Inverse Decision-Environment Constraint Dynamics: A Formal Reconstruction Theory

We formalize the inverse problem for Decision-Environment Constraint Dynamics (DECD). Given a baseline environment E0 and an observed target Et, the inverse problem asks: what admissible operator traces could have produced Et from E0? The theory splits into model-intrinsic results, which hold for all admissible traces regardless of the reconstruction discipline, and discipline-relative results, which hold under a declared discipline. Model-intrinsic results include soundness, completeness, forward-feasibility necessity, and external infeasibility separation: when feasibility fails, the inverse set is provably empty. Under the default coarse reconstruction discipline, the theory yields a canonical minimal trace, its admissibility and replay correctness, minimality via a counting lower bound, and a characterization of residual ambiguity as a permutation within type-homogeneous blocks. The framework is well- behaved under extension: provenance constraints monotonically refine the inverse set, and partial observability monotonically enlarges it. All constructions are substrate-independent: the definitions invoke no domain-specific, epistemic, psychological, or normative primitives.