Levinson's method in short intervals and simple zeros of the zeta function

Abstract

For each fixed 1/2 < theta < 1, a shifted mollified second-moment formula is derived on intervals of length T^theta for fixed mollifier and differential-operator polynomials, with 0 < nu < min(1/2, (17/33)(2 theta - 1)). The argument combines a signed Gaussian representation, the shifted composite Voronoi transformation and Bettin-Chandee's trilinear Kloosterman-fraction estimate. Exact Mellin multipliers provide coefficient separation and a summable dual tail; an exact Hankel-symbol representation gives a second derivation. Both residues, coalescing shifts, unbalanced blocks, gcd sums and compact-window smoothing are retained. With a fixed previously certified degree-201 detector and Wang's recent short-interval pair-correlation preprint, the counting and parity transfer gives a positive asymptotic proportion of simple critical-line zeros in (T, T+T^theta] for every fixed theta in [0.5339, 1). At theta = 0.5339 the certified lower density exceeds 0.0003985233159135. The proof and exact arithmetic controls have undergone internal review. The result is asymptotic, depends on attributed external theorems, and supplies no effective height, external peer-review claim, worldwide-priority assertion or proof of the Riemann hypothesis. Supporting certificates, code and research artifacts are published separately at 10.5281/zenodo.23135349. This manuscript record contains only the unchanged manuscript PDF.