Kovac Spectral Horizon (KSH) and the Riemann–Maxwell Duality: A Unified Spectral Invariant for the Maxwell Operator on 2D, 3D and Non‑Orientable Manifolds

A fully unified spectral invariant for the Maxwell operator is introduced by combining the Kovac Spectral Horizon (KSH) with the inverse Riemann–Maxwell normalization. Across five distinct geometries — square, circle, annulus, 3D cube and the non‑orientable Klein bottle — both normalization regimes converge monotonically to the same universal limit ℎ = 1 . The direct KSH normalization approaches the horizon from below, while the inverse Riemann–Maxwell normalization approaches it from above. Their product satisfies the exact identity ℎK(𝑖) ℎR(𝑖) = 1, independent of shape, dimension or topology. This duality reveals a previously unidentified spectral structure of the Maxwell operator: a robust, geometry‑agnostic horizontal invariant linking physical and Riemannian behaviour. The work provides numerical evidence, theoretical formulation and graphical demonstrations confirming the universality of the spectral horizon on both orientable and non‑orientable manifolds.