The Global Geometry of the Gaussian Bures Manifold: Admissible Domain, Spectral Boundary, and Asymptotic Classicality

We construct the covariance-sector Bures geometry of centered bosonic Gaussian states from the Gaussian symmetric-logarithmic-derivative equation and determine its quantum-admissible domain. At the Williamson uncertainty floor, the boundary geometry is anisotropic: spectrum-changing radial coefficie