Trust-Monotone Temporal Recursion in Deterministic Structural Dynamics

Deterministic Structural Causal Dynamics (DSCD) provides trust-gated emergence of certifiable causal graphs via monotone observer hierarchies, algebraic invariants, and resonance-based reachability. While DSCD captures structural causal provenance in safety-critical systems, it treats temporal dynamics implicitly. This work introduces trust-monotone temporal recursion (TMTR) as a bounded, algebraic extension that enables higher-level trust envelopes to retroactively refine lower-level state trajectories over finite horizons while preserving monotonicity, acyclicity, and deterministic constraints. The recursion operator supports both hindsight correction (e.g., post-blackout drift/slew recovery) and forward algebraic prediction with certifiable interval bounds. We formalize TMTR within DSCD hierarchies, derive conditions for stability, convergence, and invariant preservation, and illustrate enhanced regime detection and disturbance rejection in hypersonic re-entry and plasma diagnostics simulations. This work establishes structural foundations for deterministic temporal recursion in causal estimation architectures. TMTR unifies structural causality with certifiable temporal refinement, advancing deterministic autonomy in extreme environments where probabilistic methods are precluded, and establishing a deterministic framework for bounded retrospective state estimation.