Explicit Isolation Bounds for Zeta Zeros at Fixed Small Spacings: Signed Complex-Block Allocation and a Certified Fourier Test
Year: 2026
Type: preprint
Abstract: This research preprint develops explicit lower bounds for the proportion of simple critical-line zeros of the Riemann zeta function whose ordinates are isolated from all other zero ordinates, including multiple zeros and zeros off the critical line. Version v1.1 presents two refined quantitative bounds: At normalized spacing 0.0057700, the lower limiting proportion exceeds 0.655208. At normalized spacing 0.0059665, the lower limiting proportion exceeds 0.655200. The method combines a signed finite-multiset Hilbert–Gram inequality, injective allocation of screening centers, a shared off-critical-line first-moment budget, unconditional fixed-test pair-correlation and zero-density inputs, and a computer-assisted forty-mode Fourier witness. This version incorporates a source-native proof revision and additional verification of the signed complex-block allocation and associated algebraic inequalities. The accompanying research package provides symbolic and rational verification scripts, audit records, and cumulative research documentation. The original full forty-mode interval-verification programs belong to earlier research archives and are not included in this version's standalone research package. The manuscript is released as a versioned research preprint. Mathematical closure and external peer review are not claimed. Further theoretical developments, numerical refinements, and corrections may be incorporated in subsequent versions.
Author: Lee, Byoungwoo
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7224089614