Universality of reliability thresholds beyond Gaussian dictionaries

Establish whether the reliability threshold for threshold-gate families remains unchanged for non-Gaussian dictionaries, in particular whether a Rademacher dictionary with midpoint pairwise conjunction has reliability threshold 4k(λ₁+λ₀)²(1+o(1)).

Background

The paper proves universality of the leading one-gate error exponent for centered, unit-variance, sub-Gaussian dictionary entries. However, the reliability analysis depends on an exact Gaussian joint-read identity and on joint extreme-value behavior, which are not established for general entry distributions.

The authors identify the Rademacher dictionary with midpoint pairwise conjunction as a concrete first target. The question concerns the box-type reliability threshold, rather than the already-established marginal expected-error threshold.

References

The reliability law uses the Gaussian joint identity; its universality remains open.

— The Ball and the Box: Two Geometries of Computation in Superposition  (2610.11744 - Li et al., 8 Oct 2026) in Section 6, subsection “Other entry laws”; Section 7, “Open problems,” subsection “Universality of the box”

A first target is the Rademacher dictionary with midpoint pairwise conjunction: is its reliability threshold $4k(\lambda_1+\lambda_0)2(1+o(1))$?

— The Ball and the Box: Two Geometries of Computation in Superposition  (2610.11744 - Li et al., 8 Oct 2026) in Section 7, “Open problems,” subsection “Universality of the box”