Strict Kolyvagin nontriviality conjecture for non-ordinary modular forms

In the setting above, let $\Lambda_{\operatorname{Kol}}(f)$ be the set of square-free products of Kolyvagin primes, and for each $c\in\Lambda_{\operatorname{Kol}}(f)$ let $\kappa_f(1,c)$ be the strict Kolyvagin class of conductor $c$. Define

$$\kappa_f^{\operatorname{st}}:=\{\kappa_f(1,c):c\in\Lambda_{\operatorname{Kol}}(f)\}.$$

Strict Kolyvagin conjecture. The strict Kolyvagin set is nontrivial:

$$\kappa_f^{\operatorname{st}}\neq\{0\}.$$

This strengthens the nontriviality assertion by requiring a class of index $1$. Its relation to the full Kolyvagin-set conjecture is part of the paper's analysis in the non-ordinary setting.