Prime Reciprocity Operator and the Riemann Hypothesis: A Conditional Proof Framework Based on ECF Conjectures

This is an updated version (V3.0) of the preprint originally deposited in 2026. The core framework remains unchanged: we propose an operator-theoretic conditional proof framework for the Riemann Hypothesis, based on five conjectures distilled from the Emergence-Convergence Framework (ECF). The five conjectures are unified under a single variational principle: under the arithmetic and self-duality constraints of the prime reciprocity structure, the information capacity functional possesses a unique global maximum.Key updates in this version:1. Conjecture 4 (Fiber Isomorphism). The original "Resolvent Fiber Decomposition" conjecture, which postulated the asymptotic vanishing of cross-fiber couplings, has been reformulated as "Fiber Isomorphism" -- the weak convergence of spectral statistics across distinct primitive quadratic character fibers to a universal distribution. This reformulation resolves a technical obstruction identified in the large sieve analysis. The new formulation is compatible with known number-theoretic facts and is supported by three independent sources of evidence: information-theoretic, number-theoretic universality, and finite-dimensional testability.2. Conjecture 5 (Arithmetic Equivalence). Aligned with the reformulated Conjecture 4, the target has been refined from all Dirichlet L-functions to the Riemann zeta function, with the principal character fiber explicitly included.3. Corrected order estimates. The Hilbert-Schmidt norm estimates, large sieve cross-term bounds, and character sum bounds have all been corrected and presented with precise parameter ranges.4. Enhanced transparency. All GRH dependencies are explicitly marked. The compactness of the error operator is correctly identified as an open problem. A summary of assumptions, a notation table, and a logical dependency analysis have been added.The conditional theorem remains unchanged: if all five conjectures hold, then the Riemann Hypothesis follows.