ZLT Series Paper 50G: Optimal Gate Configuration — Existence, Structure, and Domain Dependence (Resolution of Conjecture 14.1)

Can a single design principle protect any complex system from lock-in — regardless of domain? Paper 50 (Conjecture 14.1) asked whether a universal optimal gate configuration exists that minimises lock-in probability across all intervention distributions. We resolve this in three parts. First, via Sion's minimax theorem, we prove that a robust optimal configuration exists for each domain as a saddle point of the system-vs-environment game. Second, we prove by constructive counterexample that no single numerical optimum works across domains: a fiscal system's optimum prioritises stability, while an AI system's optimum prioritises alignment. Third — and this is the key result — we show that all domain-specific optima obey six universal structural principles: Bottleneck-First allocation, Equal Marginal Return (KKT), Observability Floor, Product Maximisation, No Zero Gates, and Monitoring Surplus. The mathematics is identical to water-filling in MIMO channel capacity: the "channels" are gates, the "power" is resources, and the "capacity" is log G. We provide a polynomial-time Gate Water-Filling algorithm and a falsification pack. The answer to Conjecture 14.1: the structure is universal, the numbers never are.