Notes on Spectral Inaccessibility on the Half-Line; A Minimal Affine Minisuperspace Model

This research note proposes a minimal affine minisuperspace framework based on the concept of spectral inaccessibility on the half-line. Rather than removing singular sectors through Euclidean continuation or boundary regularization, the framework treats singularities as spectrally inaccessible regions located at infinite affine distance from finite-energy physical states. Using the logarithmic affine coordinate u = log a and the affine-invariant measure da/a, the singular boundary a = 0 is mapped to spectral infinity. The resulting structure naturally admits no-flux probability conditions and standard self-adjoint spectral evolution. The work is intended as a minimal mathematical prototype and exploratory research note connecting affine geometry, minisuperspace quantization, and spectral approaches to singular quantum structures.