Major Conjectures and Cosmological Tests I; The Cosmological Falsifiability of the Generalized Riemann Hypothesis

This paper proposes a theoretical framework for translating the GeneralizedRiemann Hypothesis (GRH) into a multi-messenger cosmological testable hypothesis. By establishing a correspondence between Dirichlet characters and cosmologicalobservational channels (21 cm neutral hydrogen, CII emission lines, primordial gravitational waves, galaxy distribution) under the axioms of information conservation,finite computability, and weak channel coupling, we reinterpret the critical-lineconsistency of non-trivial zeros of L-functions described by GRH into the physicalprediction that the normalized phase noise spectra of different channels share thesame set of minima sequences on the critical line Re(s) = 1/2 in the complex plane.Theoretical derivation indicates that the ideal alignment precision should be better than 0.1%. Based on simulated data for next-generation observational facilities(SKA-2, CCAT-p, LISA, DESI-2), we verified the significance of multi-channel zeropoint alignment (4.3σ), with the maximum deviation below the falsifiable thresholdof 0.2%. This study provides, for the first time, a physical testing scheme for GRHbased on multi-messenger joint observations with a clear falsifiable path.