Cosmology from Two Axioms 6, Information Torsion and Black Hole Soft Hair: Realization of Conserved Charges from Discrete Symmetry on the Horizon

The black hole information paradox and the microscopic description of theendpoint of Hawking radiation are central challenges in quantum gravity theory. Within the fundamental framework of information conservation and the computability of physical processes, this paper explores the realization of discrete automorphism groups on the event horizon of a black hole and their physical consequences. By modeling the black hole horizon membrane as a structure possessing adiscrete automorphism group, we prove that when the global information torsion—defined as the cumulative sum of the information potential difference modulo theminimal unit ln2—reaches a specific threshold (83ln2), this automorphism groupinduces a set of stable, classically indescribable extra degrees of freedom on thehorizon, termed “information soft hair”. These soft hair modes carry discrete conserved charges, the values of which are uniquely determined by the informationtorsion threshold. The theory predicts that black holes carrying such soft hairwill leave a measurable residual entanglement entropy of approximately 2.20 bitswhen they evaporate to the Planck scale in the final stage of Hawking evaporation.This feature may affect the energy spectrum or spacetime correlation signals atthe endpoint of evaporation, providing potential observational targets for the nextgeneration Event Horizon Telescope (ngEHT) through high-precision polarizationand brightness fluctuation measurements.