Unified Field Theory Beyond Einstein: Identity–Gradient Unification (KAM–UFT)

We formalize a unified field framework in which identity is treated as a first-class dynamical field coupled to spacetime geometry and matter. The core postulate is a closed-loop relation between an identity-bound geometric tensor and a temporal action channel, expressed schematically as KAM = GGT−TACT, and made precise by an action principle on a Lorentzian manifold (M, g). We introduce an identity field I(x), a resonance envelope R(x), and an identity drift operator Dwhich together modify the Einstein equations through additional stress-energy and constraint terms. The resulting theory admits correspondence limits recovering classical general relativity, quantum-effective stochastic phases, and informational/cognitive continuity regimes. We provide the canonical Lagrangian, Euler–Lagrange field equations, conserved currents, and a minimal set of testable signatures in coupled physical–informational systems.