Selmer cotangent-space isomorphism conjecture

Let $S'$ be an auxiliary set, and let $\wp_{S'}$ denote the relevant ideal in the deformation ring. In the situation of Theorem 1, suppose that Theorem 1 has established an inclusion

$$\wp_{S'}/\wp_{S'}^2\subseteq\bigoplus_{i=1}^n W({\bf k})/(p^{m_i}).$$

Selmer cotangent-space conjecture. The inclusion is an isomorphism:

$$\wp_{S'}/\wp_{S'}^2\cong\bigoplus_{i=1}^n W({\bf k})/(p^{m_i}).$$

This is a proposed refinement of the previously proved subgroup statement. The supplied excerpt gives no evidence resolving it.