Boundary Geometry: From Cosmic Expansion to Wave Collapse

Cosmic acceleration and quantum state reduction are usually formulated as separate bulk problems. This paper examines whether both can be written as boundary-crossing processes governed by a single reduced law. In the macroscopic limit, with the boundary radius identified as the Hubble radius, the transition frequency identified with the Hubble parameter, and the transmission efficiency set to unity, the same law yields a horizon-scale rate proportional to pi cubed over fifteen times H0. In the microscopic limit, using the emitted photon energy and the corresponding effective temperature, the same construction yields a boundary rate proportional to pi cubed over fifteen times Rb squared times omega cubed divided by c squared, so that h-bar and kB cancel from the reduced form. Comparison with the dipole spontaneous-emission rate of QED preserves the same kinematic monomial, Rb squared omega cubed divided by c squared, and gives an explicit ratio between the QED rate and the boundary rate. For alkali p-manifolds, shell-summed inversion yields an effective length scale that tracks independently tabulated outer-shell radii monotonically. The construction is presented as a falsifiable boundary program linking horizon-scale expansion and microscopic radiative reduction within a common geometric framework