In this work, we investigate the thermodynamics of Schwarzschild black and white holes within a
q-deformed Wheeler--DeWitt framework. By introducing a
q-deformed Heisenberg--Weyl algebra at a root of unity, we derive a finite-dimensional Hilbert space, a bounded mass spectrum, and an adiabatic invariant leading to a bounded entropy-mass relation. The deformation results in a universal logarithmic correction, as well as a minimum temperature and a maximum entropy that matches the de Sitter bound. Also, we examine the interpretation of a cold remnant, which is dynamically stable because its radiation rate approaches zero, even though its heat capacity remains negative. We also explore the holographic implications of this limited entropy. Our results thus provide a consistent semiclassical picture, where quantum deformation naturally introduces an entropy bound, avoids divergences at the final evaporation stage, and suggests a smooth transition from quantum gravity to cosmology.
This paper presents a groundbreaking unified framework that bridges quantum information theory and black hole physics by introducing the concept of universal informational phase conservation. Through rigorous simulation of 8-12 qubit systems, we first establish a precise power-law scaling for information leakage: η ∝ N^(-0.43), demonstrating the emergence of near-perfect information conservation in larger quantum systems. A key structural parameter, Δ₀ ≈ 8.0, is identified as the regulator of information flow. We then perform a revolutionary extrapolation, applying this quantum scaling law to resolve the long-standing black hole information paradox. Our model demonstrates that information loss in Hawking radiation becomes negligible (η_BH ~ 10^(-33)) for astrophysical black holes, naturally ensuring information conservation without violating unitarity. The framework is further unified by reinterpreting the consciousness field (from the AOUF v2.5 model) as a cosmic-scale informational phase coordination field (Φ), which governs information dynamics from quantum to cosmic scales. Predictions for anomalous gravitational wave frequency shifts and photon ring brightness enhancements are derived and shown to be consistent with public data from LIGO and the Event Horizon Telescope. This work provides the first quantitative link between microscopic information scaling and macroscopic information paradoxes, offering a testable pathway towards a theory of quantum gravity. Keywords: Information Conservation, Black Hole Information Paradox, Quantum Scaling Laws, Page Curve, Quantum Gravity, Consciousness Field, Δ₀ Parameter, Holographic Principle