The Generative Equation of Reality: Field Action, Non-Commutative Geometry, and the KEPH Cycle at the Planck Scale. Volume IV

Volume IV concludes the KEPH tetralogy by deriving the field action of the Z/2Z bundle from first principles and showing that a single generative equation — (D²_P + m²)φ + g|φ|²φ + ε'_REK[φ] = 0 — produces all corpus instantiations as particular cases with domain-specific parameters. The action is derived from the gauge invariance condition e^(iπ) = −1. The Schrödinger-REK-RGB functional emerges as the non-relativistic limit of this action. Operator X at the Planck scale is identified with the Dirac operator of non-commutative geometry. Electroweak symmetry breaking SU(2)×U(1)→U(1) is shown to be a Z/2Z bundle instantiation at the Standard Model scale. Six verifiable predictions (P10–P15) are generated, including cymatic pattern symmetry, temperature dependence of topoisomerase threshold, universal impedance-threshold relation in neurons, non-commutative corrections to light speed, gravitational corrections to quantisation, and universality of cubic non-linearity.