The indefinite Heegner-class non-torsion conjecture

Let $K$ be the imaginary quadratic field, let $\mathcal R$ be the Hida-family coefficient ring, and let $\mathfrak Z_0\in\widetilde H^1_f(K,\mathbf T^\dagger)$ be the corestriction of the Heegner cohomology class constructed in the source. The indefinite Heegner-class non-torsion conjecture. The class $\mathfrak Z_0$ is not $\mathcal R$-torsion. This is the indefinite counterpart of a conjecture cited from Howard and is intended to imply that the big Selmer group has rank one; the source does not prove it.