Darmon's conjecture on cyclotomic units and class numbers

Let $F$ be the field and $n$ the integer in the source, write $n_+=\prod_{i=1}^{\nu_+}\ell_i$, let $\nu_-$ be the complementary prime-count parameter, let $h_n$ be the $n$-class number of $F$, and let

$$R_n=(-1)^{\nu_+}(\varphi_{\ell_1}^1\wedge\cdots\wedge\varphi_{\ell_{\nu_+}}^1)((1-\tau)u_0\wedge\cdots\wedge(1-\tau)u_{\nu_+})$$

be the regulator element defined in the source. Darmon's conjecture.

$$\theta_n=-2^{\nu_-}h_nR_n\quad\text{in }(F(\mu_n)^\times/\{\pm1\})\otimes_{\mathbb Z}I_n^{\nu_+}/I_n^{\nu_++1}.$$

The conjecture predicts an explicit relation between Darmon's element, the $n$-class number, and a regulator built from local reciprocity maps; the source provides no resolution.