Geometric Regularization of the Friedmann Singularity from a Boundary Constraint

The classical Friedmann singular limit is reconsidered in a boundary-based framework. The analysis introduces a geometric constraint relating boundary curvature to apparent-horizon scale and combines it with a Planck-scale upper cutoff on admissible curvature. This yields a finite minimum apparent-horizon radius together with a finite minimum horizon area, holographic area count, and entropy. The same boundary coefficient is traced to the black-body normalization on a spherical radiating surface and to the corresponding Bose–Einstein integral, and is interpreted as a radiative decoupling condition at a spherical boundary. Since the apparent horizon carries the standard thermodynamic attributes of temperature and entropy, the same boundary normalization is applied to it. The resulting minimum state is interpreted as the smallest horizon compatible with a thermodynamic surface rather than an arbitrary cutoff configuration. The analysis remains macroscopic throughout and does not rely on additional dynamical fields, extra dimensions, or a microscopic quantum-gravitational model.