Information Continuity at Black Hole Horizons via the Kilgore Field Equation

This paper investigates whether information at a black hole horizon is lost, preserved, or reorganized when modeled through the Kilgore Field Equation (KFE), an information-differentiation framework derived from Consciousness Field Theory. Using a one-dimensional horizon model, we simulate the evolution of an information field under self-differentiation, entropy feedback, observer coupling, and horizon-amplified gradients. Key findings include: The information field remains finite and smooth at the horizon even under extreme amplification. Coherence increases and entropy decreases across all baseline runs. Under noisy initial conditions, horizon behavior exhibits a sharp phase transition at a critical coupling δ* ≈ 3.2, distinguishing fragile and robust regimes. These results suggest that KFE horizons reorganize information rather than destroy it, providing a constructive pathway toward resolving the black hole information paradox. The full data and code required to reproduce all results are openly available in the accompanying dataset archive.