Deriving the Page Curve from First-Principles Loop Quantum Gravity and Fuzzball Horizon Operators

I present a deterministic, first-principles mathematical framework that resolves the black hole information paradox without relying on statistical Haar-random sampling or artificial stochastic seeding. By initializing the global system as an unentangled pure vacuum state |00...0>, I derive the time-dependent Page Curve strictly from the non-local unitaries of String Theory Fuzzballs and the discrete area eigenvalues of Loop Quantum Gravity (LQG). The horizon evaporation process is governed by a global cross-boundary operator that naturally entangles internal spin network punctures with outgoing radiation modes, strictly preserving quantum unitarity across the entirety of the evaporation lifespan.