Prime-Wave Phase Transition and Conditional Proof Interfaces: A Second Interface-Led Approach to the Riemann Hypothesis

This technical note presents a second Interface-Led Architecture (ILA) approach to the Riemann Hypothesis, based on prime-wave phase transition, uniform phase contracts, and conditional proof interfaces. It does not claim to prove the Riemann Hypothesis. The paper models prime-generated oscillatory modes through a finite-energy prime-wave framework and interprets the critical line Re(s) = 1/2 as a candidate phase boundary between polynomial divergence and finite-energy regimes. It introduces IUniformPhaseProvider as a minimal contract for isolating the random-phase behavior of prime logarithmic frequencies from stronger assumptions such as RH-equivalent error estimates, zero correlations, or analytic continuation. The paper further formulates an explicit-formula bridge using the Chebyshev function, von Mangoldt weights, Perron-type integrals, and zero-spectrum consistency requirements. It defines a Conditional Proof Interface that separates preconditions, target invariants, bridge requirements, and proof obligations, while preserving a fail-closed boundary against circular reasoning. This work builds on the prior ILA-based system-governance heuristic for the Riemann Hypothesis, but is published as an independent second approach rather than a revision. The English manuscript is the canonical version. The Japanese manuscript is included as a companion translation.