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

From papers

Let S(G,κ,α)\mathbf{\mathcal S}(G,\kappa,\alpha) be a statistical symmetric binary perceptron, let αults(κ)\alpha_{ult_s}(\kappa) be its ss-level ultrametric OGP critical density, and let αc(s+2)(κ)\alpha_c^{(s+2)}(\kappa) be the (s+2)(s+2)-th level parametric fl-RDT estimate. Ultrametric OGP–parametric fl-RDT conjecture in the strong sense. For every s1s\geq 1,

αults(κ)αc(s+2)(κ).\alpha_{ult_s}(\kappa)\leq\alpha_c^{(s+2)}(\kappa).

The strongest version would assert equality for some values of ss, possibly for all ss. 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.

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Sources & referencesView supporting material

Primary source

Mihailo Stojnic, “Ultrametric OGP - parametric RDT symmetric binary perceptron connection”, arXiv:2604.19712 (2026).

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