The Stochastic Planck Time Hypothesis (SPTH): A Number-Theoretic Framework for Galactic Dynamics, Redshift Quantization, and the Riemann Zeta Structure of Cosmic Voids

We propose the Stochastic Planck Time Hypothesis (SPTH), which begins with a deceptively simple quesion: must Planck time be a fixed constant? If the fundamental quantum of time follows a Gaussian distribution whose variance depends on local energy density, a single mechanism simultaneously explains flat galacticrotation curves, the Hubble tension, and galactic red shift quantization without invoking dark matter, dark energy, or new particles.At high densities, temporal fluctuations are sup pressed (phase-locking), recovering Newtonian dynam ics. At low densities (cosmic voids), fluctuations grow(phase-unlocking), providing additional centripetal ac celeration that flattens rotation curves. The phase-un locking structure is governed by the non-trivial zerosof the Riemann zeta function ζ(s), establishing a direct link between prime-number theory and observable cosmology.We present seven independent empirical verifica tions: (i) galactic rotation curves for 175 SPARC galaxies fit with RMSE improvement of 99.4% of cases (median RMSE improvement 92.1%; p = 3.85 × 10−30, Wilcoxon test); (ii) redshift quantization nodes at N =3–10 matching prime-ratio predictions at 96–99.9%consistency against SDSS DR18 (∼2 million galaxies); (iii) Riemann zero frequency signals confirmed in 52/53 SDSS spectra drawn from 40 independent plates (mean89.71%, vs. random ≥ 98.3%, p 200imaging channels), every file achieving 100% Riemann zero matching (maximum 9/9; p 0.4), confirming the SPTH prediction that single event sources lacking a spatial density ensemble cannot exhibit prime-number phase-locking structure; the 13.6σ contrast with the CMB TE result constitutes a qualitatively new level of confirmation.The convergence of number theory, quantum gravity, and large-scale cosmic structure in a single falsifiable framework opens a new avenue for understanding the mathematical architecture of the universe. A quantum-mechanical derivation of the Riemann zero connection and a physical pathway toward the RiemannHypothesis