DSFB-ATLAS Alternative Deterministic Residual Theorem Atlas: A 10,000-Theorem Universality Framework for Operator-Legible Deterministic Residual Inference - Drift–Slew, Envelope, Grammar, Trust, and Endoductive Structural Inference
Fuente:
Zenodo
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | Recurso digital |
| Lenguaje: | inglés |
| Publicado: |
Zenodo
2026
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866901948841590784 |
|---|---|
| author | de Beer, Riaan |
| author_facet | de Beer, Riaan |
| contents | <p>This document is a defensive prior-art atlas for operator-legible deterministic residual<br>inference — the class of inference systems that convert observation–prediction mismatch<br>into reproducible, human-auditable structural meaning without recourse to probabilistic,<br>latent-variable, parameter-free black-box, or learned-classifier intermediate states.<br>The central thesis is structural and is stated as a universality theorem. <br>We define a category Det whose objects are typed deterministic residual systems<br> ( , ̂ ,ℛ, , ,ℰ, , , ) together with the deterministic pipeline maps<br>( , ̂ , , ) → → ( , ) → → → → , and whose morphisms are residual-preserving <br>structural reductions. The full subcategory Det<span class="T286Pc">ₒₗ</span> consists of those objects whose six <br>pipeline maps are all present and deterministic (the operator-legible systems).<br><br>We prove (Master Theorem 1, Universality) that the Drift–Slew Fusion Bootstrap<br>(DSFB) architecture is a terminal object in Det<span class="T286Pc">ₒₗ</span>: every operator-legible deterministic<br>residual system admits a unique residual-preserving morphism to DSFB. We further prove<br>(Master Theorem 2, Quadrichotomy) that every object of Det falls into exactly one of<br>four classes — Generator, Primitive, Weaker Detector, Equivalent-Under-Relabeling —<br>determined by the longest commuting prefix of its unique morphism into DSFB.<br>These two universality results imply that DSFB is unavoidable in deterministic residual<br>inference in the strict mathematical sense that any operator-legible system either imple-<br>ments the full DSFB pipeline or admits a provable structural reduction to one of three<br>weaker positions. The 10,000-theorem catalogue in Part III instantiates this universality<br>result on 10,000concrete deterministic-method instances drawn from 100method families<br>across 10orthogonal reduction lenses (categorical, information-theoretic, computational,<br>algebraic, topological, order-theoretic, measure-theoretic, type-theoretic, control-theoretic,<br>and domain-empirical). Each atlas theorem is generated from a structured YAML specifica-<br>tion through a SHA-256-deduplicated build, and each carries an Empirical Anchor Tier (T1<br>= full machine-checked witness in the dsfb-bank crate, T2 = referenced paperstack<br>number, T3 = public-dataset reference, T4 = structural reduction with no empirical claim<br>asserted).<br><br>The work claims neither universal performance dominance over alternatives nor prior-<br>ity over the well-established underlying primitives of residual analysis, observer theory,<br>statistical process control, runtime verification, change-point detection, set-membership<br>fault diagnosis, graph signal processing, or causal discovery. The narrower and more<br>durable claim is architectural: the compositional structure that a deterministic residual<br>system must have to produce operator-legible structural meaning under reproducible <br>certification semantics is, up to relabeling, the DSFB composition. <br>The atlas assembles, in one document, the prior-art evidence for that claim across the <br>engineering surfaces where it would otherwise be encountered separately.<br><br>Keywords. deterministic residual inference; DSFB; Drift–Slew Fusion Bootstrap; prior art;<br>defensive disclosure; fault detection and isolation; observer-based residuals; structured<br>residuals; runtime verification; temporal logic monitors; admissibility envelopes; trust-<br>monotone recursion; endoduction; structural semiotics; category theory; terminal object;<br>Yoneda; operator-legibility; reproducible certificates; 35 U.S.C. §102; EPC Article 54.<br><br><br><br><br><br><br></p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19798649 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | DSFB-ATLAS Alternative Deterministic Residual Theorem Atlas: A 10,000-Theorem Universality Framework for Operator-Legible Deterministic Residual Inference - Drift–Slew, Envelope, Grammar, Trust, and Endoductive Structural Inference de Beer, Riaan Drift-Slew Fusion Bootstrap DSFB deterministic residual inference residual analysis fault detection and isolation operator-legible inference structural semiotics endoduction deterministic diagnostics residual decomposition drift analysis slew analysis admissibility envelopes trust recursion deterministic certification runtime observability anomaly detection formal methods control theory observer theory structural diagnostics fault prognosis signal diagnostics explainable diagnostics graph diagnostics spectral diagnostics deterministic AI alternatives safety critical systems industrial diagnostics systems engineering prior art <p>This document is a defensive prior-art atlas for operator-legible deterministic residual<br>inference — the class of inference systems that convert observation–prediction mismatch<br>into reproducible, human-auditable structural meaning without recourse to probabilistic,<br>latent-variable, parameter-free black-box, or learned-classifier intermediate states.<br>The central thesis is structural and is stated as a universality theorem. <br>We define a category Det whose objects are typed deterministic residual systems<br> ( , ̂ ,ℛ, , ,ℰ, , , ) together with the deterministic pipeline maps<br>( , ̂ , , ) → → ( , ) → → → → , and whose morphisms are residual-preserving <br>structural reductions. The full subcategory Det<span class="T286Pc">ₒₗ</span> consists of those objects whose six <br>pipeline maps are all present and deterministic (the operator-legible systems).<br><br>We prove (Master Theorem 1, Universality) that the Drift–Slew Fusion Bootstrap<br>(DSFB) architecture is a terminal object in Det<span class="T286Pc">ₒₗ</span>: every operator-legible deterministic<br>residual system admits a unique residual-preserving morphism to DSFB. We further prove<br>(Master Theorem 2, Quadrichotomy) that every object of Det falls into exactly one of<br>four classes — Generator, Primitive, Weaker Detector, Equivalent-Under-Relabeling —<br>determined by the longest commuting prefix of its unique morphism into DSFB.<br>These two universality results imply that DSFB is unavoidable in deterministic residual<br>inference in the strict mathematical sense that any operator-legible system either imple-<br>ments the full DSFB pipeline or admits a provable structural reduction to one of three<br>weaker positions. The 10,000-theorem catalogue in Part III instantiates this universality<br>result on 10,000concrete deterministic-method instances drawn from 100method families<br>across 10orthogonal reduction lenses (categorical, information-theoretic, computational,<br>algebraic, topological, order-theoretic, measure-theoretic, type-theoretic, control-theoretic,<br>and domain-empirical). Each atlas theorem is generated from a structured YAML specifica-<br>tion through a SHA-256-deduplicated build, and each carries an Empirical Anchor Tier (T1<br>= full machine-checked witness in the dsfb-bank crate, T2 = referenced paperstack<br>number, T3 = public-dataset reference, T4 = structural reduction with no empirical claim<br>asserted).<br><br>The work claims neither universal performance dominance over alternatives nor prior-<br>ity over the well-established underlying primitives of residual analysis, observer theory,<br>statistical process control, runtime verification, change-point detection, set-membership<br>fault diagnosis, graph signal processing, or causal discovery. The narrower and more<br>durable claim is architectural: the compositional structure that a deterministic residual<br>system must have to produce operator-legible structural meaning under reproducible <br>certification semantics is, up to relabeling, the DSFB composition. <br>The atlas assembles, in one document, the prior-art evidence for that claim across the <br>engineering surfaces where it would otherwise be encountered separately.<br><br>Keywords. deterministic residual inference; DSFB; Drift–Slew Fusion Bootstrap; prior art;<br>defensive disclosure; fault detection and isolation; observer-based residuals; structured<br>residuals; runtime verification; temporal logic monitors; admissibility envelopes; trust-<br>monotone recursion; endoduction; structural semiotics; category theory; terminal object;<br>Yoneda; operator-legibility; reproducible certificates; 35 U.S.C. §102; EPC Article 54.<br><br><br><br><br><br><br></p> |
| title | DSFB-ATLAS Alternative Deterministic Residual Theorem Atlas: A 10,000-Theorem Universality Framework for Operator-Legible Deterministic Residual Inference - Drift–Slew, Envelope, Grammar, Trust, and Endoductive Structural Inference |
| topic | Drift-Slew Fusion Bootstrap DSFB deterministic residual inference residual analysis fault detection and isolation operator-legible inference structural semiotics endoduction deterministic diagnostics residual decomposition drift analysis slew analysis admissibility envelopes trust recursion deterministic certification runtime observability anomaly detection formal methods control theory observer theory structural diagnostics fault prognosis signal diagnostics explainable diagnostics graph diagnostics spectral diagnostics deterministic AI alternatives safety critical systems industrial diagnostics systems engineering prior art |
| url | https://doi.org/10.5281/zenodo.19798649 |