Time-Dependent Equilibrium Theory via Zulfia Invexity and the Emergence Operator

We introduce Zulfia Invexity for optimization problems where feasibility thaws overtime t ∈ [0, τ ]. A function f (x, t) is Zulfia Invex iff (x, t) − f (u, t) ≥ ∇xf (u, t)T η(x, u, t) + φ(t), φ(τ ) = 0. (1)With decomposition mapping Tt(x) = x + η(x, u, t), we define the Emergence OperatorAt := T −1t .The Emergence Equilibrium Theorem shows minimizers emerge as x∗(t) = At(y∗)where y∗ is optimum in factory space Y . Interpreting At as an Awareness Operatorextends Win Invexity to dynamic games: equilibria are realized as t → τ , not given att = 0.