Completing the Dynamic Theory: Mapping Williams' 5D Mass-Density Gauge onto the Compact Tav Circle of the Tau Universe (v4.0)

Geometric synthesis embedding Pharis E. Williams’ Dynamic Theory (mass density as fifth coordinate, 5×5 gauge tensor, seven Maxwell-type equations) into the Tau v4.0 Mathematical Substrate on R3×S1 R^3 × S^1 R3×S1 with Tav topology (τ=7 h−1 τ = 7\,h⁻¹ τ=7h−1 Mpc). The unified 5D action recovers all local results of the Dynamic Theory while delivering zero-parameter cosmology (Casimir dark energy w=−1 w=-1 w=−1, ΩDM:ΩDE=5:1 Ω_DM:Ω_DE=5:1 ΩDM:ΩDE=5:1, 142857 mode, Hubble/S8 S_8 S8 resolutions). Includes falsifiable Rubin LSST predictions and the Tau Resonator concept at 21.83 GHz.