{ "vercy": "1.0-draft", "publication": { "status": "research-draft", "adjudicationStatus": "unreviewed", "publishableCanonical": false, "generatedAt": "2026-09-12T11:11:28Z", "providers": [ "Codex" ], "breadth": "recalled by Codex without web access - no source was read", "missingProviders": [], "pass": 2, "cost": { "grok": { "seconds": 16.8, "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: 01a0954f-9f86-7151-b231-4859fec07f8f\n--------\nuser\nDescribe what is already known about one registered thing. Answer as JSON only, no prose around it.\n\nThing: mathematical software\nSense to describe: (none recorded)\nDomain code: PHY.OBJ\nAlso known as: (none)\n\n\nContext for this batch of 1001 things:\n# Batch 044", "usd": 0.0, "recall": true }, "codex": { "seconds": 69.7, "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: 01a0954f-9f7b-7230-b7cb-d1d7b514855c\n--------\nuser\nYou are drafting a Vercy meta-model for one registered thing. Answer as JSON only, no prose around it.\n\nThing: mathematical software\nRegistry id: vr.tr.mathematical-software\nPlane / domain: PHY / PHY.OBJ\nRegistry definition: (none recorded)\nNames folded into t" } }, "enrichment": { "pass": 3, "engine": "claude", "producedAt": "2026-10-06T12:00:00Z", "ingestedAt": "2026-10-06T08:38:45+00:00", "fields": [ "agent_conduct", "ethics", "failure_modes_and_hazards", "owners", "standards_and_regulation" ] }, "gate": { "passed": true, "version": "1.0", "at": "2026-10-07T10:10:26+00:00", "evidence": [ "completeness 1.00", "sense: Wikidata description", "2 live sources", "review by codex: pass" ] } }, "metaModel": { "id": "THING-Q1639024", "registryId": "vr.tr.mathematical-software", "name": "mathematical software", "version": "0.1.0-research.1", "entryKind": "thing", "family": "Thing Registry", "domain": [ "PHY.OBJ" ], "status": "research-draft" }, "canonicalUrl": "https://ver.cy/models/thing/q1639024/", "model": { "registry_id": "vr.tr.mathematical-software", "name": "mathematical software", "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.", "definition": "Mathematical software is software designed to represent mathematical objects and perform or support mathematical computation, reasoning, or visualization.", "scope_statement": "This model owns mathematical software as a kind of executable tool whose primary purpose is mathematical computation, modelling, visualisation or formal reasoning, including distinctions among a software family, a release, an installation and an individual computation.", "in_scope": [ "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_of_scope": [ "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" ], "distinguishing_features": [ "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." ], "characteristics": [ { "name": "Mathematical capability profile", "kind": "category", "unit_or_values": "Symbolic algebra; numerical analysis; optimisation; statistics; geometry; visualisation; formal proof; other documented capabilities", "why_it_matters": "Identifies which mathematical tasks the software is intended to perform." }, { "name": "Supported mathematical objects", "kind": "category", "unit_or_values": "Documented number domains, expressions, arrays, equations, functions, geometric objects and logical propositions", "why_it_matters": "Prevents an agent from assuming that similarly written inputs have interchangeable meanings." }, { "name": "Computation semantics", "kind": "category", "unit_or_values": "Exact symbolic; floating-point; arbitrary-precision approximate; interval or enclosure; probabilistic; formal derivation", "why_it_matters": "Determines what an output can establish and which checks it requires." }, { "name": "Configured arithmetic precision", "kind": "measurement", "unit_or_values": "Bits or decimal digits, specifying working precision and applicable operations; not applicable where appropriate", "why_it_matters": "Working precision influences rounding behaviour but must not be mistaken for achieved accuracy." }, { "name": "Active mathematical assumptions", "kind": "state", "unit_or_values": "Explicit predicates, domains, constraints and branch conventions, with their scope", "why_it_matters": "Results may hold only under assumptions that are absent from the displayed expression." }, { "name": "Result assurance", "kind": "category", "unit_or_values": "Unverified output; heuristic estimate; residual check; conditional error bound; certified enclosure; independently checked certificate or proof", "why_it_matters": "Separates a plausible answer from a result supported by an appropriate guarantee." }, { "name": "Execution identity", "kind": "relation", "unit_or_values": "Links to software family, release, build, mathematical backend and installed extensions", "why_it_matters": "Capabilities and mathematical behaviour must be attributed to the environment actually used." }, { "name": "Computation outcome", "kind": "state", "unit_or_values": "Completed; conditional; inconclusive; nonconvergent; infeasible with stated evidence; interrupted; failed", "why_it_matters": "Avoids treating execution completion or solver termination as proof that a mathematical task was solved." }, { "name": "Permitted use", "kind": "relation", "unit_or_values": "Applicable licence and entitlement for interactive use, automation, modification and redistribution", "why_it_matters": "Determines whether the proposed mode of use is permitted." } ], "affordances": [ "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." ], "agent_conduct": { "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." ], "must_not": [ "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." ], "requires_human": [ "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." ], "affected_parties": [ "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.", "master_systems": [] }, "failure_modes_and_hazards": [ "Rounding and floating-point errors can make results silently wrong.", "Different versions or settings can give different answers to the same problem." ], "standards_and_regulation": [ "IEEE 754 Standard for Floating-Point Arithmetic, Institute of Electrical and Electronics Engineers." ], "what_it_is_for": [ "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." ], "facets_not_applicable": { "recognition": "Mathematical software is identified by its computational capabilities rather than a consistent physical appearance or distinctive visual interface." } }, "sources": [ { "id": "wikidata", "title": "Wikidata item Q1639024: mathematical software", "url": "https://www.wikidata.org/wiki/Q1639024", "url_status": "live", "what_it_supports": "identity and sense of the item", "checked_by": "wikidata-api" }, { "id": "wikipedia-en", "title": "Wikipedia: Mathematical software", "url": "https://en.wikipedia.org/wiki/Mathematical_software", "url_status": "live", "what_it_supports": "general description of the item", "checked_by": "wikidata-api sitelink" } ], "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.", "rationale": "The registry supplies no definition, and mathematical software must be distinguished from tools that merely contain arithmetic or display notation.", "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?", "kind": "definition", "id": "qualification-evidence-q01" }, { "text": "What distinguishes it from a general-purpose application with incidental arithmetic or equation display?", "kind": "boundary", "id": "qualification-evidence-q02" } ] } ] }, { "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?", "kind": "boundary", "id": "capability-attribution-q01" }, { "text": "Which release, backend or extension provides each required capability?", "kind": "provenance", "id": "capability-attribution-q02" } ] } ] } ] }, { "id": "mathematical-objects-and-semantics", "name": "Mathematical objects and semantics", "description": "Captures the meaning of mathematical inputs, internal objects and outputs.", "rationale": "Identical notation can yield different results when domains, representation or assumptions differ.", "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?", "kind": "definition", "id": "domains-and-coercions-q01" }, { "text": "Which implicit conversions can lose precision, change a domain or alter array and matrix semantics?", "kind": "boundary", "id": "domains-and-coercions-q02" } ] } ] }, { "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?", "kind": "definition", "id": "semantic-context-q01" }, { "text": "How can an agent inspect and reset assumptions before simplifying, solving or evaluating an expression?", "kind": "action", "id": "semantic-context-q02" } ] } ] } ] }, { "id": "methods-and-result-assurance", "name": "Methods and result assurance", "description": "Connects mathematical methods and their preconditions to the strength of reported results.", "rationale": "Successful execution alone does not establish correctness, convergence, completeness or numerical accuracy.", "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?", "kind": "definition", "id": "preconditions-and-selection-q01" }, { "text": "How can an agent detect unmet preconditions or an automatic switch to another method?", "kind": "action", "id": "preconditions-and-selection-q02" } ] } ] }, { "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?", "kind": "measurement", "id": "result-evidence-q01" }, { "text": "What independent check is appropriate, and which correctness or completeness claims would it still leave unresolved?", "kind": "action", "id": "result-evidence-q02" } ] } ] } ] }, { "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.", "rationale": "Precision, stopping rules, randomness and computational backends can affect mathematical outputs and termination.", "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?", "kind": "measurement", "id": "execution-criteria-q01" }, { "text": "How should an agent respond to nonconvergence, ill-conditioning, resource exhaustion or an inconclusive outcome?", "kind": "action", "id": "execution-criteria-q02" } ] } ] }, { "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?", "kind": "provenance", "id": "environment-and-randomness-q01" }, { "text": "Should repeated runs agree exactly, within a stated tolerance or only in a defined statistical sense?", "kind": "measurement", "id": "environment-and-randomness-q02" } ] } ] } ] }, { "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.", "rationale": "Automation and interoperability are useful only when mathematical meaning survives transfer and the intended execution mode is available.", "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?", "kind": "action", "id": "semantic-transfer-q01" }, { "text": "Which exchange formats preserve exact values, object structure and assumptions, and which discard them?", "kind": "boundary", "id": "semantic-transfer-q02" } ] } ] }, { "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?", "kind": "provenance", "id": "usable-capability-q01" }, { "text": "Do the applicable licence and deployment conditions permit the intended automated computation and distribution of resulting artefacts?", "kind": "action", "id": "usable-capability-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 recorded PHY.OBJ domain merits review: software is ordinarily treated as an informational artifact, distinct from the physical computer executing it.", "The kinds overlap; a single package can support symbolic, numerical, statistical, and visualization functions.", "Performance ranges, applicable standards, and identifiers depend on the specific package and application; none are asserted here." ], "questions": [ { "id": "evidence-confidence-notes-q01", "text": "Which of these check these first hold for the sense of mathematical software 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": [ "Computer algebra systems", "Numerical computing environments and libraries", "Mathematical optimization software", "Statistical computing software", "Automated theorem provers and proof assistants", "Dynamic geometry software" ], "questions": [ { "id": "evidence-kinds-q01", "text": "Which of these kinds and varieties hold for the sense of mathematical software 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": [ "Symbolic manipulation of expressions, equations, derivatives, and integrals", "Numerical solution of equations and simulation of mathematical models", "Optimization of designs, schedules, and resource allocations", "Statistical analysis and mathematical visualization", "Construction and verification of formal mathematical proofs" ], "questions": [ { "id": "evidence-real-world-use-q01", "text": "Which of these real-world use hold for the sense of mathematical software 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": [ "Rounding error, overflow, or underflow can distort numerical results.", "Ill-conditioned problems can amplify small errors in inputs.", "Iterative algorithms can fail to converge or return a local solution when a global solution is required.", "Unstated domain assumptions or branch conventions can make symbolic results inapplicable.", "Incorrect models, inputs, or software implementations can produce plausible but invalid results." ], "questions": [ { "id": "evidence-failure-modes-and-hazards-q01", "text": "Which of these failure modes and hazards hold for the sense of mathematical software 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": "Algorithm", "difference": "An algorithm specifies a procedure; mathematical software implements procedures in executable form." }, { "name": "Mathematical model", "difference": "A mathematical model represents a system or relationship; mathematical software constructs, analyzes, or evaluates such models." }, { "name": "Computer algebra system", "difference": "A computer algebra system specializes in symbolic mathematical manipulation and is one kind of mathematical software." }, { "name": "Scientific software", "difference": "Scientific software supports scientific work broadly, including instrument control and data management; mathematical software is defined by its mathematical functionality." } ], "questions": [ { "id": "evidence-neighbours-q01", "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?", "kind": "provenance" } ] } ] } ] } ] }, "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?" ], "statistics": { "bundles": 6, "layers": 11, "findings": 15, "questions": 25 } }