Task-Relative Four-Channel Stability in Stochastic Decision Systems: Dimension-General Order Non-Redundancy from Fully Interior Stochastic Constructions

This preprint develops a task-relative four-channel framework for distinguishing physical, observational, decision, and order-sensitive sources of instability in stochastic decision systems. The framework separates physical feasibility (Ω_P), observational conditioning (Ω_O = [λ_M, L_M]), decision margin (Ω_D), and an order channel represented by the signed-margin displacement vector D^J, its infinity norm D^J_∞, and the decision-reversal indicator R^J. The principal result is a dimension-general order non-redundancy theorem. For every finite simplex dimension n ≥ 3, there exist an interior probability state, a strictly positive doubly stochastic observation operator, and a strictly positive doubly stochastic transformation for which Ω_P > 0, λ_M > 0, and Ω_D > 0, yet changing the order of the two stochastic operations changes the resulting argmax decision (R^J = 1). The proof begins with an exact fully interior three-state witness and extends it to arbitrary finite dimension through block embedding and uniform positive regularization. The individual ingredients of the framework are closely related to established concepts in decision theory, stochastic garbling, contraction and conditioning theory, margin-based robustness, and order-sensitive processing. The proposed contribution is the task-relative separation of these failure channels together with an explicit dimension-general proof that the order channel is not implied by positivity of the preceding three stability channels.