Generalized Novikov additivity for perversity intersection signatures

Let $X^n$ be a pseudomanifold and let $Y\subset X$ be a compact codimension-$1$ submanifold such that

$$X=Z\bigcup_Y Z^{\prime},$$

where $Y\subset\subset X^{\mathrm{reg}}$. For a perversity function $\mathfrak{p}$, write $IH^{n/2}_{\mathfrak{p}}(X)$ for the corresponding intersection cohomology group, and let $\hat{\sigma}_{\mathfrak{p}}(Z)$ denote the signature for cohomology satisfying perversity-$\mathfrak{p}$ conditions away from $Y$ and relative boundary conditions at $Y$. Generalized Novikov additivity conjecture. The signature of the intersection pairing on $IH^{n/2}_{\mathfrak{p}}(X)$ satisfies

$$\sigma_{\mathfrak{p}}(X)=\hat{\sigma}_{\mathfrak{p}}(Z)+\hat{\sigma}_{\mathfrak{p}}(Z^{\prime}).$$

This would generalize Novikov additivity from the setting treated in the paper to arbitrary perversity intersection cohomology on pseudomanifolds; the source presents it as a proposed generalization, and no resolution is supplied.