= Solution
The <Levi-Civita connection> is the unique <affine connection> that has both vanishing <torsion tensor> and <metric compatibility>. The <affine connection decomposition> shows exactly how an arbitrary <affine connection> departs from it: the <contorsion tensor> contributes the metric-compatible torsion correction, and the <disformation tensor> contributes the nonmetricity correction. The torsion and <nonmetricity tensor>, together with the <metric tensor>, determine the difference uniquely.
In the paper's convention the actual contorsion correction is $-K$, with the corrected half factor from part (i), and the disformation correction is $W$. Both corrections are <tensors>, although the separate connection coefficients $\Gamma$ and $S$ are not <tensors>. \b[If both torsion and nonmetricity vanish, then] $\boxed{\Gamma=S}$. Vanishing nonmetricity alone permits torsion, and vanishing torsion alone permits nonmetricity.
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