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

Abstract: We establish an airtight, non-singular geometric field theory for a 4-dimensional associated fiber bundle E = P ×_{U(1)³} F → B, where the base manifold B ≅ S¹ is parameterized by θ ∈ (0, π/2) and the typical fiber F = E/B ≅ [1, 2]³ represents a scale-invariant Kaluza-Klein compactification region bounded between ultraviolet (UV) and infrared (IR) physical horizons. Over the total space E, we define a gauge-covariant top-degree 4-form Ω = ω_F ∧ dθ equipped with an Ehresmann connection 1-form A ∈ Ω¹(P, u(1)³). We prove that because dim(B) = 1, the curvature 2-form vanishes identically (F ≡ 0), rendering the connection locally flat while generating non-trivial global Wilson loop holonomy W ∈ U(1)³ around the compact base circle. Odd anisotropic scaling exponents (a, b, c) = (3, 5, 7) are derived as stationary ground-state eigenvalues of an anisotropic conformal action principle δS = 0. Subject to Rayleigh dissipative decay e^{-αt} (α > 0) and a discrete topological mode spectrum i ∈ {1, ..., n}, we evaluate the Cartan fiber-pushforward map π_* : Ω⁴(E) → Ω¹(B), proving analytically that the macroscopic state functional is an exact, closed differential 1-form defining a non-trivial de Rham cohomology class [π_* Ω] ∈ H¹_{dR}(S¹). Furthermore, we construct the explicit warped spacetime metric tensor g_μν, demonstrate that coordinate divergences represent coordinate horizons with finite Riemannian curvature invariants, and couple the geometry to an anisotropic Bianchi-type cosmological stress-energy tensor T_μν. We rigorously generalize the framework to arbitrary N-dimensional compact fibers F_N ≅ [1, 2]^N, proving the Universal N-Dimensional Product Theorem with exact closed rational factor C_N. Dual physical realizations across Kaluza-Klein cosmological moduli shears and dissipative metamaterial transformation optics are comprehensively detailed. Author Statement: Author: Navneet Dwivedi (Independent Innovator) Background: 11-Year Hiatus from Formal Mathematics and Physics Originality Declaration: Entirely original theoretical exploration in analytical differential geometry, fiber bundles, and dimensional reduction.