CET Ω: The Causal White-Phase Completion of Black Holes

Description: This work develops the Causal White-Phase Completion of black holes within the CET Ω framework, providing a fully causal, unitary, and information-preserving description of gravitational collapse and evaporation. The analysis shows that when the retarded kernel K^{-1}(\Box_R) is realized through its Stieltjes-positive spectral representation, the interior of a black hole undergoes a causal phase transition — the white phase — where spacetime regains informational coherence without singularities or violations of the second law. The theory unifies horizon dynamics, quantum information flow, and causal thermodynamics under a single nonlocal yet retarded law. The white phase corresponds to a region of reversed causal opacity where the causal flux remains finite, the generalized second law \Delta(S_{\rm CET}+S_{\rm out}) \ge 0 holds dynamically, and information is preserved through spectral continuity. Simulations based on CET Ω show the absence of curvature singularities, no information loss, and a continuous transition between black and white causal domains. These results indicate that CET Ω provides the first complete, covariant, and thermodynamically consistent resolution of the black-hole information paradox. Keywords: CET Ω theory, black-hole completion, white-phase transition, causal thermodynamics, information preservation, retarded kernel, nonlocal gravity, Stieltjes spectral representation, generalized second law, causal information flow.