Gauge-Covariant Angularly Scaled Fiber Bundle Model: Variational Derivation, Pushforward 1-Forms, and Dissipative Moduli Dynamics

We establish an airtight geometric field theory for a 4-dimensional principal fiber bundle pi: M -> B, where the base manifold B is governed by an angular coordinate theta in (0, pi/2) and the typical fiber F = M/B is a compact 3-manifold [1, 2]^3 representing a scale-invariant Kaluza-Klein compactification region bounded between UV and IR physical horizons. Over M, we define a gauge-covariant top-degree 4-form Omega = omega_F ^ dtheta equipped with an Ehresmann connection 1-form A and odd anisotropic scaling exponents (3, 5, 7) derived as stationary eigenvalues of an action principle delta S = 0. Subject to Rayleigh dissipative decay exp(-alpha*t) and a discrete topological mode spectrum, we compute the pushforward map pi_*. We prove analytically that the global state functional is a well-defined differential 1-form: I(theta, psi, phi, t) = [945 * n * (n + 1) * exp(-alpha * t)] / [131072 * lambda * sin^5(psi) * cos^7(phi) * cos^3(theta)] dtheta. The formulation rigorously resolves boundary flux balance via compactly supported relative cohomology, eliminates coordinate singularities, and establishes full gauge invariance across the bundle.