Relational Geometric Mechanics IX: Black Hole Thermodynamics — Hawking Radiation, the Information Paradox, and the Holographic Principle from the QF Foam Core

This is the ninth paper in the Relational Geometric Mechanics (RGM) series. We apply the QF foam framework to black hole physics and show that three of the deepest unsolved problems in theoretical physics — the singularity problem, the origin of Hawking radiation, and the information paradox — are resolved by a single coherent physical picture. The black hole center is not a mathematical singularity but a Planck-density foam core: the QF manifold compressed to its minimum granularity, carrying the complete attention lattice of every particle that has ever fallen in. Hawking radiation arises from the same mechanism as quark string breaking established in Paper IV — amplitude field tension at the event horizon nucleates a virtual particle-antiparticle pair. The information paradox is resolved by attention lattice unzipping: each escaping Hawking particle carries the wave signature of the lattice node it erased, preserving quantum unitarity. The holographic principle — entropy scaling with surface area rather than volume — follows in one step from maximum interior compression. No new physical assumptions are introduced.