Gauge-Covariant Angularly Scaled Fiber Bundle Model: Variational Derivation, Pushforward 1-Forms, Metric Tensors, and Universal N-Dimensional Generalization

We establish an airtight geometric field theory for a 4-dimensional principal fiber bundle pi: M -> B, where the base manifold B is parameterized by 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 ground-state eigenvalues of an action principle delta S = 0. Subject to Rayleigh dissipative decay exp(-alpha*t) and a discrete topological mode spectrum, we evaluate the pushforward map pi_*. We prove analytically that the global state functional is an exact 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. Furthermore, we construct the explicit warped spacetime metric tensor g_munu and establish its coupling to an anisotropic Bianchi-type stress-energy tensor T_munu. We rigorously extend the formulation to an arbitrary N-dimensional compact fiber, proving the Universal N-Dimensional Theorem with exact closed rational factor C_N = [n(n+1)/2] * Productₖ₌₁^N [(2^(2k) - 1) / (2k * 2^(2k))]. Dual physical realizations across Kaluza-Klein cosmological moduli shears and dissipative metamaterial transformation optics are comprehensively detailed.