Relational Fine Structure and Cosmic Vorticity: Late-Time Coherence as a Common Modulator of α and the Hubble Tension

Why 1/137? The fine-structure constant, often written as alpha approximately equal to 1/137, is one of the most famous dimensionless numbers in physics. It controls the strength of electromagnetism, appears across atomic physics and quantum electrodynamics, and remains one of the deepest numerical mysteries of modern science. At the same time, cosmology faces another persistent puzzle: the Hubble tension, the discrepancy between local and early-Universe determinations of the expansion rate H0. Doc. 77 of the ToE-2PS research program explores whether these two problems may be connected. This work proposes a falsifiable link between the fine-structure constant, cosmic vorticity, and the Hubble tension through a single late-time coherence field, denoted as Xi (x). The central hypothesis is that Xi (x) can simultaneously modulate the effective fine-structure constant alphaₑff (x) and the environment-dependent expansion rate Hₑff (z, x). Building on previous ToE-2PS developments in coherence-driven cosmology, VoidStep-H0, and laboratory-constrained coherence dynamics, the model introduces an effective scalar field coupled both to the electromagnetic Lagrangian and to non-relativistic matter. This coupling generates three correlated observational signatures: 1. a linear relation between Delta alpha/alpha and Delta H0/H0 across cosmic environments such as voids and clusters; 2. a possible dipolar modulation associated with ultra-slow cosmic vorticity; 3. a common late-time transition near zₜr = 0. 64, where the coherence field becomes dynamically relevant. The framework is tested against existing observational limits from Oklo, atomic clocks, Big Bang Nucleosynthesis, high-resolution quasar spectroscopy, Pantheon+ supernovae, DESI, and VLT/ESPRESSO. A Fisher forecast indicates that the environmental coupling beta can be strongly constrained with current and near-future data, while the electromagnetic coupling kappa around 10^-6 remains in a viable window for future tests with ELT/HIRES, ANDES, Roman, DESI, and next-generation clock experiments. The key point of the paper is falsifiability. ToE-2PS is not tested by one isolated anomaly, but by cross-correlation between environment, redshift, sky direction, cosmic expansion, and variation of fundamental constants. If no such correlation is observed, the proposed unification is ruled out at the effective-field-theory level. In this sense, Doc. 77 advances ToE-2PS from symbolic unification toward a concrete observational program: from the mystery of 1/137 to a testable cosmology of coherence, environment, and fundamental constants.