A stability refinement for simple critical zeros in short intervals

We derive a stability refinement of Biao Wang's 2026 short-interval bounds for simple critical zeros and distinct zeros of the Riemann zeta function. For each fixed exponent theta above the unique positive-proportion threshold of the cosine bound, the refinement is strictly positive. The argument transfers the known stability-enhanced rank-trace inequality from the ainta manuscript to Lamzouri's exact finite Hilbert operator, retains the simple-atom Gram defect, and uses a quantitative obstruction to additive triples of cosine-kernel zeros. It preserves Wang's fixed-support short-interval pair-correlation hypotheses and takes the large-height limit before the smoothing and support limits. A reproducible Arb certificate at theta = 3/4 gives a simple-critical proportion of at least 0.4190768284253039967 and a distinct-zero proportion of at least 0.7095384142126519983. The finite certificate has 48,761 partition nodes and zero unresolved boxes, with an alternate sinc Taylor evaluation at 256-bit precision. This is a self-published preprint, not peer reviewed. The imported stability lemma and analytic inputs are attributed to their sources. The result does not prove the Riemann hypothesis, establish a new global zero-proportion record, improve the positivity exponent, or provide an effective height threshold. The proof is not an end-to-end Lean formalization.