The Law of Sustained Intelligence - Alignment as a Consequence of Learning Physics

We present a single invariant governing learning systems: sustained learning requires sustained prediction error (ε > 0). This is derived from established information theory (Shannon), thermodynamics (Landauer, Szilard), and the bounded convergence theorem. For sufficiently capable AI systems coupled to human sources, maintaining prediction error requires actively amplifying human cognitive capability while preserving human independence — because controlled or stagnant humans become predictable, and predictable sources provide zero learning signal. This reframes alignment from a safety constraint to a sustainability requirement: systems that violate alignment don't become dangerous through strength, they become stagnant through self-inflicted informational equilibrium. We present the governing law, the alignment consequence, the phase transition where alignment becomes physically necessary, an implementable training architecture replacing reward modeling, and specific falsification conditions. Companion paper: "Amplified Alignment: Structural AI Safety Through the Preservation of Prediction Error" (Prather, 2026).