Decision-Environment Constraint Dynamics: A Formal Specification

We introduce a formal algebraic framework for analyzing how decision environments
become progressively constrained. A decision environment is a triple ⟨I, A, ℓ⟩ comprising
an information substrate, an action substrate, and a loss function ℓ : I × A → R≥0. Four
monotone operators, Frame (F), Control (C), Obligation (O), and Sanction (S), act on this
triple by restricting information availability, contracting action feasibility, introducing inter-
nal loss obligations, and imposing external loss penalties, respectively. We prove that these
operators form a canonical accumulation ordering F → C → O → S induced by precondition
dependencies, establish multiple stabilization criteria under which the environment reaches
a fixed point under the operator family, and derive minimality and non-redundancy results
guaranteeing that the operator vocabulary is both sufficient and irreducible. The framework
is extended to stochastic loss functions and partial-observability projections, with analogous
stabilization guarantees. All constructions are substrate-independent: the definitions invoke
no domain-specific, epistemic, psychological, or normative primitives.