Collatz and Riemann: source and evidence

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1 \begin{thebibliography}{99}
2 \bibitem{projectcollatzcore} Komorebi P. \emph{CollatzBlocks.lean}. Saved 7 September 2026. Exact odd map, run compression, repeated pair families, and strong induction bridge. Operation Komorebi project source.
3 \bibitem{projectcollatzaudit} Komorebi P. \emph{Komorebi Collatz: source, implication, and gap audit}. Audit dated 11 September 2026, saved 12 September 2026. Frozen v0.19 source closure and separate audit supplements.
4 \bibitem{projectcollatzbounded} Komorebi P. \emph{Komorebi Collatz All Bounded Deficit Checkpoint}. v0.6.0, 11 September 2026. Source description and verification boundary.
5 \bibitem{projectcollatzhorizon} Komorebi P. \emph{CollatzFixedHorizonObstruction.lean}. Proof Atlas branch, saved 19 September 2026. Exact obstruction to every finite fixed depth descent cover.
6 \bibitem{projectcollatzseeds} Komorebi P. \emph{CollatzUnboundedRunFamily.lean}. Proof Atlas v0.16, saved 19 September 2026. Explicit terminating seeds with unbounded first descent time.
7 \bibitem{projectcollatzlifts} Komorebi P. \emph{CollatzParametricRunExit.lean}. Proof Atlas v0.17, saved 19 September 2026. Exact arithmetic progression lifts and sufficient descent slopes.
8 \bibitem{projectcollatzresidues} Komorebi P. \emph{Findings and final verification for Proof Atlas v0.14}. 18 September 2026. Partial residue coverage and its explicit finite computation boundary.
9 \bibitem{projectcollatzboundary} Komorebi P. \emph{Audit boundary, Proof Atlas v0.17}. Updated 19 September 2026. Statements established by final Lean builds and unresolved global obligations.
10 \bibitem{projectcollatzgap} Komorebi P. \emph{Gap register, corrected after v0.19 and the serious audit}. Saved 12 September 2026. Source floor, crossing, and permanent noncrossing obligations.
11 \bibitem{projectcollatzroutes} Komorebi P. \emph{What remains, and the next research routes}. 12 September 2026. Written derivations on smaller source mergers, switching terms, and cycle divisibility.
12 \bibitem{terras1976} R. Terras. A stopping time problem on the positive integers. \emph{Acta Arithmetica} 30 (1976), 241--252. \href{https://doi.org/10.4064/aa-30-3-241-252}{doi:10.4064/aa-30-3-241-252}.
13 \bibitem{terras1979} R. Terras. On the existence of a density. \emph{Acta Arithmetica} 35 (1979), 101--102. \href{https://doi.org/10.4064/aa-35-1-101-102}{doi:10.4064/aa-35-1-101-102}.
14 \bibitem{tao2026} T. Tao. Almost all orbits of the Collatz map attain almost bounded values. \href{https://arxiv.org/html/1909.03562v7}{arXiv:1909.03562v7}, 16 July 2026. The definitions and quantifiers in Sections 1.1 and 1.2 were consulted for literature orientation.
15 \end{thebibliography}

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