{"schema":"https://ver.cy/schemas/card/1.0.0","id":"vr.wm-knw-019","code":"wm-knw-019-mathematical-computational-model","url":"https://ver.cy/models/wm-knw-019-mathematical-computational-model/","name":"Mathematical / Computational Model","alternateNames":[],"kind":"world-model","status":"published","version":"0.1.0","language":"en","classifiers":{"family":"World Models","category":"Information and virtual systems","entryKind":"entity","plane":"","domain":["INF.KNW.MATH"],"industry":["Cross-industry"],"navPath":"NAV.INF.KNW.MATH","tags":["mathematical","computational","model","inf.knw.math"],"facets":{}},"whatItIs":"A mathematical or computational model is a formal representation of a system by equations, rules or algorithms, with parameters, assumptions and a stated domain of validity, used to explain or predict behaviour. The class covers the model as a knowledge artifact with its validation evidence; the software that implements it, the data used to fit it and machine-learned models as trained artifacts are separate subjects.","purpose":"Describe one formal model, its assumptions, parameterization and qualified evidence for use.","scope":{"in":["Formal equations, rules, objectives, constraints, symbols and assumptions","Parameter-set bindings, applicability limits and credibility evidence references","Model-specific submodel coupling, representation mapping and revision impact"],"out":["Software implementation, deployment, solver execution and simulation run lifecycle","Dataset stewardship, experiment execution, training and inference lifecycle","Generic ontology management and universal proof or conformance engines","Operational authorization or automated safety-critical decisions; dangerous applications remain policy-level only"],"boundaries":[{"neighbor":"WM-KNW-001","distinction":"Registry parent Model / Ontology is conceptual alignment only until a reviewed revision binding establishes specialization; generic vocabulary lifecycle is not copied."},{"neighbor":"WM-DAT-001","distinction":"Calibration, evaluation and output datasets retain separate masters; store only revision-pinned references and model-specific roles."},{"neighbor":"WM-SFT-001","distinction":"Software implementation products retain release, deployment and execution ownership; this dossier records the formal-revision binding."},{"neighbor":"WM-ACT-022","distinction":"Experiment Run owns calibration and verification execution, attempts and deviations; only model-scoped evidence references are local."},{"neighbor":"WM-VRT-003","distinction":"Simulation owns computational run state and results; the formal model owns its equations and declared conditions."},{"neighbor":"WM-VRT-012","distinction":"Simulation Scenario owns scenario-specific inputs and environmental setup; model applicability is a separate claim."},{"neighbor":"WM-AI-007","distinction":"Candidate binding for trained artifact registration when a hybrid model uses learned components. Training and inference lifecycles remain external; registry pin requires review."},{"neighbor":"Purely abstract models and hybrid learned components","distinction":"Empirical validation can be inapplicable with rationale; proofs and consistency claims remain scoped. Learned and analytical components can coexist, so exclusion is by separately mastered artifact and activity, not a false mathematical dichotomy."}]},"distinguishingFeatures":["It is the formal model with its assumptions and validity domain, not the software code that implements it.","Credibility depends on verification and validation for a stated context of use.","It differs from a machine-learned model artifact, whose behaviour comes from training rather than stated equations.","It differs from a dataset, which the model may use for calibration or produce as output."],"structure":{"bundles":[{"id":"KNW019-B1","name":"Formulation","description":"What the model says and under which assumptions.","layers":[{"id":"KNW019-B1-L1","name":"Equations and assumptions","description":"The governing equations or rules, variables, parameters and assumptions.","findings":[{"id":"KNW019-F01","name":"Model statement","description":"The equations or rules with defined variables and units.","questions":[{"text":"Which equations or rules define the model, and are all variables and units defined?","id":"KNW019-Q01"},{"text":"Which simplifying assumptions does the model make?","id":"KNW019-Q02"}]},{"id":"KNW019-F02","name":"Parameterization","description":"Parameter values with their sources and uncertainty.","questions":[{"text":"Where do the parameter values come from, measured, fitted or assumed?","id":"KNW019-Q03"},{"text":"What uncertainty is stated for each key parameter?","id":"KNW019-Q04"}]}]}]},{"id":"KNW019-B2","name":"Credibility","description":"Why the model can be trusted for a purpose.","layers":[{"id":"KNW019-B2-L1","name":"Verification and validation","description":"Evidence that the code solves the equations correctly and that the model matches reality.","findings":[{"id":"KNW019-F03","name":"Verification","description":"Evidence that the implementation solves the model as stated.","questions":[{"text":"Has the implementation been checked against analytical solutions or reference cases?","id":"KNW019-Q05"},{"text":"How were numerical errors such as discretization error estimated?","id":"KNW019-Q06"}]},{"id":"KNW019-F04","name":"Validation for context of use","description":"Comparison with independent observations for a stated context of use.","questions":[{"text":"For which context of use was the model validated, and against which independent data?","id":"KNW019-Q07"},{"text":"Is the intended use inside the validated domain?","id":"KNW019-Q08"}]}]}]},{"id":"KNW019-B3","name":"Use and versioning","description":"Which version produced which result.","layers":[{"id":"KNW019-B3-L1","name":"Versions and runs","description":"Model versions and the runs that used them.","findings":[{"id":"KNW019-F05","name":"Reproducible result","description":"A result traceable to a model version, inputs and settings.","questions":[{"text":"Which model version, inputs and settings produced this result?","id":"KNW019-Q09"},{"text":"Can an independent party reproduce the result from the published material?","id":"KNW019-Q10"}]}]}]}]},"agentConduct":{"may":["Run a model within its validated domain and report results with their uncertainty.","Record model versions, parameters and run settings for reproducibility.","Compare model outputs against observations and report the discrepancy.","Flag uses that fall outside the stated domain of validity."],"mustNot":["Present model outputs as observed facts.","Use a model outside its validated context of use without saying so.","Tune parameters silently to reach a desired result.","Omit uncertainty or key assumptions when reporting results that inform decisions."],"requiresHuman":["Accepting a model as credible for a safety-critical or regulatory decision.","Approving a new model version for operational use.","Deciding policy or treatment based on model projections."]},"ethics":{"considerations":["Model projections can drive public decisions, so assumptions and uncertainty must be visible.","Models can embed biased assumptions that disadvantage groups they describe poorly.","Opaque models make it hard for affected people to contest decisions."],"affectedParties":["People affected by decisions based on model outputs","Modellers and research teams","Regulators and decision makers"]},"owners":{"steward":"The modelling team or research group that develops and maintains the model and answers for its validation.","roles":[{"name":"Model steward","responsibilities":["Maintains identity, revisions and evidence completeness"]},{"name":"Formulation author","responsibilities":["Records mathematics, parameters, assumptions and limitations"]},{"name":"Domain reviewer","responsibilities":["Assesses formal or empirical claims for the stated use and reports unresolved gaps"]},{"name":"Use acceptance authority","responsibilities":["Accepts or rejects a named revision for a specific consequential use under an external policy"]},{"name":"Records and access custodian","responsibilities":["Controls rights, restricted views, retention and disposition"]}],"masterSystems":["Model repositories and registries","Version control systems","Publication and data repositories"]},"relations":[{"target":"WM-KNW-001","type":"aligned","note":"Registry parent Model / Ontology is conceptual alignment only until a reviewed revision binding establishes specialization; generic vocabulary lifecycle is not copied."},{"target":"WM-DAT-001","type":"references","note":"Calibration, evaluation and output datasets retain separate masters; store only revision-pinned references and model-specific roles."},{"target":"WM-SFT-001","type":"references","note":"Software implementation products retain release, deployment and execution ownership; this dossier records the formal-revision binding."},{"target":"WM-ACT-022","type":"references","note":"Experiment Run owns calibration and verification execution, attempts and deviations; only model-scoped evidence references are local."},{"target":"WM-VRT-003","type":"references","note":"Simulation owns computational run state and results; the formal model owns its equations and declared conditions."},{"target":"WM-VRT-012","type":"references","note":"Simulation Scenario owns scenario-specific inputs and environmental setup; model applicability is a separate claim."},{"target":"WM-AI-007","type":"references","note":"Candidate binding for trained artifact registration when a hybrid model uses learned components. Training and inference lifecycles remain external; registry pin requires review."},{"target":"MathML 3.0 Second Edition","type":"aligned","note":"Optional content-expression projection; presentation markup alone is insufficient to establish semantic equivalence."},{"target":"CellML 2.0","type":"aligned","note":"Optional variables, units and component projection; unsupported formalisms require a declared gap."},{"target":"FMI 3.0.2","type":"aligned","note":"Optional implementation exchange binding with explicit interface type; no automatic solver or execution permission."},{"target":"SED-ML Level 1 Version 5","type":"aligned","note":"Reference simulation experiment descriptions without treating tasks as the formal model."},{"target":"SBML Level 3 Version 2 Core Release 2","type":"aligned","note":"Candidate biological exchange profile with explicit package declarations. Detailed normative and conformance review is deferred."},{"target":"PROV-O 2013","type":"aligned","note":"Proposed attribution and derivation mapping, not a trust or scientific validity certificate."},{"target":"WM-KNW-001","type":"neighbor","note":"Registry parent Model / Ontology is conceptual alignment only until a reviewed revision binding establishes specialization; generic vocabulary lifecycle is not copied."},{"target":"WM-DAT-001","type":"neighbor","note":"Calibration, evaluation and output datasets retain separate masters; store only revision-pinned references and model-specific roles."},{"target":"WM-SFT-001","type":"neighbor","note":"Software implementation products retain release, deployment and execution ownership; this dossier records the formal-revision binding."},{"target":"WM-ACT-022","type":"neighbor","note":"Experiment Run owns calibration and verification execution, attempts and deviations; only model-scoped evidence references are local."},{"target":"WM-VRT-003","type":"neighbor","note":"Simulation owns computational run state and results; the formal model owns its equations and declared conditions."},{"target":"WM-VRT-012","type":"neighbor","note":"Simulation Scenario owns scenario-specific inputs and environmental setup; model applicability is a separate claim."},{"target":"WM-AI-007","type":"neighbor","note":"Candidate binding for trained artifact registration when a hybrid model uses learned components. Training and inference lifecycles remain external; registry pin requires review."},{"target":"Purely abstract models and hybrid learned components","type":"neighbor","note":"Empirical validation can be inapplicable with rationale; proofs and consistency claims remain scoped. Learned and analytical components can coexist, so exclusion is by separately mastered artifact and activity, not a false mathematical dichotomy."},{"target":"WM-KNW-001","type":"parent"}],"interaction":{"identity":{"applicability":"required","items":["A model is identified by its name, version and maintaining group, and often by a persistent identifier such as a DOI.","Curated model repositories assign accession identifiers to deposited models."]},"properties":{"applicability":"not-applicable","items":[]},"recognition":{"applicability":"optional","items":["A model is recognized by stated equations or rules, defined variables, parameters and a validity domain.","Often confused with its software implementation, with a dataset or with a trained machine learning model."]},"capabilities":{"applicability":"required","items":["A model can predict or explain system behaviour within its validated domain.","Runs can be reproduced when version, inputs and settings are recorded.","Sensitivity and uncertainty analysis can show which parameters drive results."]},"hazards":{"applicability":"required","items":["Wrong decisions from models used outside their validity domain.","False confidence when uncertainty is not reported.","Irreproducible results when versions and inputs are not recorded."]},"interfaces":{"applicability":"required","items":["SBML and CellML for exchanging biological models.","Functional Mock-up Interface (FMI) for exchanging simulation models.","ASME V&V 40 for assessing model credibility in medical device contexts."]},"context":{"applicability":"required","items":["Used in science, engineering, medicine, economics and public policy for prediction and analysis.","Regulators increasingly accept modelling evidence when credibility for the context of use is shown."]}},"sources":[{"title":"NASA-STD-7009B: Standard for Models and Simulations","url":"https://standards.nasa.gov/sites/default/files/standards/NASA/B/1/NASA-STD-7009B-Final-3-5-2024.pdf","note":"NASA"},{"title":"MathML 3.0 Second Edition, Chapter 4: Content Markup","url":"https://www.w3.org/TR/MathML3/chapter4.html","note":"W3C"},{"title":"CellML 2.0: Normative Specification","url":"https://www.cellml.org/cellml/2.0","note":"CellML Project"},{"title":"Functional Mock-up Interface Specification","url":"https://fmi-standard.org/docs/3.0.2/","note":"Modelica Association"},{"title":"Simulation Experiment Description Markup Language: Level 1 Version 5","url":"https://sed-ml.org/documents/sed-ml-L1V5.pdf","note":"SED-ML Editorial Board"},{"title":"SBML Level 3 Version 2 specification release page","url":"https://sbml.org/documents/specifications/level-3/version-2/","note":"SBML Editorial Board"},{"title":"PROV-O: The PROV Ontology","url":"https://www.w3.org/TR/prov-o/","note":"W3C"},{"title":"RFC 3339: Date and Time on the Internet: Timestamps","url":"https://www.rfc-editor.org/rfc/rfc3339","note":"IETF"},{"title":"ASME V&V 40 Assessing Credibility of Computational Modeling through Verification and Validation: Application to Medical Devices, ASME"},{"title":"Functional Mock-up Interface (FMI) Standard, Modelica Association"},{"title":"Systems Biology Markup Language (SBML), SBML community"}],"openQuestions":["Verify source transport outside the sandbox and assess exact versions, errata, rights and the complete SBML normative specification before claiming detailed alignment.","Develop specialist profiles, nested schemas and counterexample fixtures for abstract, stochastic, hybrid, ill-conditioned and data-overlap cases, plus pinned mappings and submodel bindings.","Restore independent external review before any canonical or publishable-draft promotion.","Independent external review is absent; the planned local no-tools audit cannot replace it.","Direct HTTP checks are not attempted under the owner-reported sandbox block; response statuses and body hashes are unmeasured.","Full SBML normative core, current-version status, errata, licensing and detailed conformance remain unverified.","Candidate answer elements are not executable nested instance schemas. No proof checker, numerical solver, simulator or format converter is implemented.","Adoption requires specialist mathematical, statistical, domain and use-risk profiles, including stochastic and hybrid behavior and data-dependence analysis."],"resources":{"spec":"/models/wm-knw-019-mathematical-computational-model/spec.yaml","agents":"/models/wm-knw-019-mathematical-computational-model/AGENTS.md","source":"https://github.com/ver-cy/world-models/tree/feat/mega-model-registry/research/runs/wm-knw-019"},"provenance":{"origin":"world-models research","builtFrom":["models/wm-knw-019-mathematical-computational-model/spec.yaml","ver-cy/world-models/card-supplements/wm-knw-019-mathematical-computational-model.json"],"providers":["Codex"],"researchStatus":"reviewable-draft","generatedAt":"2026-10-06T21:03:49Z","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":"not-applicable","interaction.recognition":"filled","interaction.capabilities":"filled","interaction.hazards":"filled","interaction.interfaces":"filled","interaction.context":"filled","sources":"filled"},"notes":{"interaction.properties":"A mathematical or computational model is an information artifact with no physical properties to measure.","_supplement":"Sections authored in card supplement 1.0.0 by Claude (Opus 5.5) (2026-10-06, unreviewed). Written from the card's existing content and established practice in the field; no new sources were read. Unreviewed."},"score":1.0}}