Black Hole Thermodynamics and the Resolution of the Information Paradox via Random Causal Sets (RCS)

Black holes represent the ultimate frontier where General Relativity and Quantum Mechanics exhibit their most profound contradictions, namely the Singularity, the Trans-Planckian problem in Hawking radiation, and the Information Paradox. In this paper, we comprehensively resolve these impasses by replacing the continuous manifold ℝ⁴ with a Random Causal Set (RCS). We demonstrate that: (1) Gravitational collapse does not converge to a singularity but forms a super-dense Causal Core bounded by ρ_max ~ Λ_SVL⁴; (2) Bekenstein-Hawking Entropy (S ∝ A) possesses a purely microscopic origin, derived by counting severed horizon molecules; (3) Hawking radiation is truncated at near-Planck energies due to subluminal modified dispersion relations; and (4) The "No-Hair Theorem" is refuted, proving that quantum information is locally encoded in the topological defects of the spacetime lattice via Symmetron interactions and is sequentially released via a strict unitary S-matrix, completely resolving the Information Paradox.