Algebraic Deterministic Dynamics (ADD): A Non-Stochastic Structural Extension of DSFB

Safety-critical aerospace systems often rely on probabilistic state estimation and statistical modeling assumptions that degrade under adversarial disturbances, plasma blackout, non-Gaussian sensor corruption, or structural regime shifts. This work introduces Algebraic Deterministic Dynamics (ADD), a deterministic structural modeling framework that replaces probabilistic primitives with algebraic growth invariants, reachability structure, and filtration-based diagnostics. ADD demonstrates that strictly positive entropy-like growth, structural phase transitions, and cross-layer threshold invariants can arise from deterministic rewriting systems without stochastic assumptions. Finite-size scaling confirms convergence of macroscopic structural laws and transport boundaries across two decades of computational scale. When combined with Deterministic Drift–Slew Fusion Bootstrap (DSFB) estimation, ADD provides a vertically integrated deterministic architecture: structural growth invariants at the modeling layer and bounded residual envelopes at the estimation layer. Together, these methods enable robust regime detection, transport threshold identification, and state correction without reliance on Gaussian noise models or ensemble averaging. The results suggest a pathway toward deterministic modeling and estimation architectures for aerospace systems operating in adversarial, nonlinear, or sensor-degraded environments.