A Signed Fourier Multiset Criterion for Local Isolation of Zeta Zeros: Actual-State Allocation and Explicit Fourier Certificates

This research preprint develops a signed Fourier finite-multiset criterion for the isolation of simple critical-line zeros of the Riemann zeta function from all other nontrivial zeros, including off-critical-line zeros. The finite inequality uses one nonreusing actual-state FREE/ABSORB allocation of nearby centers, a correction for genuinely isolated endpoints, a self-adjoint signed operator, disjoint Gram-variance payments, and a retained Hilbert–Schmidt trace reserve. A fixed positive two-cosine Fourier source and a single compactly supported smooth-square test density are analyzed through explicit full-domain interval certificates, independent arithmetic cross-checks, and quantitative smoothing and whole-height estimates. Together with the published fixed-test pair-correlation formula of Baluyot–Goldston–Suriajaya–Turnage-Butterbaugh and Conrey’s one-sided integrated zero-density bound, the specified simultaneous analytic and computational hypotheses yield the conditional implication liminf_{T→∞} B_loc(T, 0.1895)/N(T) ≥ 46061167/91700000 > 0.50230. The numerical result is **conditional on the stated certification and applicability interfaces**. It is **not claimed as an established unconditional zeta-zero majority theorem**, nor does it prove the Riemann hypothesis. The accompanying Research/QA archive provides executable source code, interval-cover data, arithmetic checks, and a declared verification boundary; these checks are not formal proof-assistant certification. This is a standalone, reader-oriented presentation of the two-cosine branch derived from the separate 124-page cumulative working preprint *Isolation-Aware Zeta-Zero Spacings via Signed Fourier Multisets*, v3.28r1, DOI: 10.5281/zenodo.24081890. It does not replace that record or incorporate its distinct fifty-mode results.