Black Hole Uniqueness, Re-emergence, and the Recovery of Information: A CL5D Hybrid Model Analysis

The black hole information paradox has persisted as one of the most consequentialunresolved problems at the intersection of quantum mechanics and general relativity.This paper applies the CL5D Hybrid Model — a deterministic multi-phase mathematicalframework (Papers 1–7, Chakraborty, 2026) — to address three interrelatedopen problems: (i) whether distinct black holes possess unique physical identitiesbeyond the classical parameters of mass, charge, and spin prescribed by the No-HairTheorem (NHT); (ii) whether a black hole can undergo a re-emergence transitionanalogous to Phase IV in the CL5D phase taxonomy; and (iii) the mechanism bywhich quantum information is recovered during black hole evaporation, as describedby the Page curve. We apply the same Benchmark Score formulation used in Papers6 and 7 to define BS,BH as a function of the Fractal Heterogeneity Coefficient α andthe skewness and kurtosis of the black hole’s micro-event phase space. Three Propositionsare stated, each followed by a Proof of Concept. Proposition 1 establishes thatfive black holes with identical (M, Q, J) but different formation histories produceBenchmark Scores ranging from BS = 0.12 to BS = 0.99, directly disproving physicalidentity at the CL5D level. Proposition 2 demonstrates that the CL5D tunnellingamplitude Etunnel = ECt · e−2κd is analytically identical to the Hawking emissionrate with residual below machine precision. Proposition 3 shows that the CL5DEvolution set → Decay set transition at the Conjugate Balance point reproducesthe Page curve exactly, with the parameter α controlling the Page time. JWSTobservational data — Little Red Dots and the Virgil galaxy in the El Gordo cluster— provide empirical anchors consistent with elevated-α black hole populations.