Equality conjecture for local Petrovskii lacuna counts

Let $f_0:{\mathbb R}^{N-2}\to{\mathbb R}$ be a parabolic critical point, and consider a versal deformation of $f_0$. Table 1 gives, for each singularity and parity case, either an exact number of holomorphic local lacunas or an upper or lower bound for their number.

Equality conjecture. In every cell of Table 1, except possibly the cell corresponding to $X_9^2$, each inequality can be replaced by an equality.

The theorem preceding this conjecture establishes the listed exact values and bounds, with some bounds having only computer proofs. The conjecture concerns whether the remaining inequalities are sharp; the source gives no resolution status.