Partial-fraction decomposition conjecture for flat-space wavefunctions

Let $G=(V,E)$ be a Feynman graph with $n$ vertices. Let $\mathcal{F}=\{H_1,H_2,\dots,H_r\}$ be the set of spanning subgraphs of $G$, including their orientations, and write $H_i^1,\ldots,H_i^{s_i}$ for the connected components of $H_i$. For a connected oriented subgraph $H$, let $R_H(X,Y)$ be the rational function defined from the linear forms $\ell(H)$ and the admissible positive-degree connected subgraphs, with $R_H(X,Y)=0$ when $H$ contains a directed cycle.

Flat-space partial-fraction decomposition conjecture. The flat-space wavefunction can be decomposed into partial fractions as

$$\psi_{\text{flat}}=\sum_{H_i\in\mathcal{F}}(-1)^{n-1-|E(H_i)|}\prod_{j=1}^{s_i}R_{H_i^j}(X,Y).$$

This claim gives a graph-theoretic partial-fraction formula for the flat-space wavefunction. The source presents it as a conjecture but supplies no evidence of resolution in the provided text, so it remains open.