Deterministic Structural Causal Dynamics (DSCD): Trust-Gated Emergence of Certifiable Causal Graphs for Safety-Critical Aerospace Autonomy

Causal structure in safety-critical systems is typically modeled using probabilistic graphicalframeworks whose validity depends on distributional assumptions and stochastic independence.Such assumptions may degrade under adversarial disturbances, non-Gaussian sensor corruption,or abrupt regime shifts.This paper introduces Deterministic Structural Causal Dynamics (DSCD), a framework inwhich causal adjacency emerges from bounded structural growth constrained by trust-monotoneobserver hierarchies. DSCD integrates algebraic rewriting invariants, resonance-based reacha-bility, and deterministic residual envelopes to generate a locally finite directed acyclic graphwithout invoking probabilistic primitives.Under clearly stated assumptions—bounded rewriting, local finiteness, and monotone trust-gated edge creation—we prove that the induced structural graph is acyclic and interval-finite.We further establish the existence of critical trust thresholds that induce sharp structural con-nectivity transitions, analogous to deterministic percolation phenomena. Observer consistencyresults show that overlapping trust envelopes produce isomorphic causal subgraphs, ensuringstructural agreement without Bayesian consensus.A dedicated Rust implementation (dsfb-dscd) demonstrates scalable graph construction andthreshold extraction up to 105 events with O(N log N ) complexity. The resulting frameworkprovides explicit causal provenance, bounded causal intervals, and replayable regime detectionaligned with certification-oriented traceability and worst-case assurance requirements, withoutreliance on probabilistic assumptions.DSCD is not a physical spacetime model; rather, it establishes a mathematically groundedand computationally realizable method for deriving certifiable causal structure from determin-istic structural growth laws.This work focuses on the mathematical formulation, structural guarantees, and deterministiccomputational realization of the framework; validation within operational aerospace telemetrypipelines is left for future work.