Height-pairing conjecture for critical motives

Let $M$ be a motive over $K$ with coefficient field $\mathcal{F}$, and let $M^*(1)$ denote its dual Tate twist. Let $H_f^1(K,M)$ and $H_f^1(K,M^*(1))$ be the motivic cohomology groups. A motive $M$ is critical when its period map $\alpha_M$ is an isomorphism. Height-pairing conjecture. If $M$ is critical, there is a non-degenerate height pairing

$$h_M:H_f^1(K,M)\times H_f^1(K,M^*(1))\longrightarrow\mathbb{R}\otimes_\mathbb{Q}\mathcal{F}.$$

The source further records a more general conjectural exact sequence relating this pairing to the kernel and cokernel of the period map; no resolution is given.