An Informational Phase–Stability Operator for Predictive Prime Localization

This preprint introduces an informational phase–stability operator H(n)H(n)H(n) derived from the variational phase–equilibrium condition ΦA+ΦE=0\Phi_A+\Phi_E=0ΦA+ΦE=0 of the completed Riemann zeta function. The operator acts as an informational radar, identifying entropy–stable regions along the logarithmic number axis where prime numbers are most likely to occur. Instead of detecting primes directly, it predicts their locations by minimizing an informational curvature functional linked to the completed zeta phase field Ξ(s)\Xi(s)Ξ(s). The framework directly extends the operator formalism developed in An Operator–Theoretic Representation of the Completed Zeta Function, connecting analytic symmetry, Fredholm nuclearity, and informational entropy minimization within a unified operator–theoretic model. Computational benchmarks demonstrate an order–of–magnitude reduction in primality–test workload while maintaining high prediction accuracy (F1≈0.8F_1 \approx 0.8F1≈0.8). Keywords: Riemann zeta, informational phase theory, entropy minimization, operator theory, primes, analytic symmetry, phase stability.