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The recently established agreement between experiment and theory for the $g$factors of lithiumlike silicon and calcium ions manifests the most stringenttest of the many-electron bound-state quantum electrodynamics (QED) effects inthe presence of a magnetic field. In this Letter, we present a significantsimultaneous improvement of both theoretical $g_\text{th} =2.000\,889\,894\,4\,(34)$ and experimental $g_\text{exp} =2.000\,889\,888\,45\,(14)$ values of the $g$ factor of lithiumlike silicon$^{28}$Si$^{11+}$. The theoretical precision now is limited by themany-electron two-loop contributions of the bound-state QED. The experimentalvalue is accurate enough to test these contributions on a few percent level.

$g$ Factor of Lithiumlike Silicon: New Challenge to Bound-State QED