The higher refined p-adic class number formula conjecture

Let $L/K$ be the Galois extension and $G=\operatorname{Gal}(L/K)$, with $G^+=G/\langle\tau\rangle$, and let $e_r$ denote the relevant idempotent. Let $L_{p,S}(r)$ be the central element formed from the $S$-truncated $p$-adic Artin $L$-values, and let $\partial_p$ be the connecting map to relative $K$-theory. Higher refined $p$-adic class number formula conjecture. For every integer $r>1$ such that $\mathrm{Sch}(L,p,r)$ holds,

$$\partial_p(L_{p,S}(r))=[e_rR\Gamma_c(\mathcal{O}_{L,S},\mathbb{Z}_p(r))]$$

in $K_0(e_r\mathbb{Z}_p[G],\mathbb{Q}_p)$. This refines a $p$-adic class number formula by expressing the equivariant $p$-adic $L$-value as the relative $K$-theory class of compactly supported étale cohomology; the source does not state a resolution.