What question did this study set out to answer?

This research aims to embed Williams' Dynamic Theory within a specific mathematical framework and explore its implications for cosmology.

April 15, 2026Open Access

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

Key Points

This research aims to embed Williams' Dynamic Theory within a specific mathematical framework and explore its implications for cosmology.
Geometric synthesis of Dynamic Theory into the Tau v4.0 framework
Utilization of a compact Tav Circle topology
Application of seven Maxwell-type equations for analysis
Development of falsifiable predictions using Rubin LSST data
Unified 5D action aligns with local results of the Dynamic Theory
Predicts zero-parameter cosmology with Casimir dark energy
Establishes a ratio of dark matter to dark energy of 5:1
Provides specific predictions at 21.83 GHz for the Tau Resonator concept

Abstract

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 R³ S¹ R3×S1 with Tav topology (τ=7 h−1 = 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 DM: DE=5: 1 ΩDM: ΩDE=5: 1, 142857 mode, Hubble/S8 S₈ S8 resolutions). Includes falsifiable Rubin LSST predictions and the Tau Resonator concept at 21. 83 GHz.

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

Key Points

Abstract

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