Sharp Task-Visible Order-Defect Bounds in Stochastic Decision Systems: A Positive Stability Certificate for the Ayala Ω Framework

This research note derives a task-visible upper bound connecting local transformation-order fragility to decision-margin displacement in finite stochastic decision systems. For the signed-margin map, the task-visible order defect is bounded by the state-specific action of the commutator. For doubly stochastic operators, the zero-sum structure of the commutator yields the sharper bound D∞ᴶ(x) ≤ 2DΩ,2(M,L) range(x), and for probability states on the (n−1)-simplex this gives D∞ᴶ(x) ≤ 2[1−nΩP(x)]DΩ,2(M,L). A sufficient decision-invariance certificate follows by comparing this bound with the decision margin ΩD. In the three-state case, an exact one-parameter family attains equality, proving that the coefficient 2 is optimal and simultaneously exhibiting order-induced decision reversal for every nonuniform member of the family. The result complements the earlier task-relative four-channel non-redundancy theorem by providing a positive stability certificate linking physical interiority, structural order defect, and task-visible decision stability. The underlying commutator, norm, and stochastic-matrix ingredients are established mathematics; external novelty of the combined task-relative formulation is not assumed.