{"schema":"https://ver.cy/schemas/card/1.0.0","id":"vr.tr.mathematical-software","code":"thing-q1639024","url":"https://ver.cy/models/thing/q1639024/","name":"mathematical software","alternateNames":["formula editor","theorem proving software system","modular math system","statistical package","fractal-generating software","solver","numerical software","tensor software","Free statistical software","econometrics software"],"kind":"thing","status":"published","version":"0.1.0-research.1","language":"en","classifiers":{"family":"Thing Registry","category":"Physical world and living systems","entryKind":"thing","plane":"PHY","domain":["PHY.OBJ"],"industry":[],"navPath":"","tags":[],"facets":{}},"whatItIs":"Mathematical software is software designed to represent mathematical objects and perform or support mathematical computation, reasoning, or visualization.","purpose":"Enable an agent to recognise mathematical software, assess whether its mathematical capabilities and result guarantees fit a task, and determine how it may be used responsibly.","scope":{"in":["Supported mathematical domains, operations and representations","Symbolic, numerical, statistical and formal reasoning capabilities","Mathematical assumptions, algorithm preconditions and result guarantees","Computation configuration, reproducibility and verification","Interfaces, mathematical extensions and conditions of executable use"],"out":["Computing hardware and operating systems considered independently","Mathematical theories and algorithms independent of their software implementations","Scientific or engineering subjects represented by application models","Individual datasets, mathematical documents and computed results as separate artefacts","General-purpose programming languages and editors without a dedicated mathematical role"],"boundaries":[]},"distinguishingFeatures":["Its documented primary role includes operating on mathematical objects, evaluating mathematical models or checking mathematical arguments; merely displaying equations does not establish this role.","It provides executable mathematical operations or checking rules, distinguishing it from a textbook, formula collection or static mathematical reference.","Its suitability depends on mathematical semantics such as domains, precision and assumptions, beyond whether it accepts an input and produces an output.","A product family, versioned release, installed environment and computation run can be distinguished without treating them as different kinds of mathematical software.","A general-purpose application belongs here only when a dedicated mathematical purpose can be established; incidental arithmetic is insufficient."],"structure":{"bundles":[{"id":"mathematical-purpose-and-boundaries","name":"Mathematical purpose and boundaries","description":"Establishes why the software belongs to this kind and which mathematical tasks it supports.","layers":[{"id":"dedicated-mathematical-role","name":"Dedicated mathematical role","description":"Identifies the executable mathematical purpose that qualifies the software.","findings":[{"id":"qualification-evidence","name":"Qualification evidence","description":"Record the operations and intended workflows that establish a dedicated mathematical role.","questions":[{"text":"Which executable mathematical tasks define the software's intended purpose?","id":"qualification-evidence-q01","kind":"definition"},{"text":"What distinguishes it from a general-purpose application with incidental arithmetic or equation display?","id":"qualification-evidence-q02","kind":"boundary"}]}]},{"id":"capability-and-product-identity","name":"Capability and product identity","description":"Separates mathematical coverage from the release or extension that supplies it.","findings":[{"id":"capability-attribution","name":"Capability attribution","description":"Attach supported mathematical tasks and exclusions to the relevant software release and components.","questions":[{"text":"Which mathematical domains and operations are supported, and which are explicitly excluded?","id":"capability-attribution-q01","kind":"boundary"},{"text":"Which release, backend or extension provides each required capability?","id":"capability-attribution-q02","kind":"provenance"}]}]}]},{"id":"mathematical-objects-and-semantics","name":"Mathematical objects and semantics","description":"Captures the meaning of mathematical inputs, internal objects and outputs.","layers":[{"id":"object-representation","name":"Object representation","description":"Describes supported mathematical objects and conversions between representations.","findings":[{"id":"domains-and-coercions","name":"Domains and coercions","description":"Record number domains, object types and conversions that can change mathematical meaning.","questions":[{"text":"How are exact integers and rationals, approximate numbers, symbolic expressions and structured objects distinguished?","id":"domains-and-coercions-q01","kind":"definition"},{"text":"Which implicit conversions can lose precision, change a domain or alter array and matrix semantics?","id":"domains-and-coercions-q02","kind":"boundary"}]}]},{"id":"assumptions-and-conventions","name":"Assumptions and conventions","description":"Makes the contextual conditions of mathematical operations explicit.","findings":[{"id":"semantic-context","name":"Semantic context","description":"Record assumptions, branch choices and evaluation conventions needed to interpret a result.","questions":[{"text":"How are variable domains, constraints and branch conventions declared and scoped?","id":"semantic-context-q01","kind":"definition"},{"text":"How can an agent inspect and reset assumptions before simplifying, solving or evaluating an expression?","id":"semantic-context-q02","kind":"action"}]}]}]},{"id":"methods-and-result-assurance","name":"Methods and result assurance","description":"Connects mathematical methods and their preconditions to the strength of reported results.","layers":[{"id":"method-applicability","name":"Method applicability","description":"Identifies the selected method and the conditions under which it is suitable.","findings":[{"id":"preconditions-and-selection","name":"Preconditions and selection","description":"Record method selection, required mathematical properties and fallback behaviour.","questions":[{"text":"Which algorithm or solver is selected, and what preconditions does it require of the problem?","id":"preconditions-and-selection-q01","kind":"definition"},{"text":"How can an agent detect unmet preconditions or an automatic switch to another method?","id":"preconditions-and-selection-q02","kind":"action"}]}]},{"id":"verification-and-limits","name":"Verification and limits","description":"Determines what evidence supports the output and what remains unestablished.","findings":[{"id":"result-evidence","name":"Result evidence","description":"Distinguish exact representations, approximate answers, conditional results and checked proofs or certificates.","questions":[{"text":"What residual, error bound, enclosure, certificate or proof-checking evidence accompanies the result?","id":"result-evidence-q01","kind":"measurement"},{"text":"What independent check is appropriate, and which correctness or completeness claims would it still leave unresolved?","id":"result-evidence-q02","kind":"action"}]}]}]},{"id":"computation-control-and-reproducibility","name":"Computation control and reproducibility","description":"Records the configuration and execution evidence needed to interpret and repeat a mathematical computation.","layers":[{"id":"precision-and-termination","name":"Precision and termination","description":"Captures controls for approximation, convergence and bounded execution.","findings":[{"id":"execution-criteria","name":"Execution criteria","description":"Record precision, tolerances, iteration limits and the interpretation of termination diagnostics.","questions":[{"text":"What working precision, absolute or relative tolerances and stopping criteria apply to this operation?","id":"execution-criteria-q01","kind":"measurement"},{"text":"How should an agent respond to nonconvergence, ill-conditioning, resource exhaustion or an inconclusive outcome?","id":"execution-criteria-q02","kind":"action"}]}]},{"id":"reproducible-computation-record","name":"Reproducible computation record","description":"Identifies the state required to repeat a computation and compare its outputs.","findings":[{"id":"environment-and-randomness","name":"Environment and randomness","description":"Preserve mathematical inputs, relevant session state, implementation identity and sources of nondeterminism.","questions":[{"text":"Which inputs, assumptions, release identifiers, backends, random generator settings and execution-order details must be retained?","id":"environment-and-randomness-q01","kind":"provenance"},{"text":"Should repeated runs agree exactly, within a stated tolerance or only in a defined statistical sense?","id":"environment-and-randomness-q02","kind":"measurement"}]}]}]},{"id":"mathematical-integration-and-use","name":"Mathematical integration and use","description":"Determines how an agent can invoke the software and move mathematical work across its boundaries.","layers":[{"id":"interfaces-and-object-exchange","name":"Interfaces and object exchange","description":"Describes programmatic access and the fidelity of imported and exported mathematical objects.","findings":[{"id":"semantic-transfer","name":"Semantic transfer","description":"Record interfaces and formats together with their effects on domains, precision and attached assumptions.","questions":[{"text":"Which APIs, command interfaces or notebook mechanisms expose the required mathematical operations?","id":"semantic-transfer-q01","kind":"action"},{"text":"Which exchange formats preserve exact values, object structure and assumptions, and which discard them?","id":"semantic-transfer-q02","kind":"boundary"}]}]},{"id":"extensions-and-execution-conditions","name":"Extensions and execution conditions","description":"Establishes the components and permissions required for the intended mathematical workflow.","findings":[{"id":"usable-capability","name":"Usable capability","description":"Determine whether a mathematical capability is installed, compatible, licensed and available through the proposed execution mode.","questions":[{"text":"Which mathematical packages, external solvers or remote services are required, and how is their identity verified?","id":"usable-capability-q01","kind":"provenance"},{"text":"Do the applicable licence and deployment conditions permit the intended automated computation and distribution of resulting artefacts?","id":"usable-capability-q02","kind":"action"}]}]}]},{"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.","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.","questions":[{"text":"Which of these check these first hold for the sense of mathematical software this model covers, and on what evidence?","id":"evidence-confidence-notes-q01","kind":"provenance"}]},{"id":"evidence-kinds","name":"Kinds and varieties","description":"Recalled without web access and unsourced; every item is a lead to verify.","questions":[{"text":"Which of these kinds and varieties hold for the sense of mathematical software this model covers, and on what evidence?","id":"evidence-kinds-q01","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.","questions":[{"text":"Which of these real-world use hold for the sense of mathematical software this model covers, and on what evidence?","id":"evidence-real-world-use-q01","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.","questions":[{"text":"Which of these failure modes and hazards hold for the sense of mathematical software this model covers, and on what evidence?","id":"evidence-failure-modes-and-hazards-q01","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.","questions":[{"text":"Which of these neighbouring kinds and how to tell them apart hold for the sense of mathematical software this model covers, and on what evidence?","id":"evidence-neighbours-q01","kind":"provenance"}]}]}]}]},"agentConduct":{"may":["Run computations and visualizations in mathematical software the user is licensed to use.","Report which tool, version and settings produced a result so it can be checked."],"mustNot":["Present a numerical or symbolic result as exact or proven when the software only approximated it.","Use unlicensed copies or bypass licence terms of commercial packages.","Hide errors, warnings or precision loss from the person relying on the result.","Use results from untested code in safety-critical designs without independent checking."],"requiresHuman":["Relying on software results for a safety-critical or financial decision."]},"ethics":{"considerations":["Engineering, finance and science depend on correct computation; silent errors can cause real harm.","Reproducible results need openness about the tools and versions used."],"affectedParties":["Researchers and students","Engineers and users of their designs","Software authors"]},"owners":{"steward":"The developer or licensor of each package; the user answers for results they publish.","roles":[],"masterSystems":[]},"relations":[{"target":"Q15544757","type":"parent","note":"registry parent class"}],"interaction":{"identity":{"applicability":"required","items":["Vercy registry: vr.tr.mathematical-software","Wikidata: Q1639024 (https://www.wikidata.org/wiki/Q1639024)"]},"properties":{"applicability":"required","items":["Mathematical capability profile: Symbolic algebra; numerical analysis; optimisation; statistics; geometry; visualisation; formal proof; other documented capabilities","Supported mathematical objects: Documented number domains, expressions, arrays, equations, functions, geometric objects and logical propositions","Computation semantics: Exact symbolic; floating-point; arbitrary-precision approximate; interval or enclosure; probabilistic; formal derivation","Configured arithmetic precision: Bits or decimal digits, specifying working precision and applicable operations; not applicable where appropriate","Active mathematical assumptions: Explicit predicates, domains, constraints and branch conventions, with their scope","Result assurance: Unverified output; heuristic estimate; residual check; conditional error bound; certified enclosure; independently checked certificate or proof","Execution identity: Links to software family, release, build, mathematical backend and installed extensions","Computation outcome: Completed; conditional; inconclusive; nonconvergent; infeasible with stated evidence; interrupted; failed","Permitted use: Applicable licence and entitlement for interactive use, automation, modification and redistribution"]},"recognition":{"applicability":"not-applicable","items":[]},"capabilities":{"applicability":"required","items":["Match a mathematical task to supported operations, object domains and required guarantees.","Configure assumptions, arithmetic precision, tolerances and solver methods before execution.","Run authorised computations while preserving inputs, environment identity and diagnostic output.","Check results using substitution, residuals, independent methods, certificates or proof checking as appropriate.","Exchange mathematical objects with other tools while checking for changes in meaning or precision.","Reproduce a computation and investigate differences across releases, backends or configurations."]},"hazards":{"applicability":"required","items":["Rounding and floating-point errors can make results silently wrong.","Different versions or settings can give different answers to the same problem."]},"interfaces":{"applicability":"required","items":["IEEE 754 Standard for Floating-Point Arithmetic, Institute of Electrical and Electronics Engineers."]},"context":{"applicability":"required","items":["Mathematical software is used in education, research and engineering to calculate results, manipulate expressions and explore mathematical models.","Its applications include numerical simulation, symbolic algebra, geometric construction and visualization of mathematical relationships."]}},"sources":[{"title":"Wikidata item Q1639024: mathematical software","url":"https://www.wikidata.org/wiki/Q1639024","note":"identity and sense of the item"},{"title":"Wikipedia: Mathematical software","url":"https://en.wikipedia.org/wiki/Mathematical_software","note":"general description of the item"}],"openQuestions":["Does an existing Vercy world model already cover mathematical software, requiring this registry entry to link to it?","How should the registry distinguish dedicated mathematical software from spreadsheets, calculators, statistical packages and general-purpose languages with mathematical libraries?","Does the assigned PHY / PHY.OBJ placement refer to a distributed or installed software artefact, and how should it relate to informational software identity?","Which authoritative documentation should establish operation-specific guarantees and verification requirements across symbolic, numerical and proof-oriented software?","Which conventions or standards, if any, should govern interchange of mathematical objects and preservation of assumptions across the software families included here?"],"resources":{"spec":"/models/things/publications/thing-q1639024/spec.json"},"provenance":{"origin":"thing registry research (pass 2)","builtFrom":["models/things/publications/thing-q1639024/spec.json"],"providers":["Codex"],"researchStatus":"unreviewed","generatedAt":"2026-09-12T11:11:28Z","builder":"tools/build_cards.py@1.0.0"},"completeness":{"sections":{"classifiers":"filled","whatItIs":"filled","purpose":"filled","distinguishingFeatures":"filled","structure":"filled","agentConduct":"filled","ethics":"filled","owners":"filled","relations":"filled","interaction.identity":"filled","interaction.properties":"filled","interaction.recognition":"not-applicable","interaction.capabilities":"filled","interaction.hazards":"filled","interaction.interfaces":"filled","interaction.context":"filled","sources":"filled"},"notes":{"_gate":"Published through the thing publication gate 1.0 on 2026-10-07T10:10:26+00:00: completeness 1.00; sense: Wikidata description; 2 live sources; review by codex: pass","interaction.recognition":"Mathematical software is identified by its computational capabilities rather than a consistent physical appearance or distinctive visual interface."},"score":1.0}}