From Landscape to Proof: The Even-Dominance Route to the Riemann Hypothesis

This record is the three-part Landscape and audit-trail series for the even-dominance route to the Riemann Hypothesis. It documents the development path from foundations and obstruction analysis through failed routes, interval-arithmetic certificates, and the Direct Frontier-Dominance route. The compact proof-only extraction is published separately as A Conditional Proof of the Riemann Hypothesis via Even Dominance of the Weil Quadratic Form (DOI: 10.5281/zenodo.20011910). Cite this record for the full research landscape, audit trail, excluded strategies, supporting certificates, and historical development of the route. For the shortest proof-core citation, use the separate proof-only record above. PAPERS Part I Foundations (14p), Part II Even Dominance (44p), Part III Conclusio (18p). English + German (152 pages total). KEY RESULTS Shift Parity Lemma: each prime individually favors even eigenfunctions 33 finite-range computer-assisted gap diagnostics (λ = 100 to 1,300,000), conditional on odd-sector tail validation Leading-Mode Cancellation (c = 2 + √2) Proposition A6: three-regime/direct-frontier variational bridge (conditional reduction) OP2 (simplicity of ground state): interval-arithmetic certified at all 33 values 17 independent results, 11 explored alternatives CHANGELOG 2.4 Changelog (23 May 2026): Parallel programme addition and converged empirics. Critical: no theorem-strengthening changes; the record remains a conditional reduction and audit-trail series. New subsection in Part III (EN and DE): “Parallel Programme: Connes--vS Error Collapse and I-1 Normal-Family Reframe” (sec:parallel-route-b). Documents Route B: (a) A1 = CvS Theorem 5.6 + err→0 ⇔ (i)+(ii) rigorously, (ii)⇒RH rigorously; (b) I-1 Normal-Family Reframe (§E.1–E.18 Companion): wall (ii) = (ii-a)+(ii-c) via Montel/Vitali, (ii-c) absorbed into (ii-a) via parity and Hadamard order (under zero-coincidence assumption (Z)); remaining open bridge: uniform a-priori strip bound (ii-a). Canonical criterion object §E.15: ξ̂(z) = (2/√L)·sin(zL/2)·F(z). New empirics table (tab:route-b-empirics, EN and DE): six converged λ-values (λ ∈ {3,5,7,9,11,13}): sup|ξ̂|ℜ ≈ 0.86–0.89; Aλ(0.4) flat at ≈ 1.004; Bλ/λ0.4 plateau at 0.68 (λ≥9). λ=11 and λ=13 bit-identical across two independent dps-runs. DOI correction for \bibitem{Geiger2026evendom}: updated from 10.5281/zenodo.20011910 (older version record) to 10.5281/zenodo.20291994 (v1.6 record). DE bibitem added. Note: after EvenDom v1.7 push, update again to the new v1.7 record DOI (TBD nach EvenDom-v1.7-Push). Version strings: four occurrences of “v2.3 status” updated to “v2.4 status” in Part II EN and DE. Parts I (EN+DE) unchanged. Former Changelogs (v2.3, v2.1, v2.0, v1.5, v1.4, v1.3, v1.2, v1.1): Former changelogs can be viewed in the earlier uploaded versions of this record. The full version history is available via the Concept-DOI 10.5281/zenodo.19035640 (use the “Versions” tab on Zenodo to browse).