FPF Reference

    Source and governing basis

    Preface node heading:source-and-governing-basis:51631

    What this page is

    This is generated FPF reference text from the specification preface or supporting sections. It helps interpret FPF; it is not FPF Reference product documentation.

    Methodology

    Use it to understand how the specification wants to be read, then return to a route, pattern, or work packet for active work. Cite generated IDs only when the wording changes the task decision.

    Content

    Basis idBasis itemWhat it contributesUse in C.29
    FPF-CORE-2026Current FPF Core Specification, especially E.9, E.10, C.2.P, A.6.P, A.3.3, A.19, A.10, A.15, A.15.1, A.15.4, B.3, C.11, C.16, C.18.1, C.19.1, C.26, C.27, C.28, E.17.EFP, E.17.ID.CR, A.6.3.RT, A.6.3.CSC, F.9, G.5, G.9.Governs C.29 adequacy, lexical precision repair, epistemic precision repair, pattern placement, bridge discipline, decision boundaries, work boundaries, evidence boundaries, assurance boundaries, explanation boundaries, comparison boundaries, representation boundaries, state boundaries, measurement boundaries, dynamics boundaries, temporal boundaries, causal-use boundary, and evidence and assurance escalation.Governing inheritance. C.29 applications satisfy E.9 and phrase-local episteme material, publication material, and source-use material through C.2.P.
    SAND-THREAD-MATH-LINKS-2026-05-12Accessible mirror of Sandberg thread, lines headed “Math,” linking to the original X post.Recognition examples of structural sameness: generalized Stokes, CLT as RG or fixed-point interpretation, Lawvere-style diagonal family, Noether, Legendre transforms.Adopt as recognition cue and examples, not proof authority. Direct X content was not treated as a formal source.
    VAN-GEOM-LEARNING-2025/2026Vitaly Vanchurin, Geometric Learning Dynamics, arXiv:2504.14728 v3, last revised 2026-03-14 and accepted for publication in Biological Cybernetics.Candidate lens family: geometric learning dynamics over the relation between metric tensor, noise covariance, and learning regime; useful as a replayable source for metric-tensor, noise-covariance, and learning-dynamics lens selection.Adapt, not adopt. Use as SoTA-echo candidate lens or stress test for CandidateMathObject, LensMappingMode, preserved structure and lost structure, validation boundary, and stop condition; do not accept the physical or biological interpretation as FPF law.
    RODIN-2023Andrei Rodin, One Mathematic(s) or Many? Foundations of Mathematics in Today's Mathematical Practice, arXiv:2301.08131.Contributes plural-foundations source material and mutual-interpretability caution.Adopt as source material for multiple structural families checked through local adequacy, declared mapping, and recoverable loss.
    FONG-SPIVAK-2018/2019Brendan Fong and David I. Spivak, Seven Sketches in Compositionality and An Invitation to Applied Category Theory, arXiv:1803.05316 and book publication context.Contributes applied category theory as one useful family for composition, interfaces, views, transformations, and bridges.Adopt and adapt for examples and transport discipline when those structures matter to the stated use.
    GDL-BRONSTEIN-2021Bronstein et al., Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges, arXiv:2104.13478.Contributes lens-discovery cues through symmetry, invariance, equivariance, group action, geometric structure, and graph structure.Adapt as discovery source. Helps find a candidate lens; does not supply domain evidence, causal mechanism, or validation by itself.
    PEYRE-CUTURI-2019Gabriel Peyré and Marco Cuturi, Computational Optimal Transport, arXiv:1803.00567 and Foundations and Trends in Machine Learning publication context.Contributes distribution-geometry discovery cues through transport plans, couplings, Wasserstein-like distances, movement cost, and shape or population shift.Adapt as discovery source. Helps formulate comparison and movement questions; does not supply causal, fairness, mechanism, or policy-effect evidence by itself.
    PUCA-ETAL-2023Puca, Hadzihasanovic, Genovese, Coecke, Obstructions to Compositionality, arXiv:2307.14461.Contributes source material for making failures and obstructions to compositional transfer explicit.Adapt into LostStructure, StopCondition, and checks that not every transfer preserves the needed structure.
    MODEL-REPORTING-2018/2021Mitchell et al., Model Cards for Model Reporting; Gebru et al., Datasheets for Datasets.Contributes intended-use, evaluation-condition, limitation, dataset-context, and out-of-scope-use declarations for model and data-bearing lenses.Adapt. Use for admissibleUse, nonAdmissibleUse, validation regime, limitation notes, and domain-of-applicability fields; do not treat documentation presence as evidence or assurance by itself.
    CAUSAL-ABSTRACTION-2017/2019Rubenstein et al., Causal Consistency of Structural Equation Models; Beckers and Halpern, Abstracting Causal Models.Contributes the question of whether abstraction, quotient, macro-model, or coarse-graining preserves intervention and counterfactual structure.Adapt. Feeds MathLensUse.CausalAbstractionCheck; causal-use question and verdict still belongs to C.28.
    APPROX-CAUSAL-ABSTRACTION-2019/2020Beckers, Eberhardt, and Halpern, Approximate Causal Abstraction and Approximate Causal Abstractions, arXiv:1906.11583 and PMLR 2020.Contributes the distinction between approximate and exact micro-to-macro causal abstraction, including discrepancy between micro-model and macro-model causal descriptions and uncertainty in probabilistic causal models.Adapt. Justifies the approximated value in MathLensUse.CausalAbstractionCheck; causal-use question and verdict still belongs to C.28.
    CAUSAL-ABSTRACTION-JMLR-2025Causal Abstraction: A Theoretical Foundation for Mechanistic Interpretability, JMLR 2025.Contributes generalized mechanism transformation, graded faithfulness, and abstraction checks for learned systems, including where representation mappings become too flexible to license explanation or causal use.Adapt. Strengthens the abstraction-preservation question; causal-use question and verdict still belongs to C.28.
    SCHOLKOPF-ETAL-2021Scholkopf et al., Towards Causal Representation Learning, Proceedings of the IEEE 2021, arXiv:2102.11107.Contributes distinctions among learned latent representations, causal variables, interventions, assignments, environment invariance, and causal-use claims.Adapt as discovery source. Helps detect when C.28 applies; does not make a latent representation causal by itself.
    SCIML-NEURAL-OPERATORS-2019/2021Raissi, Perdikaris, and Karniadakis on PINNs; Karniadakis et al. on physics-informed machine learning; Lu et al. on DeepONet; Li et al. on Fourier neural operators.Contributes learned-lens obligations: observation map, data or training regime, discretization or resolution policy, generalization claim, validation regime, uncertainty, and stop condition.Adapt. Use as source material for the lightweight learned-lens overlay; do not promote a full SciML specialization or assume out-of-domain generalization.
    SCIML-DIETRICH-SCHILDERS-2025Dietrich and Schilders, Scientific machine learning, Mathematische Semesterberichte 2025, DOI 10.1007/s00591-025-00399-4.Contributes the hybrid first-principles and data-driven framing: conservation laws, constitutive relations, boundary conditions, physical consistency, operator learning, probabilistic approaches, uncertainty, robustness, and validation limits.Adapt. Reinforces plural first-principles discipline and validation boundaries; does not make SciML a universal FPF foundation.
    PIML-SURVEY-2025When physics meets machine learning: a survey of physics-informed machine learning, Machine Learning for Computational Science and Engineering 2025, DOI 10.1007/s44379-025-00016-0.Contributes physics-informed learning as integration of prior physics knowledge with data-driven models for data efficiency, generalization, and plausibility, including Lagrangian or Hamiltonian mechanics, energy conservation, physics-informed losses, and physics-informed optimization as current first-principles lens families.Adapt. Strengthens the learned-lens and variational-principle use; does not make physics-informed wording sufficient evidence or assurance.
    NEURAL-OPERATORS-NRP-2024Neural operators for accelerating scientific simulations and design, Nature Reviews Physics 2024, DOI 10.1038/s42254-024-00712-5.Contributes neural operators as learned mappings between functions over continuous domains, often constrained by physics and domain structure, with generalization and validation boundaries.Adapt. Contributes operator lens discovery and function-space lens discovery and validation-regime prompts; does not license out-of-regime solver replacement.
    PHYSICS-FOUNDATION-MODEL-2025Towards a Physics Foundation Model, arXiv:2509.13805.Contributes SoTA pressure around broad pretraining, in-context dynamics inference, cross-domain simulation, zero-shot transfer, and long-horizon prediction.Adapt as candidate and stress-test. Does not make a foundation model accepted physics, causal-use verdict, assurance, or a universal first-principles source.
    KOOPMAN-SINDY-DMD-2016Brunton, Proctor, and Kutz, Discovering governing equations from data by sparse identification of nonlinear dynamical systems; Kutz et al., Dynamic Mode Decomposition: Data-Driven Modeling of Complex Systems.Contributes operator and system-identification discovery cues through observables, dynamic-mode decomposition, sparse identification, forecast use, and control-oriented representation.Adapt as discovery source. Does not make the identified operator a real mechanism or validate temporal-use claims by itself.
    BAYES-WORKFLOW-PPL-2018/2020van de Meent et al., An Introduction to Probabilistic Programming; Gelman et al., Bayesian Workflow.Contributes probabilistic-model discovery and criticism cues through priors, likelihood assumptions, posterior predictive checks, prior-data conflict, model mismatch, uncertainty, and iterative model revision.Adapt as discovery and criticism source. Does not make posterior fit truth, evidence, or assurance by itself.
    MODERN-BED-2023/2024Rainforth, Foster, Ivanova, and Bickford Smith, Modern Bayesian Experimental Design, arXiv:2302.14545; accepted/published in Statistical Science context.Contributes current BED as utility-driven and computationally constrained, with recent methods for tractable expected information gain, sequential or adaptive design, and practical deployment limits.Adapt as current discovery source. Does not make C.29 a measurement-construction, evidence, causal-use, or experiment-planning pattern.
    MODERN-OED-2024/2026Huan, Jagalur, and Marzouk, Optimal experimental design: Formulations and computations, Acta Numerica 2024; arXiv:2407.16212 v2 2026.Contributes broad current OED framing: design variables, utility criteria, computational methods, sequential design, complex models, and prediction-oriented data acquisition.Adapt as current discovery source. C.29 may ask what data acquisition would make the lens usable, but neighboring patterns govern experiments, evidence, causal-use verdict, and work planning.
    BO-AL-ADAPTIVE-SAMPLING-2024Di Fiore, Nardelli, and Mainini, Active Learning and Bayesian Optimization: A Unified Perspective to Learn with a Goal, Archives of Computational Methods in Engineering 2024, DOI 10.1007/s11831-024-10064-z.Contributes active learning, Bayesian optimization, and adaptive sampling as goal-driven acquisition schemes, not as generic "collect more data" advice.Adapt as current discovery source. Use only for the candidate observation, probe, or acquisition move; do not import selector, evidence, or assurance authority.
    EIG-DENSITY-APPROX-2024/2026Li, Baptista, and Marzouk, Expected information gain estimation via density approximations: Sample allocation and dimension reduction, arXiv:2411.08390 v3 2026.Contributes current computational caution: EIG estimation itself can require density approximation, sample-allocation, and dimension-reduction choices before it is usable.Adapt as computational-tractability source. A claimed information-gain lens needs estimation and approximation fields when the computation is required for the declared lens use.
    ROBUST-GBOED-2025Barlas, Sloman, and Kaski, Robust Experimental Design via Generalised Bayesian Inference, arXiv:2511.07671.Contributes robustness prompts for model misspecification, outliers, and incorrect noise assumptions through generalized Bayesian OED or Gibbs Bayesian OED and Gibbs expected information gain.Adapt as robustness source. If model misspecification is plausible, the C.29 output records the robustness note; it does not turn robustness into evidence or assurance by itself.
    VVUQ-UQ-PREDICTION-2010/2012/2007Oberkampf and Roy, Verification and Validation in Scientific Computing; National Research Council, Assessing the Reliability of Complex Models; Gneiting and Raftery, Strictly Proper Scoring Rules, Prediction, and Estimation.Contributes validation, uncertainty, prediction scoring, calibration caution, sensitivity or robustness notes, and domain-of-applicability boundaries.Adapt. Prediction, publication-as-model, benchmark, model-selection, or assurance-input uses need validation or uncertainty fields; source prestige does not supply those fields.
    Source-basis idLocator(s)Recoverability and use in C.29
    SAND-THREAD-X-2026-05-12Original X post locator: https://x.com/anderssandberg/status/2053757849918939364Source identity locator. Keep the X link because the source being mirrored matters. Do not rely on direct X content as proof text unless the post content is actually retrievable in the checking environment.
    SAND-THREAD-MATH-LINKS-2026-05-12Accessible mirror or quotation carrier: https://axisofordinary.substack.com/p/links-for-2026-05-12, section headed Math, linking to the X post above.Checked source-text carrier. Supplies the recognition examples: generalized Stokes and boundary-exterior derivative duality; de Rham, cohomology, and topological obstruction; CLT as RG viewpoint or fixed-point viewpoint; Lawvere-style diagonal family; Noether and symmetry-conservation; Legendre, duality, and tropical-limit family.
    VAN-GEOM-LEARNING-2025/2026https://arxiv.org/abs/2504.14728; arXiv v3 revised 2026-03-14; accepted in Biological CyberneticsCandidate-lens source. Supplies a replayable geometric-learning-dynamics source for metric tensor, noise covariance, learning-regime, and validation-boundary questions. Use as SoTA-echo stress test for lens selection and stop condition; do not use as accepted physics, biological mechanism, evidence, assurance, or FPF law.
    RODIN-2023https://arxiv.org/abs/2301.08131Plural-foundations source. Contributes multiple interpretable mathematical foundations or families checked through local adequacy, declared mapping, and recoverable loss.
    FONG-SPIVAK-2018/2019https://arxiv.org/abs/1803.05316; Cambridge page: https://www.cambridge.org/core/books/an-invitation-to-applied-category-theory/D4C5E5C2B019B2F9B8CE9A4E9E84D6BCApplied-category-theory source. Contributes category theory as one useful organizer for composition, interfaces, views, transformations, and bridges when those structures matter to the stated use.
    GDL-BRONSTEIN-2021https://arxiv.org/abs/2104.13478Geometric-deep-learning discovery source. Contributes symmetry, invariance, equivariance, group action, graph structure, and geometric structure cues for candidate-lens discovery; not evidence that a domain law, causal mechanism, or validation claim holds.
    PEYRE-CUTURI-2019https://arxiv.org/abs/1803.00567Optimal-transport discovery source. Contributes transport plans, couplings, Wasserstein-like geometry, costed movement, and distribution, population, shape, shift, or allocation comparison; not causal, fairness, mechanism, or policy-effect evidence by itself.
    PUCA-ETAL-2023https://arxiv.org/abs/2307.14461Obstruction source. Contributes source material for making failures of transfer explicit; feeds LostStructure, StopCondition, and the rule that not every functor-like transfer preserves the needed structure.
    MODEL-CARDS-2018/2019https://arxiv.org/abs/1810.03993Model-reporting source. Supplies intended-use, evaluation-slice, limitation, and out-of-scope-use structure for model-bearing lenses; does not make reported model use admissible by itself.
    DATASHEETS-2018/2021https://arxiv.org/abs/1803.09010; CACM page: https://cacm.acm.org/research/datasheets-for-datasets/Dataset-documentation source. Supplies provenance, composition, collection, recommended use, and limitation prompts when a lens depends on data or dataset-derived representation.
    CAUSAL-CONSISTENCY-2017https://arxiv.org/abs/1707.00819Causal-abstraction source. Supports checking whether SEM descriptions at different granularities agree about intervention effects; feeds the intervention-preservation question without giving C.29 causal authority.
    CAUSAL-ABSTRACTION-2019https://arxiv.org/abs/1812.03789; AAAI page: https://ojs.aaai.org/index.php/AAAI/article/view/4117Causal-abstraction source. Supports distinguishing transformations, abstractions, and named abstraction classes; used only to require explicit C.28 application when causal use is being claimed.
    APPROX-CAUSAL-ABSTRACTION-2019/2020https://arxiv.org/abs/1906.11583; PMLR page: https://proceedings.mlr.press/v115/beckers20a.htmlApproximate causal-abstraction source. Contributes approximated intervention and counterfactual preservation value in the lightweight causal-abstraction check; does not let C.29 decide causal-use question and verdict without C.28.
    CAUSAL-ABSTRACTION-JMLR-2025https://jmlr.org/beta/papers/v26/23-0058.htmlCurrent causal-abstraction source. Contributes generalized mechanism-transformation and graded-faithfulness checks for learned systems; keeps causal-use question and verdict with C.28.
    SCHOLKOPF-ETAL-2021https://arxiv.org/abs/2102.11107; DOI 10.1109/JPROC.2021.3058954Causal-representation discovery source. Contributes the question whether a learned latent representation has intervention, assignment, outcome, and environment-invariance evidence path before causal use; causal-use question and verdict are governed by C.28 when causal use is being claimed.
    PINN-2019DOI 10.1016/j.jcp.2018.10.045Physics-informed ML source. Contributes validation, training-regime, governing-equation, and inverse-problem and forward-problem distinctions for learned mathematical lenses.
    PIML-2021DOI 10.1038/s42254-021-00314-5Physics-informed machine-learning survey source. Contributes physics-informed learning as a broad learned-lens family requiring problem, prior-knowledge, validation, and uncertainty boundaries.
    DEEPONET-2021DOI 10.1038/s42256-021-00302-5Neural-operator source. Contributes operator-learning as a learned mathematical lens over function spaces; requires training domain, observation map, generalization claim, and stop condition.
    FNO-2020/2021https://arxiv.org/abs/2010.08895Neural-operator source. Contributes resolution and PDE-family generalization checks; does not license out-of-regime solver replacement without validation.
    SCIML-DIETRICH-SCHILDERS-2025DOI 10.1007/s00591-025-00399-4; https://link.springer.com/article/10.1007/s00591-025-00399-4Current SciML survey source. Contributes hybrid first-principles and data-driven framing, physical consistency, operator learning, probabilistic approaches, uncertainty, robustness, and validation limits.
    PIML-SURVEY-2025DOI 10.1007/s44379-025-00016-0; https://link.springer.com/article/10.1007/s44379-025-00016-0Current physics-informed ML survey source. Contributes prior-physics integration as data-efficiency, generalization, and plausibility cues; not evidence or assurance by itself.
    NEURAL-OPERATORS-NRP-2024DOI 10.1038/s42254-024-00712-5; https://www.nature.com/articles/s42254-024-00712-5Neural-operator review source. Contributes function-space lens obligations and operator lens obligations, physics constraints and domain constraints, and validation boundaries for scientific simulation and design.
    PHYSICS-FOUNDATION-MODEL-2025https://arxiv.org/abs/2509.13805Physics-foundation-model candidate source. Contributes candidate and stress-test handling of broad scientific foundation-model claims; does not make those claims accepted FPF law.
    KOOPMAN-SINDY-DMD-2016SINDy DOI 10.1073/pnas.1517384113; DMD DOI 10.1137/1.9781611974508Operator-dynamics and system-identification discovery source. Contributes observable, dynamic-mode-decomposition, or sparse-identification lens choices for nonlinear dynamics; dynamics semantics, evidence, and temporal-use adequacy still require A.3.3, A.10, or C.27 when those claims are being made.
    BAYES-WORKFLOW-PPL-2018/2020Probabilistic programming arXiv https://arxiv.org/abs/1809.10756; Bayesian Workflow arXiv https://arxiv.org/abs/2011.01808Probabilistic-model discovery and criticism source. Contributes prior, likelihood, posterior predictive, prior-data conflict, model mismatch, uncertainty, and revision cues; does not make probabilistic fit a truth, evidence, or assurance result by itself.
    MODERN-BED-2023/2024https://arxiv.org/abs/2302.14545; DOI 10.48550/arXiv.2302.14545Modern Bayesian experimental design source. Contributes current BED as utility-driven and computationally constrained, with tractable EIG, sequential/adaptive design, and deployment limits; neighboring patterns still govern measurement construction, evidence, causal-use verdict, and work planning.
    MODERN-OED-2024/2026https://arxiv.org/abs/2407.16212; Cambridge Core DOI 10.1017/S0962492924000023Modern optimal experimental design source. Contributes broad OED formulations and computations for complex models; C.29 uses it only to ask what acquisition would make a candidate lens usable.
    BO-AL-ADAPTIVE-SAMPLING-2024DOI 10.1007/s11831-024-10064-z; https://link.springer.com/article/10.1007/s11831-024-10064-zAdaptive-sampling source. Supports goal-driven acquisition and the BO and active-learning relation; does not create selector, evidence, or assurance authority.
    EIG-DENSITY-APPROX-2024/2026https://arxiv.org/abs/2411.08390; DOI 10.48550/arXiv.2411.08390EIG computation source. Supports density-approximation, sample-allocation, and dimension-reduction caution for expected-information-gain claims.
    ROBUST-GBOED-2025https://arxiv.org/abs/2511.07671; DOI 10.48550/arXiv.2511.07671Robust experimental-design source. Supports generalized-Bayesian robustness for model misspecification, outliers, and incorrect noise assumptions.
    OBERKAMPF-ROY-2010Cambridge page: https://www.cambridge.org/core/books/verification-and-validation-in-scientific-computing/contents/9399D588DE8B3D49E392CF0436D5A67DVerification-and-validation source. Supports separation of verification, validation, uncertainty, calibration, and prediction-use boundaries.
    NRC-VVUQ-2012DOI 10.17226/13395; https://nap.nationalacademies.org/catalog/13395/assessing-the-reliability-of-complex-models-mathematical-and-statistical-foundationsVVUQ source. Supports uncertainty quantification and reliability limits for complex model use.
    GNEITING-RAFTERY-2007DOI 10.1198/016214506000001437Prediction-scoring source. Supports proper scoring and prediction-evaluation fields when a lens claims predictive use.

    Last Updated: 2026-06-08 — upstream FPF commit 093d30e8 (github.com/ailev/FPF)