Framed instanton moduli space (${\dim }_{\mathbb{R}}{\mathcal{M}}_k^{\mathrm{framed}}=8k$)

Fix a trivialization at infinity and divide smooth finite-action instantons only by gauge transformations tending to the identity there. Global gauge orientations remain genuine parameters. For regular $SU(2)$ instantons of charge magnitude $k$, the real dimension is $8k$ by the ADHM construction. Forgetting the framing divides by the three-dimensional global group action of $SU(2)$, giving $8k-3$ on the irreducible locus. For one instanton the framed parameters are four center coordinates, one positive size, and three orientation coordinates.