Shelah's first-fix-point pseudopower conjecture

Let $\aleph_\delta$ be the first fix point, meaning the first ordinal index satisfying $\aleph_\delta=\delta$, and hence having cofinality $\aleph_0$. Shelah's first-fix-point pseudopower conjecture. Then $\operatorname{pp}(\aleph_\delta)$ is less than the $(2^{\aleph_0})^+$-th fix point. The source notes weaker and stronger possible targets, but presents this bound as the conjectural assertion. It is motivated by known bounds on powers at strong-limit cardinals and remains unresolved in the supplied text.