Ultrametric organization of TAP states

Let $D$ be the open set from the quenched complexity formula. For $f\in D$, let $\theta$ be the optimizer in that formula and let $\zeta$ minimize

$$\widetilde{\Lambda}(\theta)=\theta\inf_{\zeta:\,\zeta([0,\sup(\operatorname{supp}\zeta)))=\theta}\mathcal{P}\mathrm{arisi}(\zeta).$$

Ultrametric organization conjecture. The TAP critical points at free-energy level $f$ are organized in an ultrametric tree; uniformly sampled overlaps between two such states take values in the support of $\zeta$. If $f\neq f_{\mathrm{eq}}:=\inf_\zeta\mathcal{P}\mathrm{arisi}(\zeta)$, the ancestor states have TAP free energy $\mathcal{P}\mathrm{arisi}(\zeta)\neq f$, and the quenched complexity of the ancestor states is $0$, so their number grows at most subexponentially in $N$.