The determinant-lattice conjecture for elliptic units

Let $\Lambda$ be the Iwasawa algebra in the source, let $Q(\Lambda)$ be its total ring of fractions, and let $\Delta^\infty$ be the determinant module constructed from the inverse limits of units and divisors. Let $\mathcal L\in\operatorname{Det}_{Q(\Lambda)}(\Delta^\infty\otimes_\Lambda Q(\Lambda))$ be the element defined from the elliptic-unit system and the archimedean divisor. Determinant-lattice conjecture. There is an equality of invertible $\Lambda$-submodules

$$\Lambda\cdot\mathcal L=\operatorname{Det}_{\Lambda}\Delta^\infty$$

of $\operatorname{Det}_{Q(\Lambda)}(\Delta^\infty\otimes_\Lambda Q(\Lambda))$. This assertion is the integral determinant formulation associated with elliptic units and is distinct from the preceding local ETNC statement. The supplied context does not state whether it is proved or remains open.