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…