General partial fraction decomposition conjecture for Gorenstein-symmetric rational functions

Let $P(t)=\frac{H(t)}{\prod_{i=1}^N(1-t^{b_i})}$ be a rational function with integral numerator $H(t)\in\mathbb Z[t]$ satisfying Gorenstein symmetry. Let $n+1$ be the dimension of the support in the graded Gorenstein setting, and let $k$ denote the symmetry degree of $P(t)$. For each sequence $A=\{a_1,\ldots,a_{n+1}\}$, write $r=a_{n+1}$ for its main period, require $a_i\mid r$, and define

$$k_A=k+\sum_{a\in A}a.$$

Also set

$$F_A=\frac{1-t^r}{\operatorname{hcf}\left(1-t^r,\prod_{a\in A,\,a<r}(1-t^a)\right)}.$$

General partial fraction decomposition conjecture. Under these assumptions, $P(t)$ has a unique partial fraction decomposition

$$P(t)=\sum_A\frac{N_A}{\prod_{a\in A}(1-t^a)}.$$

The sum is over sequences $A$ as above, with each $a_i$ dividing one of the original $b_j$. Each numerator $N_A$ is an integral polynomial symmetric of degree $k_A$, and is of shortest support: it is a minimal residue modulo $F_A$, supported in an interval of length less than $\deg F_A$ centred at $k_A/2$. The decomposition may be restricted to quasismooth orbifolds if necessary.

This conjecture proposes a canonical decomposition of Gorenstein-symmetric Hilbert-series-type rational functions into contributions indexed by periods and their divisors. The stated uniqueness, integrality, and shortest-support properties are the substantive points; the source does not provide a resolution status.