Finite-level ultrametric OGP–parametric RDT comparison conjecture for the symmetric binary perceptron

Let $\mathbf{\mathcal S}(G,\kappa,\alpha)$ be a statistical symmetric binary perceptron, let $\alpha_{ult_s}(\kappa)$ be its $s$-level ultrametric OGP critical density, and let $\alpha_c^{(s+2)}(\kappa)$ be the $(s+2)$-th level parametric fl-RDT estimate. Ultrametric OGP–parametric fl-RDT conjecture in the strong sense. For every $s\geq 1$,

$$\alpha_{ult_s}(\kappa)\leq\alpha_c^{(s+2)}(\kappa).$$

The strongest version would assert equality for some values of $s$, possibly for all $s$. This is a finite-level refinement of the proposed limiting equivalence, but the source provides numerical evidence only for low levels and leaves the general comparison open.