From Landscape to Atlas: Multi-Route Cartography of an Ongoing Expedition Toward the Riemann Hypothesis

1 Changelog (31 May 2026): Additive cross-route diagnostic phase; no theorem-strengthening changes, Atlas / conditional-reduction status unchanged. New section in Part IV "The Sharpened Common Wall: A Criticality Lens and an Analytic-Continuation Localization": (a) a heuristic criticality lens (RH ⇔ Λ=0; explicitly an analogy, not a theorem) re-weighting the routes toward exact-structural mechanisms without refuting the margin-type proof slots; (b) the common wall localized as the analytic continuation across Re s=1 (Euler pole-comb marker); (c) a computable diagnostic operationalising the classical Laguerre–Pólya / Herglotz / Voros criterion (no novelty claimed for the criterion itself); (d) four closures of concrete constructions (OS reflection natural form, naïve Möbius Ls−, Toeplitz-symbol sub-method, relative-determinant bypass). Part IV updates: dormant routes (P-M obstruction theorem; M and the global adelic trace route P-A strategically elevated as the exact-structural type); new external line Watson 2026 (arXiv:2602.01248 — archimedean Markov Laguerre–Pólya construction, an independent triangulation of the identification wall); independent-results table extended (concentration lemma, finite Sylvester inertia, residue-calibration channel); a hypothesis-correction subsection (relative-determinant bypass: proposed and refuted). Part V: coherence updates carrying the criticality lens and sharpened common wall into the condensed atlas, the achievements list, and the outlook. Status: no new proof claim; the Atlas remains "From Landscape to Atlas" and all routes remain conditional reductions. The diagnostic re-derives a classical criterion as a computable instrument; the closures concern concrete constructions, not whole routes. 3.0 Changelog (26 May 2026): Structural reorganisation from trilogy to five-part series ("From Landscape to Atlas"). Conditional reduction status unchanged. Title changed: "From Landscape to Atlas: Multi-Route Cartography of an Ongoing Expedition Toward the Riemann Hypothesis". Five-part structure: Part I Foundations, Part II Even Dominance / Branch A, Part III Spectral Routes / Branches B and Z, Part IV Cross-Route Synthesis, Part V Conclusio. English and German versions are included for all five parts. Part III refit: multiplicative canonical form Aλ(δ) = AΞ(δ)(1+κ(λ)δ2) with κ(20)=1.527×10-3 and conservative saturation range κ∞ ∈ 1.6,1.8×10-3. Theorem B-1 remains conditional on uniform log-curvature control. Part II GF1 correction: the boundary-moment benchmark sLI ∼ (64π2/3)λ/(NL) is supported in the converged tested λ≥5 regime. The λ=3 sweep is recorded as a low-bandwidth outlier; GF1 is not a uniform all-λ theorem. Part IV added: cross-route synthesis, shared Galerkin pattern, isolated proof slots, dormant routes, and correction chain. Part V added: condensed atlas, open problems OP1--OP5, five-gate promotion protocol, and future scenarios. Old Part III (Conclusio): archived locally; its material is split across the new Parts III--V and is not included as a current upload file. This record is the five-part Landscape/Atlas and audit-trail series for a multi-route investigation toward the Riemann Hypothesis. It documents foundations, obstruction analysis, route failures, computer-assisted diagnostics, spectral route design, and cross-route synthesis. The record is a conditional reduction and research atlas, not an unconditional proof of the Riemann Hypothesis. Cite this record for the full landscape, audit trail, excluded strategies, supporting certificates, and historical development of the programme. For focused companion records, see EvenDom v1.8 and Zookeeper v1.4 under Related records below. PAPERS IN v3.0 Part I: Foundations and Obstructions (English, 15 pages; German, 15 pages). Part II: Even Dominance / Branch A (English, 55 pages; German, 56 pages). Part III: Spectral Routes / Branches B and Z (English, 13 pages; German, 14 pages). Part IV: Cross-Route Synthesis (English, 9 pages; German, 9 pages). Part V: Conclusio / Atlas Summary (English, 7 pages; German, 7 pages). Total current upload: 10 PDFs, English and German, 200 pages combined. KEY RESULTS AND CLAIM LEVEL Claim level: conditional reduction / audit-trail series. No DZT2, MS2, or RH closure is claimed. Branch A (Even Dominance): finite-range diagnostics and variational structure remain conditional on odd-sector lower-bound validation and asymptotic eigenvalue-ordering closure. Branch B (Hadamard strip / I-1 normal-family): the current numerical picture supports a uniform strip-bound route, but Theorem B-1 is conditional on uniform log-curvature control. Branch Z (CCM microcluster): the Zookeeper route is retained as a conditional reduction depending on the stated C2ca inputs and fixed-waterline/microcluster closure. GF1 boundary-moment benchmark: C* = 64π2/3 is the conservative λ≥5 boundary-moment benchmark in the tested converged regime; λ=3 is treated separately. Cross-route synthesis: the atlas isolates shared Galerkin structure and identifies the main remaining proof slots rather than merging them into a theorem-level closure. RELATED RECORDS EvenDom companion v1.8: 10.5281/zenodo.20396370; concept DOI 10.5281/zenodo.19764771. Spectral Zookeeper companion v1.4: 10.5281/zenodo.20396399; concept DOI 10.5281/zenodo.19673126. Landscape/Atlas concept DOI: 10.5281/zenodo.19035640. VERSION HISTORY Former changelogs can be viewed in earlier versions of this record via the Zenodo Versions tab. The v3.0 record supersedes the older three-part description and stale v2.4 companion DOI notes.