Explicit reciprocity conjecture for the twisted Perrin-Riou-Stark element

Let $A$ be the CM abelian variety in the source, let $g=\dim A$, let $\mathbb{T}_{\mathfrak{P}}(A)$ be its $p$-adic representation, and let $\mathfrak{S}_{\mathrm{cyc}}=\mathfrak{S}_{\mathrm{cyc}}^{(1)}\wedge\cdots\wedge\mathfrak{S}_{\mathrm{cyc}}^{(g)}\in\bigwedge^gH^1(K_+,\mathbb{T}_{\mathfrak{P}}(A))$. For a primitive character $\chi$ of $\Gamma_n$, let $\mathbb{M}(\mathfrak{S}_{\mathrm{cyc}},\omega,\chi)$ be the matrix formed from the Perrin-Riou symbols, and let $\mathscr{E}(\chi\psi)$ and $\Omega_\infty(\epsilon)$ be the Euler factor and period defined in the source. Explicit reciprocity conjecture. There exists a choice of a Néron differential on $A$ such that

$$\det\mathbb{M}(\mathfrak{S}_{\mathrm{cyc}},\omega,\chi)=\mathscr{E}(\chi\psi)\cdot\frac{L(1/2,\chi_\epsilon\psi_\epsilon)}{\Omega_\infty(\epsilon)}$$

for every primitive character $\chi$ of $\Gamma_n$. This is proposed as a natural higher-dimensional extension of the Coates-Wiles explicit reciprocity law for elliptic units; no proof or disproof is stated in the supplied text.