A Formal Derivation of Non-Volumetric Singularities: Matter-to-Radiation Phase Transition and Information Conservation via Spectral Orthogonality

We present a rigorous mathematical framework for a non-singular black hole interior. We propose that gravitational collapse induces a phase transition where baryonic matter is converted into a stationary coherent radiation (SCR) state. Utilizing the Eddington-Finkelstein coordinate system, we demonstrate that as the radial coordinate approaches the Planck scale, the manifold undergoes dimensional reduction, leading to a nullification of the metric volume element. Information con- servation is established through the mapping of quantum states into an orthogonal frequency basis within an atemporal frame, effectively resolving the black hole information paradox. The result- ing energy density provides a natural mechanism for a radiation-dominated cosmological bounce, consistent with the requirements of a cyclic universe.