Resolving the Hubble Tension via Geometric Early Dark Energy in the Zhang Effective Metric

The Hubble tension—a >5σ discrepancy between local (SH0ES) and early-universe (Planck) measurements of H₀—is a major crisis in modern cosmology. We demonstrate that the rotational-order geometric unification framework naturally resolves this tension via the Zhang Effective Metric. The internal S³ orientation field undergoes a rapid phase transition prior to recombination, acting as a transient Early Dark Energy (EDE). The geometric potential (derived from compact S³ topology) generates a negative pressure that enhances the pre-recombination expansion rate, reducing the comoving sound horizon r_s. This mechanism perfectly aligns the CMB-inferred H₀ with local measurements without disrupting late-time cosmological evolution or requiring ad-hoc parameter fine-tuning.