Scalar Waze: the Polymath 15 upper bound Λ ≤ 0.22 — waypoint reconstruction

Reconstruction note — 20 September 2026 Waypoint-by-waypoint reconstruction of the Polymath 15 (2019) proof that the de Bruijn–Newman constant satisfies Λ ≤ 0.22, rebuilt from the published TeX source (debruijn.tex, arXiv:1904.12438) and the cited computation repository (github.com/km-git-acc/dbn_upper_bound). Each of the 18 waypoints carries exactly one label: solid (independently re-verified in-session by re-derivation, line-by-line proof check, or recomputation), sketch (read and believed, not re-verified line by line), or need-to-verify (depends on an external computation not re-run, or carries an open discrepancy flag). Discrepancies against the source are resolved in writing next to their waypoint — e.g. the paper’s region-(c) constant A ≤ 1.88 was not reproduced (A = 1.9063 at N0 = 69098; LHS < 1.955 proved instead via a rigorous uniform majorant), and the fractional-part table digits differ while the underlying heuristic verifies. Attribution, kept straight: Polymath 15 (2019) proved Λ ≤ 0.22. The bound Λ ≤ 0.2 is the later Platt–Trudgian (2020) improvement and is not used here. Scope. This is a reconstruction of a published proof, not a new result. It does not prove the Riemann Hypothesis. The surviving open flag: Proposition 26 is stated o(T log3T) but proved o(T log3+T); the trap 0 ≤ Λ ≤ 0.22 stands modulo that flag. References D. H. J. Polymath, “Effective approximation of heat flow evolution of the Riemann ξ function, and a new upper bound for the de Bruijn–Newman constant,” arXiv:1904.12438, 2019. N. G. de Bruijn, “The roots of trigonometric integrals,” Duke Math. J. 17 (1950), 197–226. B. Rodgers and T. Tao, “The de Bruijn–Newman constant is non-negative,” Forum Math. Pi 8 (2020), e6; arXiv:1801.05914. D. Platt and T. Trudgian, “The Riemann hypothesis is true up to 3·1012,” Bull. Lond. Math. Soc. 53 (2021); the Λ ≤ 0.2 improvement, 2020.