  We introduce the notion of a tight cofinitary group, which captures forcing
indestructibility of maximal cofinitary groups for a long list pf partial
orders, including Cohen, Sacks, Miller, Miller partition forcing, Shelah's
poset for diagonalizing maximal ideal. Introducing a new robust coding
technique, we establish the relative consistency of
$\mathfrak{a}_g=\mathfrak{d}<\mathfrak{c}=\aleph_2$ alongside the existence of
a $\Delta^1_3$-wellorder of the reals and a co-analytic witness for
$\mathfrak{a}_g$.
