{ "model": { "rank": 3196, "code": "thing-q121416", "model_id": "vr.tr.discrete-mathematics", "name": "discrete mathematics", "purpose": "Enable an agent to recognise discrete mathematics as a field, assess the scope and justification of its knowledge, and select appropriate discrete representations and reasoning methods.", "family": "Thing Registry", "category": "Information and virtual systems", "status": "research-draft", "kind": "thing", "plane": "INF", "domain": "INF.KNW", "industry": "", "version": "", "url": "/models/thing/q121416/", "tier": 2, "score": 89, "payload": { "layer": "wikidata", "aliases": [], "aliasCount": 0, "merged": 0, "knownIn": 89, "facets": null, "markers": [], "lexicalClass": "", "senseRank": null, "alsoRegisteredAs": null, "source": { "dataset": "wikidata", "item": "Q121416", "url": "https://www.wikidata.org/wiki/Q121416", "license": "CC0 1.0" } }, "research": { "vercy": "1.0-draft", "publication": { "status": "research-draft", "adjudicationStatus": "unreviewed", "publishableCanonical": false, "generatedAt": "2026-09-07T14:06:53Z", "providers": [ "Codex" ], "breadth": "recalled by Codex without web access - no source was read", "missingProviders": [], "pass": 2, "cost": { "grok": { "seconds": 22.8, "error": "Reading additional input from stdin...\nOpenAI Codex v0.153.3\n--------\nworkdir: R:\\02_PROJECTS\\02_Meta_Models_Platforms\\Ver.cy\\current\\thing-registry-backlog\nmodel: gpt-6-astra\nprovider: openai\napproval: never\nsandbox: read-only\nreasoning effort: none\nreasoning summaries: none\nsession id: 01a07c30-34da-7b01-8262-1b55f71795dd\n--------\nuser\nDescribe what is already known about one registered thing. Answer as JSON only, no prose around it.\n\nThing: discrete mathematics\nSense to describe: (none recorded)\nDomain code: INF.KNW\nAlso known as: (none)\n\n\nContext for this batch of 546 things:\n# Batch 003: ", "usd": 0, "recall": true }, "codex": { "seconds": 84.9, "error": "Reading additional input from stdin...\nOpenAI Codex v0.153.3\n--------\nworkdir: R:\\02_PROJECTS\\02_Meta_Models_Platforms\\Ver.cy\\current\\thing-registry-backlog\nmodel: gpt-6-astra\nprovider: openai\napproval: never\nsandbox: read-only\nreasoning effort: none\nreasoning summaries: none\nsession id: 01a07c30-34de-7e10-885b-04914a4fd76a\n--------\nuser\nYou are drafting a Vercy meta-model for one registered thing. Answer as JSON only, no prose around it.\n\nThing: discrete mathematics\nRegistry id: vr.tr.discrete-mathematics\nPlane / domain: INF / INF.KNW\nRegistry definition: (none recorded)\nNames folded into thi" } } }, "metaModel": { "id": "THING-Q121416", "registryId": "vr.tr.discrete-mathematics", "name": "discrete mathematics", "version": "0.1.0-research.1", "entryKind": "thing", "family": "Thing Registry", "domain": [ "INF.KNW" ], "status": "research-draft" }, "canonicalUrl": "https://ver.cy/models/thing/q121416/", "model": { "registry_id": "vr.tr.discrete-mathematics", "name": "discrete mathematics", "purpose": "Enable an agent to recognise discrete mathematics as a field, assess the scope and justification of its knowledge, and select appropriate discrete representations and reasoning methods.", "definition": "Discrete mathematics is the field of mathematics concerned with discrete structures, including finite sets, integers, graphs and finite sequences, studied through methods such as logical proof, combinatorial counting and recursive construction.", "scope_statement": "This model owns discrete mathematics as a field of knowledge concerned with discrete structures and their properties, including its subject areas, proof methods, computational connections and convention-dependent boundaries; it does not own individual practitioners, publications or software implementations.", "in_scope": [ "Discrete structures such as graphs, finite sequences, sets, relations, partially ordered sets and combinatorial configurations", "Questions of existence, enumeration, structure, extremal behaviour and discrete optimisation", "Proof techniques including induction, bijection, invariants, contradiction and combinatorial probabilistic arguments", "Relationships between mathematical results, constructive procedures and computational complexity", "Declared curricular, research and classification conventions that determine the field's boundaries" ], "out_of_scope": [ "Continuous analysis and differential equations as independent fields, while retaining their use in discrete problems", "The full scope of logic, number theory, algebra and probability beyond their identified discrete-mathematical contributions", "Software engineering and concrete implementations of algorithms", "Empirical application domains whose situations are represented using discrete structures", "Practitioners, departments, societies and publications as independently modelled people, organisations or information objects" ], "distinguishing_features": [ "A problem centrally concerns distinguishable elements and combinatorial relationships, rather than merely using digitally stored numbers.", "The subject includes infinite discrete structures; finite size alone neither defines membership nor establishes the field's boundary.", "A contribution may establish existence, counting or structural properties without supplying an algorithm, distinguishing the field from a purely computational treatment.", "An application enters this model through its discrete abstraction and mathematical questions, rather than through the application domain's full empirical behaviour.", "Membership of neighbouring subjects such as logic or number theory is recorded against an explicit curricular or research convention, rather than assumed from the label alone." ], "characteristics": [ { "name": "Boundary convention", "kind": "category", "unit_or_values": "Named curricular, research, bibliographic or institutional convention, with version or date where available", "why_it_matters": "Introductory courses and research communities can use discrete mathematics with different breadth." }, { "name": "Structure family", "kind": "category", "unit_or_values": "Graphs and hypergraphs; sets and relations; orders; sequences and words; combinatorial configurations; other specified discrete structures", "why_it_matters": "Determines which properties, representations and methods are relevant." }, { "name": "Underlying size regime", "kind": "category", "unit_or_values": "Finite; countably infinite; other explicitly justified infinite setting; unspecified", "why_it_matters": "Controls whether finite enumeration and finite-case arguments apply." }, { "name": "Identification rule", "kind": "category", "unit_or_values": "Labelled objects; equality of representations; isomorphism classes; equivalence under a specified action or relation", "why_it_matters": "Counting and classification change when equivalent representations count as the same object." }, { "name": "Mathematical objective", "kind": "category", "unit_or_values": "Existence; enumeration; classification; extremal bound; optimisation; construction; decidability; complexity", "why_it_matters": "Identifies what would constitute a successful result." }, { "name": "Justification status", "kind": "state", "unit_or_values": "Definition; conjecture; proved under stated assumptions; computationally checked over a stated range; refuted; unresolved", "why_it_matters": "Prevents examples and bounded computations from being treated as general proofs." }, { "name": "Constructive and computational content", "kind": "relation", "unit_or_values": "Links to constructions or algorithms, with input model, correctness conditions and any established resource bounds", "why_it_matters": "Separates mathematical existence from an executable or efficient way to obtain an object." }, { "name": "Problem size parameters", "kind": "measurement", "unit_or_values": "Dimensionless counts such as vertices n, edges m, sequence length or input bit length, each explicitly defined", "why_it_matters": "Makes bounds and complexity statements interpretable and comparable." } ], "affordances": [ "Classify a topic or problem within discrete mathematics using an explicit boundary convention.", "Translate a stated problem into a graph, relation, order, sequence or other discrete structure and record what the translation preserves.", "Select proof or counting methods suited to the structure, assumptions and desired result.", "Assess whether a claim is supported by proof, a restricted computation, examples or a counterexample.", "Identify whether a result supplies existence, an explicit construction or an algorithm with established resource requirements.", "Connect topics to verified classifications, curricula and research sources while recording disputed or overlapping membership." ] }, "sources": [], "structure": { "bundles": [ { "id": "field-scope-and-placement", "name": "Field scope and placement", "description": "Locate discrete mathematics within mathematical knowledge using explicit conventions and evidence.", "rationale": "The field has overlapping research and curricular boundaries that cannot be inferred from its name alone.", "layers": [ { "id": "subject-boundaries", "name": "Subject boundaries", "description": "Determine which discrete subjects the selected convention includes.", "findings": [ { "id": "core-and-overlapping-subjects", "name": "Core and overlapping subjects", "description": "Record the treatment of combinatorics, graph theory and neighbouring areas such as logic, number theory, algebra and theoretical computer science.", "questions": [ { "text": "Under the chosen convention, which subjects constitute discrete mathematics and which are supporting or overlapping fields?", "kind": "boundary", "id": "core-and-overlapping-subjects-q01" }, { "text": "Does the intended scope describe an introductory curriculum, a research field or another explicitly named use?", "kind": "definition", "id": "core-and-overlapping-subjects-q02" } ] } ] }, { "id": "classification-and-community-evidence", "name": "Classification and community evidence", "description": "Connect field placement to documented classifications and institutional usage.", "findings": [ { "id": "documented-field-placement", "name": "Documented field placement", "description": "Record verified classification mappings and the scope statements of relevant curricula, handbooks, journals or learned societies.", "questions": [ { "text": "Which inspected classification scheme and edition places the relevant discrete subjects, and does it treat them as one field or several categories?", "kind": "provenance", "id": "documented-field-placement-q01" }, { "text": "Which defining handbook, curriculum or research-community scope statement supports the proposed boundary?", "kind": "provenance", "id": "documented-field-placement-q02" } ] } ] } ] }, { "id": "discrete-structures-and-representations", "name": "Discrete structures and representations", "description": "Specify the mathematical objects and representation choices on which discrete reasoning operates.", "rationale": "Apparently similar problems can differ because their objects, admissible relations or equality conventions differ.", "layers": [ { "id": "objects-and-relations", "name": "Objects and relations", "description": "Identify the elements and structural rules of the discrete setting.", "findings": [ { "id": "structure-signature", "name": "Structure signature", "description": "Record the chosen structure family, its defining constraints and its finite or infinite setting.", "questions": [ { "text": "Are the objects graphs, hypergraphs, orders, relations, words or another discrete structure, and what conditions define admissible instances?", "kind": "definition", "id": "structure-signature-q01" }, { "text": "Is the underlying set finite or infinite, and which arguments depend on that distinction?", "kind": "boundary", "id": "structure-signature-q02" } ] } ] }, { "id": "equivalence-and-encoding", "name": "Equivalence and encoding", "description": "Separate mathematical identity from labels and implementation representations.", "findings": [ { "id": "representation-sensitive-claims", "name": "Representation-sensitive claims", "description": "Record whether objects are distinguished by labels, isomorphism or another equivalence, and how encodings preserve relevant structure.", "questions": [ { "text": "When do two labelled graphs, sequences or configurations count as the same mathematical object?", "kind": "definition", "id": "representation-sensitive-claims-q01" }, { "text": "Which properties and size parameters are preserved or changed by the selected encoding?", "kind": "measurement", "id": "representation-sensitive-claims-q02" } ] } ] } ] }, { "id": "combinatorial-questions-and-results", "name": "Combinatorial questions and results", "description": "Distinguish the main questions asked about discrete structures and the forms their answers take.", "rationale": "An exact count, existence theorem, extremal bound and optimisation solution answer different questions and support different actions.", "layers": [ { "id": "existence-and-enumeration", "name": "Existence and enumeration", "description": "Specify whether a problem asks for admissible objects, their number or their classification.", "findings": [ { "id": "existence-counting-and-classification-target", "name": "Existence, counting and classification target", "description": "Record the admissibility conditions and whether the requested answer is a witness, count, recurrence, generating function, estimate or classification.", "questions": [ { "text": "Is the task to prove existence, construct an example, count objects or classify them up to a stated equivalence?", "kind": "definition", "id": "existence-counting-and-classification-target-q01" }, { "text": "For enumeration, is the result exact or asymptotic, and over which parameters and admissible objects does it range?", "kind": "measurement", "id": "existence-counting-and-classification-target-q02" } ] } ] }, { "id": "extremal-and-structural-behaviour", "name": "Extremal and structural behaviour", "description": "Capture bounds, optimal configurations and structural consequences.", "findings": [ { "id": "bounds-and-attaining-configurations", "name": "Bounds and attaining configurations", "description": "Specify the constrained family, quantity being bounded and conditions under which equality or an optimum is attained.", "questions": [ { "text": "What discrete quantity is minimised or maximised, and which constraints define the feasible structures?", "kind": "definition", "id": "bounds-and-attaining-configurations-q01" }, { "text": "Is the bound tight, and are attaining configurations known for all stated parameter values or only some?", "kind": "measurement", "id": "bounds-and-attaining-configurations-q02" } ] } ] } ] }, { "id": "proof-and-epistemic-status", "name": "Proof and epistemic status", "description": "Record how discrete-mathematical claims are justified and where their validity ends.", "rationale": "Finite examples often suggest patterns, but a field model must distinguish those patterns from established statements.", "layers": [ { "id": "proof-strategy-and-assumptions", "name": "Proof strategy and assumptions", "description": "Connect a claim to its proof mechanism and required hypotheses.", "findings": [ { "id": "discrete-proof-obligations", "name": "Discrete proof obligations", "description": "Record the assumptions and critical steps of induction, bijective counting, invariants, extremal arguments or probabilistic existence proofs.", "questions": [ { "text": "Which proof mechanism establishes the claim, and what are its essential obligations, such as an induction base and step or a bijection's inverse?", "kind": "definition", "id": "discrete-proof-obligations-q01" }, { "text": "Which inspected proof source supports the claim, and what hypotheses or exceptional cases does it require?", "kind": "provenance", "id": "discrete-proof-obligations-q02" } ] } ] }, { "id": "computational-evidence-and-counterexamples", "name": "Computational evidence and counterexamples", "description": "Assess what enumeration, search and machine-assisted reasoning actually establish.", "findings": [ { "id": "verification-coverage", "name": "Verification coverage", "description": "Separate sampled examples, exhaustive bounded checks, independently checkable certificates and justified reductions to finite verification.", "questions": [ { "text": "Which instances were checked, and what establishes coverage of the claimed finite range or reduction?", "kind": "measurement", "id": "verification-coverage-q01" }, { "text": "What additional proof, certificate verification or counterexample search is needed before the claim can support the proposed use?", "kind": "action", "id": "verification-coverage-q02" } ] } ] } ] }, { "id": "construction-computation-and-application", "name": "Construction, computation and application", "description": "Connect discrete knowledge to usable procedures and defensible abstractions of other problems.", "rationale": "Agents need to know both whether an object can be obtained and whether conclusions about the abstraction transfer to the original task.", "layers": [ { "id": "constructive-and-algorithmic-consequences", "name": "Constructive and algorithmic consequences", "description": "Distinguish existence from construction and evaluate computational requirements where established.", "findings": [ { "id": "existence-to-procedure", "name": "Existence to procedure", "description": "Record whether a result yields an explicit construction or algorithm and what guarantees accompany it.", "questions": [ { "text": "Does the result establish existence only, or supply a procedure that produces an admissible object?", "kind": "action", "id": "existence-to-procedure-q01" }, { "text": "For an associated algorithm, what input encoding, size parameters, computational model and proven resource bounds apply?", "kind": "measurement", "id": "existence-to-procedure-q02" } ] } ] }, { "id": "application-abstraction-and-transfer", "name": "Application abstraction and transfer", "description": "Record how external tasks become discrete problems and which conclusions transfer back.", "findings": [ { "id": "discrete-model-fidelity", "name": "Discrete model fidelity", "description": "Make explicit the interpretation of graph vertices, edges, order relations or combinatorial constraints in the application.", "questions": [ { "text": "What do the discrete elements and relations represent, and which relevant features of the original task are omitted?", "kind": "boundary", "id": "discrete-model-fidelity-q01" }, { "text": "Which assumptions must be checked before a colouring, matching, ordering or other discrete solution can guide action in the application?", "kind": "action", "id": "discrete-model-fidelity-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 listed kinds are overlapping subject areas, not a universally agreed partition; field boundaries depend on disciplinary and curricular conventions.", "Discrete does not mean finite: infinite graphs, integer structures and other infinite discrete objects are included.", "MSC codes identify component subjects rather than a single classification encompassing all discrete mathematics; these statements are recalled, not source-verified." ], "questions": [ { "id": "evidence-confidence-notes-q01", "text": "Which of these check these first hold for the sense of discrete mathematics 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": [ "Combinatorics", "Graph theory", "Elementary number theory", "Order theory", "Discrete geometry", "Discrete probability" ], "questions": [ { "id": "evidence-kinds-q01", "text": "Which of these kinds and varieties hold for the sense of discrete mathematics 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": "Mathematics Subject Classification (MSC 2020)", "value_or_pattern": "05", "note": "Combinatorics; covers a central part of discrete mathematics, not the whole field." }, { "scheme": "Mathematics Subject Classification (MSC 2020)", "value_or_pattern": "05C", "note": "Graph theory; a major area within discrete mathematics." }, { "scheme": "Mathematics Subject Classification (MSC 2020)", "value_or_pattern": "11", "note": "Number theory; overlaps discrete mathematics but also includes methods and topics beyond its usual curricular scope." } ], "questions": [ { "id": "evidence-identifiers-q01", "text": "Which of these identifiers and schemes hold for the sense of discrete mathematics 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": [ "Designing algorithms and proving their correctness and complexity bounds.", "Modelling communication, transport and dependency networks with graphs.", "Constructing cryptographic systems and error-correcting codes.", "Solving scheduling, matching, allocation and routing problems.", "Specifying and verifying software and digital logic using formal reasoning." ], "questions": [ { "id": "evidence-real-world-use-q01", "text": "Which of these real-world use hold for the sense of discrete mathematics 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": [ "Counting arguments can overcount or undercount when cases overlap or omit possibilities.", "Inductive proofs can fail through missing base cases or an invalid induction step.", "Graph models can give misleading results when direction, weights or multiple edges are represented incorrectly.", "Finite problems can remain computationally infeasible because their search spaces grow rapidly.", "Discrete models can misrepresent applications when relevant continuous behaviour is omitted." ], "questions": [ { "id": "evidence-failure-modes-and-hazards-q01", "text": "Which of these failure modes and hazards hold for the sense of discrete mathematics this model covers, and on what evidence?", "kind": "provenance" } ] }, { "id": "evidence-regional-variation", "name": "Regional variation", "description": "Recalled without web access and unsourced; every item is a lead to verify.", "evidence": [ "Curricular scope varies across institutions: computer science courses often emphasize logic, graphs, counting and recurrences, while mathematics courses may include more number theory or discrete geometry." ], "questions": [ { "id": "evidence-regional-variation-q01", "text": "Which of these regional variation hold for the sense of discrete mathematics 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": "Combinatorics", "difference": "Focuses on counting, arranging and analysing discrete configurations; it is a major constituent of the broader field." }, { "name": "Graph theory", "difference": "Studies vertices and their connecting edges specifically; discrete mathematics includes many structures that are not graphs." }, { "name": "Theoretical computer science", "difference": "Centres on computation, algorithms and computational resources; discrete mathematics studies discrete structures whether or not computation is the objective." }, { "name": "Mathematical logic", "difference": "Studies formal languages, inference, models and foundations; discrete mathematics uses logic and often includes introductory logic without encompassing the entire subject." }, { "name": "Number theory", "difference": "Centres on integers and arithmetic relationships; it overlaps discrete mathematics but also uses substantial analytic and geometric machinery." }, { "name": "Mathematical analysis", "difference": "Centres on limits, convergence and related structures; discrete mathematics centres on discrete objects, though it can use analytic methods." } ], "questions": [ { "id": "evidence-neighbours-q01", "text": "Which of these neighbouring kinds and how to tell them apart hold for the sense of discrete mathematics this model covers, and on what evidence?", "kind": "provenance" } ] } ] } ] } ] }, "openQuestions": [ "Which researched definition and boundary convention should anchor this registry entry: introductory curricular usage, research usage or an explicitly layered combination?", "Which classification schemes and editions provide defensible mappings for the field and its constituent subjects without implying a single universal classification code?", "How much logic, elementary number theory, discrete probability and algebra should this entry own, and which neighbouring registry models should own their broader treatment?", "Does an existing Vercy world model already cover this field or a materially equivalent concept, requiring a link instead of a separate publication?", "Which inspected handbooks, reviews and institutional scope statements best support the treatment of infinite discrete structures and methods borrowed from continuous mathematics?" ], "statistics": { "bundles": 6, "layers": 11, "findings": 17, "questions": 27 } }, "draft": { "generator": "vr.draft.v3", "status": "draft-generated", "researched": false, "archetype": "discipline or field of knowledge", "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 discrete mathematics, record what state it is in, and decide what may be done with it.", "whatItIs": "Enable an agent to recognise discrete mathematics as a field, assess the scope and justification of its knowledge, and select appropriate discrete representations and reasoning methods.", "characteristics": { "substance": "information", "origin": "conceptual", "agency": "inert" }, "whatYouCanDoWithIt": [ "read and interpreted" ], "distinguishingFeatures": [ "Described in 89 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 discrete mathematics, 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" ], "howItIsRecognised": [], "relatedModels": [], "standing": "Described in 89 Wikipedia languages, which measures how widely it is written about rather than how important or how common it is.", "structure": { "bundles": [ { "id": "identity-and-classification", "name": "Identity, naming and classification", "description": "How an agent tells one discrete mathematics from another, and a discrete mathematics 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 discrete mathematics, 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 discrete mathematics, 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 discrete mathematics 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 discrete mathematics, 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 discrete mathematics, 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 discrete mathematics 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 discrete mathematics 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 discrete mathematics, 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 discrete mathematics, 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 discrete mathematics 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 discrete mathematics from the things most often confused with it.", "questions": [ { "id": "distinguishing-features-q01", "text": "What identifies and describes what distinguishes a discrete mathematics, 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 discrete mathematics, 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 discrete mathematics 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 discrete mathematics 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 discrete mathematics between them.", "questions": [ { "id": "stages-and-transitions-q01", "text": "What identifies and describes the lifecycle of a discrete mathematics, 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 discrete mathematics, 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 discrete mathematics 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 discrete mathematics, how often and by whom.", "findings": [ { "id": "observation-record", "name": "Observation record", "description": "How an observation of a discrete mathematics 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 discrete mathematics, 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 discrete mathematics, 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 discrete mathematics 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 discrete mathematics 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 discrete mathematics contains and in what form it is held.", "questions": [ { "id": "content-and-format-q01", "text": "What identifies and describes the content of a discrete mathematics, 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 discrete mathematics, 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 discrete mathematics 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 discrete mathematics and the period it survives.", "questions": [ { "id": "access-rules-q01", "text": "What identifies and describes access to a discrete mathematics, 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 discrete mathematics, 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 discrete mathematics is known, and what must it refuse?", "kind": "action", "answer_data": [ "permitted actions", "preconditions", "refusals", "escalation" ] } ] } ] } ] }, { "id": "subject-and-method", "name": "Subject matter and method", "description": "What discrete mathematics studies and how it establishes anything.", "rationale": "A field is identified by its questions and its methods, and those are what distinguish it from the fields next to it.", "layers": [ { "id": "subject", "name": "Subject matter", "description": "The questions it takes as its own.", "findings": [ { "id": "subject-record", "name": "Questions and objects of study", "description": "What it is about, stated so a neighbouring field can be told apart.", "questions": [ { "id": "subject-record-q01", "text": "What questions and objects does discrete mathematics take as its own?", "kind": "definition" }, { "id": "subject-record-q02", "text": "Which questions does it share with a neighbouring field, and who claims them?", "kind": "boundary" } ] } ] }, { "id": "method", "name": "Method and evidence", "description": "How claims are established and what counts as evidence.", "findings": [ { "id": "method-record", "name": "Methods and standards of evidence", "description": "The methods used and what they are taken to establish.", "questions": [ { "id": "method-record-q01", "text": "By what methods does discrete mathematics establish claims, and what counts as sufficient evidence?", "kind": "provenance" }, { "id": "method-record-q02", "text": "What kind of claim can this field not settle, and where should an agent look instead?", "kind": "action" } ] } ] } ] }, { "id": "institutions-and-classification", "name": "Institutions and classification", "description": "Where discrete mathematics is practised and how catalogues place it.", "rationale": "The institutional footprint is the evidence that a field exists as a field rather than as a topic.", "layers": [ { "id": "institutions", "name": "Institutional markers", "description": "Societies, journals, degrees and departments.", "findings": [ { "id": "institution-record", "name": "Bodies and venues", "description": "Where the field organises itself.", "questions": [ { "id": "institution-record-q01", "text": "Which societies, journals or degrees mark discrete mathematics as an established field?", "kind": "provenance" }, { "id": "institution-record-q02", "text": "What would show that it is emerging or dissolving rather than established?", "kind": "boundary" } ] } ] }, { "id": "classification", "name": "Classification schemes", "description": "Where library and research classifications put it.", "findings": [ { "id": "classification-record", "name": "Codes and their disagreements", "description": "The classification codes that place it, and where they differ.", "questions": [ { "id": "classification-record-q01", "text": "Which classification schemes place discrete mathematics, under what codes?", "kind": "definition" }, { "id": "classification-record-q02", "text": "Where do those schemes disagree about its scope?", "kind": "boundary" } ] } ] } ] }, { "id": "provenance-and-evidence", "name": "Provenance, evidence and time", "description": "Where every claim about a discrete mathematics 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 discrete mathematics and how confident it is.", "questions": [ { "id": "claim-provenance-q01", "text": "What identifies and describes a claim about a discrete mathematics, 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 discrete mathematics, 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 discrete mathematics 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 discrete mathematics is retired without being erased.", "questions": [ { "id": "validity-and-supersession-q01", "text": "What identifies and describes the validity of a claim about a discrete mathematics, 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 discrete mathematics, 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 discrete mathematics 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 } } } }