CSF-CMT vΩ.25.4: Magnetic Monopole Mass and Detection Window from String-Magnetic Topological Coarse-Graining

Abstract

This paper derives the magnetic monopole as a topological defect of the string-magnetic mode \chi_{\text{string}}^M and calculates its mass as a function of the coarse-graining scale L_c, yielding an experimentally accessible window distinct from GUT predictions. The winding number w_M = \frac{1}{2\pi}\oint \nabla_{CG}^M \cdot dl \in \mathbb{Z} is shown to be a topological invariant of the first-space meta-field. When w_M \neq 0, the coarse-graining operator \hat{\mathcal{C}}_{L_c}^{(M)} cannot smooth the knot, producing a residual \delta-function magnetic charge. The mass formula m_{\text{mono}}(L_c) = \alpha_{\text{mag}} M_{Pl}(l_{\text{string}}/L_c)^2 gives m_{\text{mono}} \sim 10^8 GeV for L_c \sim 10^{-20} m, within reach of cosmic-ray and heavy-ion collision searches. Two detection channels are proposed: transient magnetic charge signals in Pb-Pb collisions at \sqrt{s_{NN}} = 5.5 TeV, and galactic magnetic field deflection anomalies in ultra-high-energy cosmic rays.