Deterministic Structural Causal Dynamics (DSCD): Trust-Gated Emergence of Certifiable Causal Graphs for Safety-Critical Aerospace Autonomy
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| Sprache: | Englisch |
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2026
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| _version_ | 1866901741403897856 |
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| author | de Beer, Riaan |
| author_facet | de Beer, Riaan |
| contents | <p>Causal structure in safety-critical systems is typically modeled using probabilistic graphical<br>frameworks whose validity depends on distributional assumptions and stochastic independence.<br>Such assumptions may degrade under adversarial disturbances, non-Gaussian sensor corruption,<br>or abrupt regime shifts.<br>This paper introduces Deterministic Structural Causal Dynamics (DSCD), a framework in<br>which causal adjacency emerges from bounded structural growth constrained by trust-monotone<br>observer hierarchies. DSCD integrates algebraic rewriting invariants, resonance-based reacha-<br>bility, and deterministic residual envelopes to generate a locally finite directed acyclic graph<br>without invoking probabilistic primitives.<br>Under clearly stated assumptions—bounded rewriting, local finiteness, and monotone trust-<br>gated edge creation—we prove that the induced structural graph is acyclic and interval-finite.<br>We further establish the existence of critical trust thresholds that induce sharp structural con-<br>nectivity transitions, analogous to deterministic percolation phenomena. Observer consistency<br>results show that overlapping trust envelopes produce isomorphic causal subgraphs, ensuring<br>structural agreement without Bayesian consensus.<br>A dedicated Rust implementation (dsfb-dscd) demonstrates scalable graph construction and<br>threshold extraction up to 105 events with O(N log N ) complexity. The resulting framework<br>provides explicit causal provenance, bounded causal intervals, and replayable regime detection<br>aligned with certification-oriented traceability and worst-case assurance requirements, without<br>reliance on probabilistic assumptions.<br>DSCD is not a physical spacetime model; rather, it establishes a mathematically grounded<br>and computationally realizable method for deriving certifiable causal structure from determin-<br>istic structural growth laws.<br>This work focuses on the mathematical formulation, structural guarantees, and deterministic<br>computational realization of the framework; validation within operational aerospace telemetry<br>pipelines is left for future work.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_18867217 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Deterministic Structural Causal Dynamics (DSCD): Trust-Gated Emergence of Certifiable Causal Graphs for Safety-Critical Aerospace Autonomy de Beer, Riaan deterministic causality causal graphs structural causality trust-gated systems deterministic dynamical systems causal topology causal dependency graphs safety-critical systems aerospace autonomy deterministic state estimation residual envelope methods trust-adaptive systems deterministic sensor fusion causal provenance deterministic graph dynamics regime transition detection finite causal intervals structural phase transitions deterministic replay certification-oriented autonomy certifiable autonomy DSFB Drift-Slew Fusion Bootstrap Algebraic Deterministic Dynamics Deterministic Structural Causal Dynamics <p>Causal structure in safety-critical systems is typically modeled using probabilistic graphical<br>frameworks whose validity depends on distributional assumptions and stochastic independence.<br>Such assumptions may degrade under adversarial disturbances, non-Gaussian sensor corruption,<br>or abrupt regime shifts.<br>This paper introduces Deterministic Structural Causal Dynamics (DSCD), a framework in<br>which causal adjacency emerges from bounded structural growth constrained by trust-monotone<br>observer hierarchies. DSCD integrates algebraic rewriting invariants, resonance-based reacha-<br>bility, and deterministic residual envelopes to generate a locally finite directed acyclic graph<br>without invoking probabilistic primitives.<br>Under clearly stated assumptions—bounded rewriting, local finiteness, and monotone trust-<br>gated edge creation—we prove that the induced structural graph is acyclic and interval-finite.<br>We further establish the existence of critical trust thresholds that induce sharp structural con-<br>nectivity transitions, analogous to deterministic percolation phenomena. Observer consistency<br>results show that overlapping trust envelopes produce isomorphic causal subgraphs, ensuring<br>structural agreement without Bayesian consensus.<br>A dedicated Rust implementation (dsfb-dscd) demonstrates scalable graph construction and<br>threshold extraction up to 105 events with O(N log N ) complexity. The resulting framework<br>provides explicit causal provenance, bounded causal intervals, and replayable regime detection<br>aligned with certification-oriented traceability and worst-case assurance requirements, without<br>reliance on probabilistic assumptions.<br>DSCD is not a physical spacetime model; rather, it establishes a mathematically grounded<br>and computationally realizable method for deriving certifiable causal structure from determin-<br>istic structural growth laws.<br>This work focuses on the mathematical formulation, structural guarantees, and deterministic<br>computational realization of the framework; validation within operational aerospace telemetry<br>pipelines is left for future work.</p> |
| title | Deterministic Structural Causal Dynamics (DSCD): Trust-Gated Emergence of Certifiable Causal Graphs for Safety-Critical Aerospace Autonomy |
| topic | deterministic causality causal graphs structural causality trust-gated systems deterministic dynamical systems causal topology causal dependency graphs safety-critical systems aerospace autonomy deterministic state estimation residual envelope methods trust-adaptive systems deterministic sensor fusion causal provenance deterministic graph dynamics regime transition detection finite causal intervals structural phase transitions deterministic replay certification-oriented autonomy certifiable autonomy DSFB Drift-Slew Fusion Bootstrap Algebraic Deterministic Dynamics Deterministic Structural Causal Dynamics |
| url | https://doi.org/10.5281/zenodo.18867217 |