Beyond KKT Assumptions: Zulfia Optimality Condition as Universal Sufficiency

Sufficiency was never lost. It was buried under centuries of as-sumptions. We restore it with one inequality.Classical optimality theory relies on convexity, differentiability, and constraintqualifications. The Karush-Kuhn-Tucker conditions inherit these burdens andfail outside them. We propose Zulfiability and the Zulfia Optimality Condition(ZOC) based on Decomposition. ZOC requires only:∥η(y, x∗)∥ ≤ κZ ∥y − x∗∥, κZ ∈ [0, 1)No convexity. No gradients. No constraint qualifications. We prove sufficiencyfor global optimality and show ZOC strictly generalizes KKT.