "name": "Levels of the thing", "description": "Work, expression, manifestation and item, in plain terms.", "findings": [ { "id": "level-rules", "name": "What belongs at each level", "description": "Which facts hold for the work and which only for one copy.", "questions": [ { "id": "level-rules-q01", "text": "For Diophantine equation, which facts belong to the work itself, which to a version, and which to a single copy?", "kind": "boundary" }, { "id": "level-rules-q02", "text": "What identifier exists at each level, and which one is being cited?", "kind": "definition" } ] } ] }, { "id": "versions", "name": "Versions, editions and variants", "description": "How versions differ and which is canonical to whom.", "findings": [ { "id": "version-record", "name": "Versions and canonicity", "description": "Differences that matter and who calls one authoritative.", "questions": [ { "id": "version-record-q01", "text": "Which versions or editions of Diophantine equation exist, and how do they differ substantively?", "kind": "definition" }, { "id": "version-record-q02", "text": "Who treats which version as authoritative, and for what purpose?", "kind": "provenance" } ] } ] } ] }, { "id": "authorship-and-rights", "name": "Authorship, rights and permitted use", "description": "Who made Diophantine equation and what may be done with it.", "rationale": "Rights are jurisdictional, time-limited and attached to a level, and an agent that ignores that will copy what it may not.", "layers": [ { "id": "authorship", "name": "Authorship and contribution", "description": "Who contributed what, and in what capacity.", "findings": [ { "id": "contribution-record", "name": "Contributors and roles", "description": "The people and bodies behind it, with their roles.", "questions": [ { "id": "contribution-record-q01", "text": "Who authored or contributed to Diophantine equation, in what roles, and how is that attested?", "kind": "provenance" }, { "id": "contribution-record-q02", "text": "Where authorship is disputed or anonymous, what is recorded instead?", "kind": "boundary" } ] } ] }, { "id": "rights", "name": "Rights and permissions", "description": "Which rights subsist, where, until when, and what they permit.", "findings": [ { "id": "rights-record", "name": "Rights, term and permitted acts", "description": "The regime in force and what it allows.", "questions": [ { "id": "rights-record-q01", "text": "What rights subsist in Diophantine equation, in which jurisdictions, and until when?", "kind": "definition" }, { "id": "rights-record-q02", "text": "Which acts are permitted without further permission, and which must an agent refuse?", "kind": "action" } ] } ] } ] }, { "id": "provenance-and-evidence", "name": "Provenance, evidence and time", "description": "Where every claim about a Diophantine equation 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 Diophantine equation and how confident it is.", "questions": [ { "id": "claim-provenance-q01", "text": "What identifies and describes a claim about a Diophantine equation, 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 Diophantine equation, 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 Diophantine equation 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 Diophantine equation is retired without being erased.", "questions": [ { "id": "validity-and-supersession-q01", "text": "What identifies and describes the validity of a claim about a Diophantine equation, 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 Diophantine equation, 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 Diophantine equation is known, and what must it refuse?", "kind": "action", "answer_data": [ "permitted actions", "preconditions", "refusals", "escalation" ] } ] } ] } ] } ] }, "statistics": { "bundles": 6, "layers": 12, "findings": 14, "questions": 38 } } } }