Kilgore Field Equation: A Dynamic Framework for Consciousness as Information Differentiation

What holds a conscious-like state together? This study introduces the Kilgore Field Equation (KFE), a nonlinear, noisy field model where continuity emerges when information differentiates within itself. Two complementary formulations (diffusive–reactive and damped-wave) are tested across a structured program (Series A–F), revealing a reproducible continuity threshold (λ*) and a coherent band (ℂ) in parameter space. Stochastic input becomes useful signal through entropy feedback, selecting a finite spectral peak k*, while anisotropic diffusion (even in k) is cleanly separated from advection-driven drift (odd in k). Dispersion fits match theory; robustness holds under grid refinement, seeds, and parameter sweeps. This archive includes run cards, manifests, metrics, and figure sources to regenerate results end-to-end.