ψ-Retention Beyond the Singularity: A Structural Cosmology Without Coordinates, Observers, or Dynamical Time

This work extends ψ-Retention Cosmology into regimes where classical spacetime dissolves—near black-hole interiors, early-universe singularities, and collapse boundaries where coordinates, observers, and the dynamical time parameter cease to exist. We show that the ψ-retentive variables (Δψ, Ξ, the retentive radius R(a), and the functional 𝓘ψ) remain well-defined even when the metric gμν loses meaning. By replacing dynamical evolution with τ-ordered retentive evolution, ψ-Retention provides a structural law of persistence beyond geometry, yielding post-singularity fixed points, horizon resilience, and a coherent ontology of difference where classical curvature diverges but ψ-structure remains finite. The framework establishes ψ-Retention as a candidate for post-metric cosmology and a universal structural principle valid at and beyond gravitational collapse.