{ "model": { "rank": 4281, "code": "thing-q11203", "model_id": "vr.tr.system-of-linear-equations", "name": "system of linear equations", "purpose": "Enable an agent to recognise a system of linear equations, assess its solution status, and choose valid transformations or solution methods under explicit mathematical and numerical assumptions.", "family": "Thing Registry", "category": "Information and virtual systems", "status": "research-draft", "kind": "thing", "plane": "INF", "domain": "INF.KNW", "industry": "", "version": "", "url": "/models/thing/q11203/", "tier": 2, "score": 77, "payload": { "layer": "wikidata", "aliases": [ "homogeneous system of linear equations" ], "aliasCount": 1, "merged": 1, "knownIn": 77, "facets": null, "markers": [], "lexicalClass": "", "senseRank": null, "alsoRegisteredAs": null, "source": { "dataset": "wikidata", "item": "Q11203", "url": "https://www.wikidata.org/wiki/Q11203", "license": "CC0 1.0" } }, "research": { "vercy": "1.0-draft", "publication": { "status": "research-draft", "adjudicationStatus": "unreviewed", "publishableCanonical": false, "generatedAt": "2026-09-09T19:52:37Z", "providers": [ "Codex" ], "breadth": "recalled by Codex without web access - no source was read", "missingProviders": [], "pass": 2, "cost": { "grok": { "seconds": 18.6, "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: 01a087b9-c3f3-70a3-9cab-0d564c73863e\n--------\nuser\nDescribe what is already known about one registered thing. Answer as JSON only, no prose around it.\n\nThing: system of linear equations\nSense to describe: (none recorded)\nDomain code: INF.KNW\nAlso known as: (none)\n\n\nContext for this batch of 695 things:\n# Batch", "usd": 0, "recall": true }, "codex": { "seconds": 64.1, "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: 01a087b9-c400-75a1-a9c0-67e96915477e\n--------\nuser\nYou are drafting a Vercy meta-model for one registered thing. Answer as JSON only, no prose around it.\n\nThing: system of linear equations\nRegistry id: vr.tr.system-of-linear-equations\nPlane / domain: INF / INF.KNW\nRegistry definition: (none recorded)\nNames fol" } } }, "metaModel": { "id": "THING-Q11203", "registryId": "vr.tr.system-of-linear-equations", "name": "system of linear equations", "version": "0.1.0-research.1", "entryKind": "thing", "family": "Thing Registry", "domain": [ "INF.KNW" ], "status": "research-draft" }, "canonicalUrl": "https://ver.cy/models/thing/q11203/", "model": { "registry_id": "vr.tr.system-of-linear-equations", "name": "system of linear equations", "purpose": "Enable an agent to recognise a system of linear equations, assess its solution status, and choose valid transformations or solution methods under explicit mathematical and numerical assumptions.", "definition": "A system of linear equations is a collection of equations, each linear in a shared set of unknowns over a specified field, whose solutions are assignments that satisfy every equation simultaneously.", "scope_statement": "This model owns a finite collection of simultaneous equations linear in specified unknowns, its coefficient domain, equivalent representations, solution set, and conditions governing exact or approximate solution.", "in_scope": [ "Equations, shared unknowns, coefficients, constants, and their representation as Ax = b", "Scalar domain and any parameters on which coefficients or constants depend", "Consistency, rank, degrees of freedom, and solution-set structure", "Transformations that preserve solutions or explicitly relate different solution coordinates", "Exact and numerical solution methods, residuals, and sensitivity" ], "out_of_scope": [ "Linear algebra as a discipline, including its institutions and literature", "Nonlinear systems and systems of inequalities", "Differential or difference equations whose unknowns are functions or sequences", "Optimisation objectives used to select approximate or preferred solutions", "The physical, economic, or other originating system and its independent validity", "Software libraries and computing infrastructure used to solve equations" ], "distinguishing_features": [ "After simplification, every equation has the form sum(a_ij x_j) = b_i, with coefficients independent of the designated unknowns.", "The equations constrain one shared assignment of unknowns simultaneously; solving each equation independently does not establish a system solution.", "Products between unknowns, nonlinear powers, or nonlinear functions of unknowns place an equation outside scope unless an explicitly restricted equivalent linear formulation is established.", "An augmented matrix represents a system only when its coefficient columns, right-hand-side column, unknown ordering, and scalar domain are identified.", "Linearity depends on which symbols are unknowns: a x = b is linear in x when a is a fixed coefficient or parameter, but generally not linear jointly in a and x." ], "characteristics": [ { "name": "Scalar domain", "kind": "category", "unit_or_values": "Named field, such as rational, real, complex, or finite field; other domains explicitly qualified", "why_it_matters": "Permitted operations and solution classifications depend on the domain; field-based rank criteria do not directly settle integer solvability." }, { "name": "Equation and unknown counts", "kind": "measurement", "unit_or_values": "Ordered pair (m, n) of nonnegative integer counts", "why_it_matters": "Determines matrix dimensions and the rectangular shape of the system without alone determining consistency or uniqueness." }, { "name": "Homogeneity", "kind": "category", "unit_or_values": "Homogeneous when b = 0; nonhomogeneous otherwise", "why_it_matters": "A homogeneous system always admits the zero solution and has a linear solution space over a field." }, { "name": "Coefficient and augmented ranks", "kind": "measurement", "unit_or_values": "Integer pair rank(A), rank([A|b]); numerical estimates include a tolerance", "why_it_matters": "Over a field, equal ranks establish consistency, and comparison with n determines uniqueness." }, { "name": "Solution status", "kind": "state", "unit_or_values": "Undetermined; inconsistent; unique solution; multiple solutions; conditional on parameters", "why_it_matters": "Controls whether to solve, parameterise, analyse parameter cases, or report infeasibility." }, { "name": "Solution-space dimension", "kind": "measurement", "unit_or_values": "n − rank(A) for a consistent system over a field; not applicable to an empty solution set", "why_it_matters": "Counts free directions; positive dimension implies infinitely many solutions over an infinite field but finitely many over a finite field." }, { "name": "Coefficient structure", "kind": "category", "unit_or_values": "Properties such as sparse, dense, banded, triangular, symmetric, Hermitian, or positive definite, where applicable", "why_it_matters": "Provides concrete eligibility conditions for specialised solution methods and storage choices." }, { "name": "Residual", "kind": "measurement", "unit_or_values": "Vector r = b − A x̂ and a named norm or scaled residual measure", "why_it_matters": "Measures equation satisfaction for a candidate solution without alone establishing closeness to an exact solution." }, { "name": "Condition measure", "kind": "measurement", "unit_or_values": "Named condition measure with norm, perturbation model, scaling, and applicability conditions", "why_it_matters": "Relates perturbations in data to solution sensitivity and helps interpret numerical accuracy." }, { "name": "Originating constraints", "kind": "relation", "unit_or_values": "Links from equations and variables to source statements, measurements, or derivations", "why_it_matters": "Allows an agent to trace a disputed coefficient or equation without treating mathematical solvability as validation of the originating model." } ], "affordances": [ "Validate linearity relative to declared unknowns and construct Ax = b with a recoverable variable ordering.", "Determine consistency and uniqueness exactly, numerically with stated tolerances, or conditionally on parameters.", "Apply justified elimination or coordinate transformations while tracking their effects on solutions.", "Construct an exact solution or describe all solutions using a particular solution and a null-space basis.", "Choose a numerical method from verified matrix properties and check its output using residual and sensitivity evidence.", "Identify redundant or contradictory equations and trace them to their originating constraints." ] }, "sources": [], "structure": { "bundles": [ { "id": "linear-formulation", "name": "Linear formulation", "description": "Establish what the equations mean and whether they form a linear system.", "rationale": "Linearity and valid algebraic operations cannot be assessed without distinguishing unknowns, parameters, and the scalar domain.", "layers": [ { "id": "unknowns-and-domain", "name": "Unknowns and domain", "description": "Declare the symbols being solved for and the arithmetic governing them.", "findings": [ { "id": "declared-linear-dependence", "name": "Declared linear dependence", "description": "Each equation must be linear in the designated unknowns, with coefficients independent of those unknowns.", "questions": [ { "text": "Which symbols are unknowns, which are fixed data or parameters, and in what scalar domain do solutions lie?", "kind": "definition", "id": "declared-linear-dependence-q01" }, { "text": "After simplification, does every equation have coefficients independent of the unknowns, and are any domain restrictions required by that simplification?", "kind": "boundary", "id": "declared-linear-dependence-q02" } ] } ] }, { "id": "matrix-correspondence", "name": "Matrix correspondence", "description": "Connect the written equations to coefficient and augmented matrices.", "findings": [ { "id": "recoverable-matrix-encoding", "name": "Recoverable matrix encoding", "description": "The representation Ax = b must preserve equation identities, unknown ordering, coefficients, and constants.", "questions": [ { "text": "What are A, x, and b, and which equation and unknown correspond to each row and column?", "kind": "definition", "id": "recoverable-matrix-encoding-q01" }, { "text": "Can every matrix entry be traced to the original equation or a documented derivation?", "kind": "provenance", "id": "recoverable-matrix-encoding-q02" } ] } ] } ] }, { "id": "solution-set", "name": "Solution set", "description": "Characterise whether simultaneous solutions exist and how much freedom they contain.", "rationale": "Equation counts alone cannot distinguish an inconsistent system from one with a unique solution or free variables.", "layers": [ { "id": "consistency-and-uniqueness", "name": "Consistency and uniqueness", "description": "Establish solution status using domain-appropriate evidence.", "findings": [ { "id": "rank-based-classification", "name": "Rank-based classification", "description": "Over a field, consistency requires rank(A) = rank([A|b]); a consistent system is unique precisely when rank(A) equals the number of unknowns.", "questions": [ { "text": "What are the coefficient and augmented ranks, and are they exact results or numerical estimates under a stated tolerance?", "kind": "measurement", "id": "rank-based-classification-q01" }, { "text": "Do those ranks establish inconsistency, uniqueness, or multiple solutions under the declared scalar domain?", "kind": "definition", "id": "rank-based-classification-q02" } ] } ] }, { "id": "solution-parameterisation", "name": "Solution parameterisation", "description": "Represent all solutions and any parameter-dependent changes in their structure.", "findings": [ { "id": "particular-and-null-solutions", "name": "Particular and null solutions", "description": "For a consistent system over a field, every solution is a particular solution plus an element of the null space of A.", "questions": [ { "text": "What particular solution and null-space basis describe all solutions, and how many free coordinates remain?", "kind": "definition", "id": "particular-and-null-solutions-q01" }, { "text": "For which coefficient-parameter values do consistency, rank, or the proposed parameterisation change?", "kind": "boundary", "id": "particular-and-null-solutions-q02" } ] } ] } ] }, { "id": "equivalence-and-reduction", "name": "Equivalence and reduction", "description": "Track transformations and the mathematical evidence exposed by elimination.", "rationale": "An agent must distinguish operations that preserve the original solution set from operations that change coordinates or discard constraints.", "layers": [ { "id": "valid-transformations", "name": "Valid transformations", "description": "Record the conditions under which transformed equations retain their intended meaning.", "findings": [ { "id": "solution-preserving-operations", "name": "Solution-preserving operations", "description": "Invertible row operations preserve solutions over a field; transformations of unknown coordinates require an explicit mapping back.", "questions": [ { "text": "Which row operations or coordinate substitutions were applied, and how is their invertibility established?", "kind": "action", "id": "solution-preserving-operations-q01" }, { "text": "Does any division require a parameter to be nonzero, and how is the zero case handled?", "kind": "boundary", "id": "solution-preserving-operations-q02" } ] } ] }, { "id": "dependency-and-contradiction", "name": "Dependency and contradiction", "description": "Use reduction to expose repeated information and incompatible requirements.", "findings": [ { "id": "reduction-certificates", "name": "Reduction certificates", "description": "Tracked equation combinations can certify redundancy or produce a contradiction of the form 0 = c with c nonzero.", "questions": [ { "text": "Which combinations of original equations demonstrate redundancy or inconsistency?", "kind": "provenance", "id": "reduction-certificates-q01" }, { "text": "Which equations can be removed while preserving the complete solution set?", "kind": "action", "id": "reduction-certificates-q02" } ] } ] } ] }, { "id": "solution-computation", "name": "Solution computation", "description": "Select a suitable computational procedure and assess the reliability of its result.", "rationale": "Exact solvability, practical computation, and numerical accuracy are separate properties of a linear system.", "layers": [ { "id": "method-eligibility", "name": "Method eligibility", "description": "Match algorithm assumptions to verified coefficient structure and required output.", "findings": [ { "id": "structure-guided-method", "name": "Structure-guided method", "description": "Dimensions, domain, sparsity, matrix properties, and desired exactness determine which elimination, factorisation, or iterative procedures are appropriate.", "questions": [ { "text": "What matrix properties and arithmetic requirements have been verified sufficiently to justify the selected method?", "kind": "measurement", "id": "structure-guided-method-q01" }, { "text": "Is the required output one solution, all solutions, a consistency certificate, or a numerical approximation, and which procedure supplies it?", "kind": "action", "id": "structure-guided-method-q02" } ] } ] }, { "id": "numerical-reliability", "name": "Numerical reliability", "description": "Assess equation satisfaction and sensitivity under finite precision or uncertain data.", "findings": [ { "id": "residual-and-sensitivity-evidence", "name": "Residual and sensitivity evidence", "description": "Residuals measure equation satisfaction, while conditioning and error analysis determine what that evidence implies about solution accuracy.", "questions": [ { "text": "What residual or backward-error measure was computed, using which norm, scaling, precision, and acceptance threshold?", "kind": "measurement", "id": "residual-and-sensitivity-evidence-q01" }, { "text": "What sensitivity evidence supports the reported solution accuracy, particularly when the matrix is nearly rank deficient?", "kind": "measurement", "id": "residual-and-sensitivity-evidence-q02" } ] } ] } ] }, { "id": "interpretation-and-use", "name": "Interpretation and use", "description": "Connect algebraic results to their source meanings and permitted downstream uses.", "rationale": "A correct algebraic answer can still violate external restrictions or answer a modified problem without making that modification explicit.", "layers": [ { "id": "constraint-meaning", "name": "Constraint meaning", "description": "Preserve variable meanings, units where relevant, and the origin of each equation.", "findings": [ { "id": "traceable-formulation-assumptions", "name": "Traceable formulation assumptions", "description": "Applied systems require traceable assumptions and compatible term units; abstract systems may have no physical units.", "questions": [ { "text": "What source statements, observations, or assumptions justify each equation and coefficient?", "kind": "provenance", "id": "traceable-formulation-assumptions-q01" }, { "text": "Where variables have units, are terms within each equation compatible, and what scaling converts computational coordinates back to those units?", "kind": "measurement", "id": "traceable-formulation-assumptions-q02" } ] } ] }, { "id": "downstream-admissibility", "name": "Downstream admissibility", "description": "Distinguish solving the equations from selecting or accepting an answer under additional requirements.", "findings": [ { "id": "additional-restrictions-and-objectives", "name": "Additional restrictions and objectives", "description": "Nonnegativity, integrality, least-squares objectives, and regularisation introduce requirements beyond an unconstrained field-based system.", "questions": [ { "text": "Which additional restrictions determine whether an algebraic solution is admissible, and which neighbouring model owns those restrictions?", "kind": "boundary", "id": "additional-restrictions-and-objectives-q01" }, { "text": "If no exact solution exists or several exist, what explicit objective authorises approximation or selection, and how will the resulting problem be identified?", "kind": "action", "id": "additional-restrictions-and-objectives-q02" } ] } ] } ] }, { "id": "evidence-and-external-alignment", "name": "Evidence and external alignment", "description": "What the world already says about this thing, gathered so the model can be checked against it.", "rationale": "A model that cannot be lined up against existing standards, identifiers and practice cannot be adopted by anyone who already uses them.", "layers": [ { "id": "reported-evidence", "name": "Reported evidence", "description": "Findings from the breadth pass, kept separate from the structural claims.", "findings": [ { "id": "evidence-confidence-notes", "name": "Check these first", "description": "Recalled without web access and unsourced; every item is a lead to verify.", "evidence": [ "This describes a mathematical object, not a discipline, despite the batch context.", "The measurement statements assume finite systems; numerical conditioning statements concern real or complex coefficients.", "The listed kinds overlap: equation count alone does not establish consistency or uniqueness. Over a finite field, a nonunique solution set is finite." ], "questions": [ { "id": "evidence-confidence-notes-q01", "text": "Which of these check these first hold for the sense of system of linear equations 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": [ "Homogeneous systems", "Nonhomogeneous systems", "Consistent systems", "Inconsistent systems", "Underdetermined systems", "Overdetermined systems" ], "questions": [ { "id": "evidence-kinds-q01", "text": "Which of these kinds and varieties hold for the sense of system of linear equations 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": [ "Computing currents and voltages in linear electrical circuit models", "Solving discretized differential equations in engineering and physics", "Estimating parameters in linear least-squares problems", "Balancing chemical reaction equations through homogeneous linear constraints", "Solving linear input-output models in economics" ], "questions": [ { "id": "evidence-real-world-use-q01", "text": "Which of these real-world use hold for the sense of system of linear equations 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": "Number of equations m and unknowns n", "typical_range": "Positive integers; no universal typical range", "unit": "count" }, { "quantity": "Rank of the coefficient matrix", "typical_range": "0 to min(m, n)", "unit": "dimensionless integer" }, { "quantity": "Dimension of the solution set for a consistent system", "typical_range": "n minus the rank of the coefficient matrix", "unit": "dimension" }, { "quantity": "Condition number of a nonsingular square coefficient matrix in an induced matrix norm", "typical_range": "At least 1, with no finite upper bound", "unit": "dimensionless" } ], "questions": [ { "id": "evidence-measurements-q01", "text": "Which of these typical measurements hold for the sense of system of linear equations 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": [ "Inconsistent equations admit no simultaneous solution.", "A consistent system with coefficient rank below the number of unknowns does not determine a unique solution.", "Ill-conditioning can amplify small perturbations in coefficients or data into large solution changes.", "Floating-point roundoff and unsuitable elimination procedures can produce inaccurate numerical solutions.", "Treating a least-squares approximation as an exact solution can conceal incompatible constraints." ], "questions": [ { "id": "evidence-failure-modes-and-hazards-q01", "text": "Which of these failure modes and hazards hold for the sense of system of linear equations 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": "Linear algebra", "difference": "Linear algebra is the broader mathematical field; a system of linear equations is an object studied within it." }, { "name": "Linear equation", "difference": "A linear equation supplies one constraint; a system requires simultaneous satisfaction of a collection of such constraints." }, { "name": "Matrix", "difference": "A matrix is an array of entries; a finite linear system can be represented as Ax = b using a coefficient matrix and a right-hand-side vector." }, { "name": "System of nonlinear equations", "difference": "A nonlinear system contains at least one equation that is not linear in the chosen unknowns." }, { "name": "Linear least squares", "difference": "Linear least squares minimizes a residual measure and can return an approximation when the corresponding linear system has no exact solution." }, { "name": "Linear programming", "difference": "Linear programming optimizes a linear objective subject to linear constraints; solving a linear system requires satisfying equalities without an optimization objective." } ], "questions": [ { "id": "evidence-neighbours-q01", "text": "Which of these neighbouring kinds and how to tell them apart hold for the sense of system of linear equations this model covers, and on what evidence?", "kind": "provenance" } ] } ] } ] } ] }, "openQuestions": [ "Does an existing Vercy world model already cover this concept, requiring a registry link instead of a separate publication?", "Should this entry cover systems over general rings and integer-restricted systems directly, or reference specialised models while retaining a field-based core?", "Does the registry intend to include infinite systems or operator equations, beyond the finite scalar systems assumed in this draft?", "Which authoritative sources should support the published definitions, transformation rules, and numerical reliability criteria?", "What evidence and tolerance conventions should Vercy require when an agent reports numerical rank, approximate consistency, or solution accuracy?" ], "statistics": { "bundles": 6, "layers": 11, "findings": 16, "questions": 26 } }, "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 system of linear equations, record what state it is in, and decide what may be done with it.", "whatItIs": "Enable an agent to recognise a system of linear equations, assess its solution status, and choose valid transformations or solution methods under explicit mathematical and numerical assumptions.", "characteristics": { "substance": "information", "origin": "conceptual", "agency": "inert" }, "whatYouCanDoWithIt": [ "read and interpreted" ], "distinguishingFeatures": [ "Names folded into this entry, which a task may need to split apart again: homogeneous system of linear equations.", "1 finer distinctions are held as aliases rather than separate entries, because telling them apart needs a task that asks for it.", "Described in 77 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 system of linear equations, 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": [ { "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": [ "homogeneous system of linear equations" ] } ], "standing": "Described in 77 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 system of linear equations from another, and a system of linear equations 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 system of linear equations, 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 system of linear equations, 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 system of linear equations 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 system of linear equations, 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 system of linear equations, 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 system of linear equations 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 system of linear equations 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 system of linear equations, 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 system of linear equations, 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 system of linear equations 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 system of linear equations from the things most often confused with it.", "questions": [ { "id": "distinguishing-features-q01", "text": "What identifies and describes what distinguishes a system of linear equations, 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 system of linear equations, 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 system of linear equations 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 system of linear equations 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 system of linear equations between them.", "questions": [ { "id": "stages-and-transitions-q01", "text": "What identifies and describes the lifecycle of a system of linear equations, 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 system of linear equations, 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 system of linear equations 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 system of linear equations, how often and by whom.", "findings": [ { "id": "observation-record", "name": "Observation record", "description": "How an observation of a system of linear equations 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 system of linear equations, 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 system of linear equations, 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 system of linear equations 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 system of linear equations 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 system of linear equations contains and in what form it is held.", "questions": [ { "id": "content-and-format-q01", "text": "What identifies and describes the content of a system of linear equations, 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 system of linear equations, 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 system of linear equations 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 system of linear equations and the period it survives.", "questions": [ { "id": "access-rules-q01", "text": "What identifies and describes access to a system of linear equations, 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 system of linear equations, 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 system of linear equations 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 system of linear equations 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 system of linear equations 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 system of linear equations 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 system of linear equations 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 system of linear equations 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 system of linear equations, 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 system of linear equations 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 system of linear equations and how confident it is.", "questions": [ { "id": "claim-provenance-q01", "text": "What identifies and describes a claim about a system of linear equations, 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 system of linear equations, 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 system of linear equations 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 system of linear equations is retired without being erased.", "questions": [ { "id": "validity-and-supersession-q01", "text": "What identifies and describes the validity of a claim about a system of linear equations, 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 system of linear equations, 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 system of linear equations 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 } } } }