Loss-Cutting Equation under JX Theory: A Closed Alpha-Axis Kernel for Intelligent Termination under Uncertainty

We introduce the α-axis kernel of JX Theory as a closed-form equilibrium for intelligent loss-cutting under uncertainty. The model isolates a minimal functionalLopt(x) = R(x) − S(x) − E(x) − λσ²(x) + ϕΔF(x),where λ penalizes variance (uncertainty) and ϕΔF(x) corrects cognitive framing bias through ΔF(x) = Vp(x) − Vr(x).Under monotonicity and sign-change conditions, we prove existence and uniqueness of the optimal cut boundary x⋆ satisfying Lopt(x⋆) = 0 and derive comparative statics with respect to (λ, ϕ).This static α-kernel provides a domain-agnostic structural base for intelligent termination, unifying behavioral, institutional, and algorithmic decision systems. The framework serves as the α-axis of JX Theory, extensible to learning (β), coordination (γ), and welfare (δ) axes in future work.