Simple critical zeros in short intervals: stability, parity, localization, and Hilbert compression

Abstract

For a conjugation-invariant finite multiset, let N count copies, S simple real support, O distinct odd-multiplicity real support, and Q the squared-kernel pair sum. The paper proves the sharp inequality (Q-S)(N-O) >= 2(N-S)^2 by retaining Lamzouri's first Hilbert-subspace dimension and coupling it to odd support. Combined with Wang's short-interval pair theorem and the localized rank-three Selberg detector, it gives liminf S/N >= max{0,c(theta),(c(theta)+2k3(theta))/3,h3(theta)}. Exact directed rational arithmetic places the unique positivity root of h3 in (0.545884,0.545885). At theta=0.5459, where the previous linear term remains negative, the new lower bound exceeds 0.0000168381638551244569880374399. The coefficient two is sharp, and a scalar zero-simple witness explains why retaining the Hilbert dimension matters. The result is asymptotic and depends on recent attributed preprints. No effective starting height, global zero-density record, external peer review, or proof of the Riemann hypothesis is claimed. Source code, data, and computational records are available at https://github.com/fsantibanezleal/CAOS_RESEARCH.