Uniqueness conjecture for Hilbert polynomials of homology-triplet complexes

Let $(B,H,C)$ be a homology triplet, and let $\mathcal{E}^{\bullet}$ be a complex of coherent sheaves corresponding to it as in the realization conjecture. Hilbert-polynomial uniqueness conjecture. The Hilbert polynomial $P(\mathcal{E}^{\bullet},d)$ is uniquely determined up to an additive constant. This conjecture concerns the remaining numerical ambiguity after the linear equations governing the Hilbert polynomial are expected to be independent. The supplied context does not give a resolution status.