Collatz and Riemann: source and evidence

Download original file

This is the original TeX manuscript source. Use the paper’s PDF for typeset equations.

1 \usepackage[T1]{fontenc}
2 \usepackage[utf8]{inputenc}
3 \usepackage{mathpazo}
4 \usepackage[scaled=0.92]{helvet}
5 \usepackage{courier}
6 \usepackage{amsmath,amssymb,amsthm,mathtools}
7 \usepackage[a4paper,left=27mm,right=27mm,top=26mm,bottom=27mm,headheight=15pt]{geometry}
8 \usepackage{microtype}
9 \usepackage{graphicx}
10 \usepackage[dvipsnames]{xcolor}
11 \usepackage{booktabs,array,longtable,tabularx}
12 \usepackage{enumitem}
13 \usepackage{titlesec,fancyhdr}
14 \usepackage{caption}
15 \usepackage{hyperref}
16 \definecolor{Ink}{HTML}{243138}
17 \definecolor{Teal}{HTML}{21676B}
18 \definecolor{Copper}{HTML}{A45C36}
19 \definecolor{Soft}{HTML}{E9F0EF}
20 \definecolor{Gray}{HTML}{627078}
21 \hypersetup{colorlinks=true,linkcolor=Teal,citecolor=Teal,urlcolor=Teal,pdfauthor={Komorebi P.}}
22 \urlstyle{same}
23 \setlength{\parindent}{1.2em}
24 \setlength{\parskip}{0.15em}
25 \linespread{1.09}
26 \setlist{itemsep=0.22em,topsep=0.45em,leftmargin=1.55em}
27 \setlist[description]{style=nextline,leftmargin=0pt,labelwidth=0pt,labelsep=0pt,font=\normalfont\bfseries}
28 \setcounter{tocdepth}{2}
29 \setlength{\emergencystretch}{1.4em}
30 \titleformat{\section}{\Large\bfseries\color{Ink}}{\thesection}{0.7em}{}
31 \titleformat{\subsection}{\large\bfseries\color{Ink}}{\thesubsection}{0.7em}{}
32 \titleformat{\subsubsection}{\normalsize\bfseries\color{Ink}}{\thesubsubsection}{0.7em}{}
33 \titlespacing*{\section}{0pt}{1.8em}{0.7em}
34 \titlespacing*{\subsection}{0pt}{1.3em}{0.5em}
35 \captionsetup{font=small,labelfont={bf,color=Teal},skip=8pt}
36 \pagestyle{fancy}
37 \fancyhf{}
38 \fancyhead[L]{\sffamily\scriptsize\color{Gray}OPERATION KOMOREBI}
39 \fancyhead[R]{\sffamily\scriptsize\color{Gray}\ShortTitle}
40 \fancyfoot[L]{\sffamily\scriptsize\color{Gray}CONJECTURE SERIES / 8 OCTOBER 2026}
41 \fancyfoot[R]{\sffamily\small\color{Ink}\thepage}
42 \renewcommand{\headrulewidth}{0.25pt}
43 \renewcommand{\footrulewidth}{0pt}
44 \theoremstyle{plain}
45 \newtheorem{theorem}{Theorem}[section]
46 \newtheorem{proposition}[theorem]{Proposition}
47 \newtheorem{lemma}[theorem]{Lemma}
48 \newtheorem{corollary}[theorem]{Corollary}
49 \newtheorem{conjecture}[theorem]{Conjecture}
50 \theoremstyle{definition}
51 \newtheorem{definition}[theorem]{Definition}
52 \newtheorem{example}[theorem]{Example}
53 \theoremstyle{remark}
54 \newtheorem{remark}[theorem]{Remark}
55 \newtheorem{hypothesis}[theorem]{Hypothesis}
56 \numberwithin{equation}{section}
57 \providecommand{\N}{\mathbb N}
58 \providecommand{\Z}{\mathbb Z}
59 \providecommand{\Q}{\mathbb Q}
60 \providecommand{\R}{\mathbb R}
61 \providecommand{\C}{\mathbb C}
62 \providecommand{\eps}{\varepsilon}
63 \providecommand{\dd}{\mathrm d}
64 \providecommand{\norm}[1]{\left\lVert #1\right\rVert}
65 \providecommand{\abs}[1]{\left\lvert #1\right\rvert}
66 \graphicspath{{../shared/figures/}}
67 \newcommand{\figplaceholder}[2]{\begin{figure}[tbp]\centering\includegraphics[width=0.97\linewidth]{#1.pdf}\caption{#2}\label{fig:#1}\end{figure}}
68 \newcommand{\Cover}[4]{%
69 \hypersetup{pageanchor=false}
70 \begin{titlepage}\thispagestyle{empty}
71 \noindent{\sffamily\small\color{Teal}OPERATION KOMOREBI\hfill CONJECTURE SERIES #1}\par
72 \vspace{27mm}
73 \noindent{\fontsize{43}{47}\selectfont\color{Ink}#2}\par
74 \vspace{5mm}\noindent{\LARGE\color{Ink}#3}\par
75 \vspace{9mm}\noindent{\color{Teal}\rule{\linewidth}{1.1pt}}\par
76 \vspace{8mm}\noindent{\large Komorebi P.}\par
77 \vspace{2mm}\noindent{\sffamily\small\color{Gray}READER EDITION 1.1 / 8 OCTOBER 2026}\par
78 \vfill
79 \noindent\begin{minipage}{0.96\linewidth}{\large\color{Ink}#4}\end{minipage}\par
80 \vspace{9mm}\noindent{\sffamily\small\color{Teal}EXACT IDENTITIES\quad /\quad FINITE EVIDENCE\quad /\quad OPEN CONJECTURE}\par
81 \end{titlepage}\hypersetup{pageanchor=true}}

Back to source controls

Back to Collatz and Riemann: source and evidence