Generalized Deligne conjecture for critical motives

Let $M$ be a critical motive over $K$ with coefficient field $\mathcal{F}$, let $\Omega_{\gamma,\delta}$ be its period, and assume the height pairing $h_M$ is available. If $x$ and $y$ are bases of the determinant lines of $H_f^1(K,M)$ and $H_f^1(K,M^*(1))$, let $R_{x,y}$ be the associated regulator. Generalized Deligne conjecture. Assuming the height-pairing conjecture,

$$\frac{L^*(M,0)}{\Omega_{\gamma,\delta}R_{x,y}}\in\mathcal{F}.$$

This extends Deligne's rationality statement to the case of vanishing central value by incorporating the leading term and regulator; the source gives no general resolution.