Isolation-Aware Small-Spacing Bounds for Zeta Zeros via Signed Fourier Multisets
Year: 2026
Type: preprint
Abstract: Description This preprint is version v2.0r1 of the H14W research program, updating the previously published v1.3r1 (DOI: 10.5281/zenodo.23851529). We investigate quantitative ordinate isolation of simple critical-line zeros of the Riemann zeta function without assuming the Riemann hypothesis. Building on an exact signed Hilbert–Schmidt identity for conjugation-invariant finite multisets, the paper develops an isolation-aware allocation method, explicit Gram-variance compensation, and a global trace-centered mechanism for controlling losses from three- and four-point zero configurations. Using a fixed smooth-square Fourier density with fifty cosine modes, the integrated manuscript presents a computer-assisted proof candidate for the explicit one-sixth isolation bound $$\liminf_{T\to\infty} \frac{B_{\mathrm{loc}}(T, 1/6)}{N(T)} > 0.5203.$$ Here $N(T)$ counts nontrivial zeta zeros with multiplicity, and $B_{\mathrm{loc}}(T, c)$ counts simple critical-line zeros whose ordinates are separated from every other zero, including off-critical-line zeros, by more than $2\pi c / \log\gamma$. The argument uses the explicit global cutoff $c_g = 1/6 + 10^{-10}$, a nonreusing occurrence ledger, internal and cross-block Gram compensation, and a uniform zero-toll estimate for nonreal conjugate centers of arbitrary positive integer multiplicity. The arithmetic transfer relies on published unconditional results of Baluyot–Goldston–Suriajaya–Turnage-Butterbaugh on pair correlation and Conrey on integrated off-critical-line zero density. The manuscript also retains the earlier fixed-spacing isolation bounds from v1.3r1, including proportions exceeding $0.65155$ at spacing $0.04999$ and $0.64857$ at spacing $0.06666$. Reproducibility: A separate Proof Supplement archive provides the exact fifty-mode coefficients, interval-arithmetic verification programs, certified block calculations, height-envelope and zero-toll checks, and exact-rational deductions supporting the computer-assisted argument. Research status: This is an unrefereed mathematical research preprint. The computational certificates are reproducible but have not been formally verified, and the complete argument remains subject to independent mathematical review. The paper does not claim to prove the Riemann hypothesis. Creator Lee Byoungwoo Independent Researcher, Daejeon, Republic of Korea Keywords Riemann zeta function; isolated zeros; critical line; zeta zeros; pair correlation; unconditioned bounds; computer-assisted proof; interval arithmetic; rigorous numerics; Hilbert–Schmidt identity; Fourier density; zero spacing; H14W research program
Author: Lee, Byoungwoo
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7224991815