Benois's trivial-zero formula for arithmetic L-invariants

Let $p$ be an odd prime and let $\rho:G_{\mathbb{Q}}\to \operatorname{GL}(n,\overline{\mathbb{Q}}_p)$ be a continuous Galois representation unramified at all but finitely many primes and semistable at $p$. Let $D\subset \operatorname{D}_{\operatorname{st}}(\rho|_{G_{\mathbb{Q}_p}})$ be a regular submodule, and suppose an analytic $p$-adic $L$-function $L_p(\rho,D,s)$ exists with the interpolation property described in the source. Benois's trivial-zero conjecture. If $\rho$ is critical, $L(\rho,0)\neq 0$, $L_p(\rho,D,s)$ has order of vanishing $e$ at $s=0$, and $D$ satisfies the stated conditions, then

$$\lim_{s\to 0}\frac{L_p(\rho,D,s)}{s^e}=(-1)^e\mathcal{L}(\rho,D)\mathcal{E}^+(\rho,D)\frac{L(\rho,0)}{\Omega_\infty(\rho)}.$$

Here $\mathcal{E}^+(\rho,D)$ is the relevant Euler-like factor and $\mathcal{L}(\rho,D)$ is the arithmetic $\mathcal{L}$-invariant. This is the trivial-zero formula the paper introduces from Benois's conjectural framework; the supplied text gives no resolution status.