Covariant Phase–Cone Inequality in Curved Space: A Riemann–Finsler Extension of Analytic Phase Geometry

AKTAŞ, BORA

Published Nov 23, 2025• 0 citations

Abstract

Abstract We present a covariant generalization of the Phase–Cone Inequality to curved geometries, formulating it within both Riemannian and Finsler frameworks. In the flat limit, the inequality reduces to vϕ2≤κn(ΔΦ)2,v_{\phi}^{2} \leq \kappa_{n} (\Delta \Phi)^{2},vϕ2≤κn(ΔΦ)2, where κn\kappa_{n}κn is the multicarrier curvature coefficient characterizing interference order. Here, curvature and analytic continuation introduce two new covariant terms: the geometric curvature penalty K[u,ω]K[u,\omega]K[u,ω], governed by the Ricci or Finsler–Ricci tensor, and the analytic continuation term An[g;Φ]A_{n}[g;\Phi]An[g;Φ], carrying the transcendental constants (π,ζ(3),ζ(5),…)(\pi, \zeta(3), \zeta(5), \ldots)(π,ζ(3),ζ(5),…) that encode the parity–driven analytic hierarchy previously identified in flat CnC_{n}Cn manifolds. The resulting covariant form, vϕ2≤κn(ΔΦ)2−K[u,ω]+An[g;Φ],v_{\phi}^{2} \leq \kappa_{n} (\Delta \Phi)^{2} - K[u,\omega] + A_{n}[g;\Phi],vϕ2≤κn(ΔΦ)2−K[u,ω]+An[g;Φ], links quantum phase transport to local spacetime curvature and analytic number–theoretic structure. In the Finsler extension, anisotropic phase propagation introduces direction–dependent curvature coupling through the Finsler–Ricci scalar. These results imply that phase dynamics in curved or anisotropic backgrounds are constrained by both geometric focusing (Ricci contraction) and analytic opening (zeta hierarchy), offering a unified geometric–analytic limit for the speed of quantum evolution.

DOI: 10.5281/zenodo.17692563

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