Riemann Zeta-Phase Winding in Simultaneous Resonance Theory Version 02

This version adds an exact algebraic bridge between the Riemann construction, the 1049 matrix and the finite architecture of Simultaneous Resonance Theory (SRT). With the Riemann index represented by k=2n+3, the independently derived 1049 automorphism J(k)=25k (mod 64) induces the affine map T(n)=25n+4 (mod 32) on the Riemann index space. The resulting identity T^8=id establishes exact eight-step modular closure, showing that the Riemann indexing is governed by the same finite 64-state transformation already present in the 1049 framework. This provides a direct structural link from SRT to 1049 and from 1049 to the Riemann architecture within one common algebraic system. This correspondence demonstrates that the Riemann construction is embedded within the 1049 modular architecture. These two independent frameworks converge directly at the level of their underlying transformation law. By providing an exact structural bridge between the Riemann indexing and the 1049/SRT geometry, this connection brings the present analysis to a mathematically unified and clear close. This paper examines the structural and energetic relationship between the discrete phase geometry of Simultaneous Resonance Theory (SRT) and the continuous analytical ordinates of the Riemann zeta function. Within a strict framework of non-temporal simultaneity, a discrete dyadic phase grid is mapped into a non-temporal Keplerian profile through a parameter-free elliptical-torsion construction derived from the fundamental SRT baseline constants. The study establishes a correspondence between the modular phase-winding and eigenvalue structure of the SRT grid and an invariant periodic wave pattern within the continuous Riemann landscape. This relationship is governed by a compressed precession operator. The Law of Inherent Energy Decay and a Spectral Flux Balance condition subsequently define the analytical boundary at which continuous logarithmic phase space maps into stable resonant organization around the SRT observer axis. By connecting discrete algebraic structure, continuous phase space and the energetic constraints of matter-closure, the resulting construction offers a consistent, unfitted geometric model illustrating how the Riemann zeros emerge naturally from the boundary conditions of matter-closure.