Kovac Spectral Horizon (KSH) and the Riemann–Maxwell Duality — A Unified Spectral Invariant in the Direct and Inverse Regime of the Maxwell Operator on 2D, 3D and Non‑Orientable Manifolds
Year: 2026
Type: preprint
Abstract: This article introduces a unified spectral invariant arising from the combination of the Kovac Spectral Horizon (KSH) and the Riemann--Maxwell duality. We show that the Maxwell operator on a broad class of 2D, 3D and topologically non-orientable domains exhibits a dual normalization regime that structurally converges to a single common horizon h=1. In the direct normalization (KSH), the spectral invariant h_K(i) = λ_i / λ_max monotonically approaches the horizon 1 from below, while in the inverse Riemann--Maxwell normalization h_R(i) = λ_max / λ_i it approaches the same limit from above. Both regimes are mutual inverses and satisfy the central identity h_K(i) · h_R(i) = 1, which proves robust across all tested geometries: the square, the circle, the annulus, the 3D cube and the non-orientable Klein bottle. This identity represents a new type of spectral duality linking the Maxwell operator with Riemannian behaviour in the inverse regime and reveals a unified horizontal limit independent of shape, dimension or topology. The results suggest that the horizon h=1 is a universal spectral invariant of the Maxwell operator and forms a natural bridge between the physical and analytical structure of the spectrum.
Source: Open Science Framework
Author: Aleš Kováč
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7222878865
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