Blind directions and the restated bound

42 X coordinates (30 in the $K\cdot c\cdot h$ sector, 12 in the $c^{\ast }cc$ sector) enter no three-point row and no Bose condition. 24 of these survive the ghost equation. They are free at this order and unconstrained by the rows. $\dim N-\dim (N\cap \mathrm{span}\mathrm{of}\mathrm{all}Q08\mathrm{pieces})=152-116=36$ is exact linear algebra, but the spanning pieces are not verified $\sigma$-images. So 36 bounds only the directions outside that span. It is neither a lower bound on physical directions nor an upper bound on trivial ones.