Signed Iwasawa main conjecture for diagonal cycles

Let $M$ be the residual-representation lattice and let $A=(M\otimes_{\mathbb{Z}_p}\mathbb{Q}_p)/M$. For each choice of signed local condition indexed by $\bullet\in\lbrace\sharp,\flat\rbrace$, let $H^1_{\bullet,\bullet}(K[p^\infty],M)$ be the corresponding signed Selmer group, let $\mathrm{Sel}_{\bullet,\bullet}(K[p^\infty],A)$ be its dual local-condition Selmer group, and let $X_{\bullet,\bullet}(K[p^\infty],A)$ be its Pontryagin dual. Write $\Lambda$ for the relevant Iwasawa algebra and $z_1^\bullet\in H^1(K[p^\infty],M)$ for the diagonal-cycle class. Signed Iwasawa main conjecture. For every $\bullet\in\lbrace\sharp,\flat\rbrace$, the class $z_1^\bullet$ lies in $H^1_{\bullet,\bullet}(K[p^\infty],M)$, is not $\Lambda$-torsion, both $H^1_{\bullet,\bullet}(K[p^\infty],M)$ and $X_{\bullet,\bullet}(K[p^\infty],A)$ are rank-one $\Lambda$-modules, and

$$\mathrm{char}_{\Lambda}\left(X_{\bullet,\bullet}(K[p^\infty],A)_{\mathrm{tors}}\right)=\mathrm{char}_{\Lambda}\left(\frac{H^1_{\bullet,\bullet}(K[p^\infty],M)}{\Lambda\cdot z_1^\bullet}\right)^2.$$

These conjectures are signed analogues of Heegner-point Iwasawa main conjectures in the non-ordinary setting. The supplied material gives the formulation but no evidence resolving their status.