Limsup-one conjecture for p-adic torsion growth

Let ${\mathcal K}_{\rm real}$ be the set of all totally real number fields, let $D_K$ be the discriminant of $K$, and fix a prime $p\geq 2$. For each $K$, let ${\mathcal T}_K$ be the torsion group of the Galois group of the maximal abelian $p$-ramified pro-$p$-extension of $K$ under Leopoldt's conjecture. Limsup-one conjecture.

$$\limsup_{K\in{\mathcal K}_{\rm real},\,D_K\to\infty}\frac{v_p(\# {\mathcal T}_K)\log_\infty(p)}{\log_\infty(\sqrt{D_K})}=1.$$

This conjecture predicts that the principal p-adic Brauer–Siegel upper-bound scale is asymptotically sharp over all totally real fields. The source offers it as a proposal based on numerical behavior and gives no proof.