
Cosmic expansion and radiative quantum state reduction are usually treated as separate bulk problems at opposite ends of scale. This paper examines a different possibility: both may be described as boundary-crossing processes governed by a common reduced geometric law defined by a dimensionless transmission efficiency, a characteristic boundary radius, and a transition frequency. In the macroscopic regime, the same boundary normalization yields a horizon-scale rate proportional to the Hubble parameter and, when written in present-epoch form, gives a dark-energy density fraction close to current cosmological determinations. In the microscopic regime, the same reduced structure yields a boundary-limited radiative rate in which both Planck’s constant and Boltzmann’s constant cancel from the final expression. Comparison with the dipole spontaneous-emission rate of quantum electrodynamics preserves the same kinematic monomial and gives an explicit ratio between the realized QED rate and the boundary ceiling. For alkali p-manifolds, shell-summed inversion yields an effective length scale that tracks independently tabulated outer-shell radii monotonically. No complete dynamical unification is claimed. The framework is presented instead as a falsifiable boundary program in which horizon-scale expansion and microscopic radiative reduction appear as distinct regimes of a common geometric structure. If you want, I can also give you an even tighter version in the style of a Springer abstract.
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