This document presents a formal definition of δ as a deterministic state transition function within the Intelligent Deterministic Decision Architecture (IDDA). The model defines four possible outcomes for any state transition: EXECUTE, HOLD, BLOCK, and RESET. These outcomes are governed by an admissibility predicate and a recovery pressure measure, enabling the system to control not only whether a decision is made, but how the system evolves when a decision is not admissible. A key contribution of this work is the transformation of inadmissibility from a terminal condition into a controlled transition. Instead of allowing undefined behavior, oscillation, or cascading errors, the model introduces a structured recovery mechanism through RESET to a designated baseline state. The repeated application of δ induces a piecewise-stable trajectory of system states under admissibility constraints. This ensures bounded response, non-oscillatory behavior, and continuity of operation even under high uncertainty or degraded input conditions. The model is domain-agnostic and applicable to decision-driven systems in areas such as logistics, industrial automation, infrastructure monitoring, and distributed control environments. This work forms part of the broader IDDA research framework, which focuses on deterministic, auditable, and stability-oriented decision architectures. Implementation details and production systems remain proprietary at this stage.
Piotr Pietruszewski (Wed,) studied this question.