= Theta-weighted instanton sectors
{title2=$Z(\vartheta)=\sum_{k\in\mathbb Z}e^{ik\vartheta}Z_k$}
For integer <instanton number> $k$, a topological angle can weight each Euclidean gauge-field sector by $e^{ik\vartheta}$ in a stated convention. The sector sum is then $2\pi$-periodic in $\vartheta$. In temporal gauge, the same integer describes a change in the vacuum winding or <Chern-Simons number>, with compatible orientation conventions. Classical instanton action fixes exponential suppression, while determinants and collective-coordinate integrals supply prefactors.
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