The Riemann–Einstein Phase Bridge

This publication forms Part II of the Riemann–Einstein Phase Bridge framework and continues the operator–theoretic construction introduced in the companion paper “An Operator–Theoretic Representation of the Completed Zeta Function” (Zenodo DOI: 10.5281/zenodo.17295379). Building upon the completed zeta operator that unifies the arithmetic (Eulerian) and geometric (Archimedean) domains, this paper explores the physical and cosmological implications of that structure. It introduces the concept of phase equilibrium between discrete and continuous sectors, interpreting the so-called critical line of the Riemann function as a state of perfect balance between geometry and information. From this equilibrium, a number of physical phenomena naturally arise: a logarithmic cosmic expansion law that reproduces both inflation and the present-day slowdown of expansion without invoking dark energy constants; an explanation of the Hubble tension as a small measurable shift in the phase of the arithmetic lattice between early and late cosmic epochs; a unified origin of dark energy and dark matter as complementary manifestations of the same arithmetic phase, one as a smooth global dilution and the other as a residual tail beyond the observable horizon; a phase-preserving view of black holes, where information is conserved through a self-adjoint operator structure rather than destroyed; the emergence of quantization and the Planck constant as structural invariants of the same phase balance. Together, these results suggest that the large-scale dynamics of the universe, including cosmic acceleration and entropy growth, can be understood as expressions of an underlying arithmetic–geometric equilibrium encoded in the completed zeta structure. Note:This work is a conceptual and theoretical continuation of the operator model presented in Part I. It has not undergone peer review and is released for open scientific discussion and independent verification.