Towards a Geometric Resolution of the Black Hole Information Paradox via Phase Encoding in the Zhang Effective Metric

We propose a geometric phase mechanism for information recovery within the rotational-order geometric unification framework. Using the Zhang Effective Metric, we model the black hole interior as a non-singular topological core. We analyze the Parikh-Wilczek tunneling process under the modified geometry and identify a geometry-dependent phase contribution associated with the internal S³ orientation field. This phase provides a candidate channel for non-thermal correlations in Hawking radiation. Crucially, we emphasize that these correlations are non-local geometric correlations inherited from the global KK fiber structure, avoiding superluminal signaling. The existence of this geometric phase is a necessary, not sufficient, condition for unitary evaporation and the Page curve. This work establishes a plausible geometric pathway for solving the information paradox without invoking firewalls.