% main.tex — Euclid's Elements, encoded as an rrxiv paper.
%
% Build with tectonic via ./scripts/build.sh.

\documentclass{rrxiv}

\rrxivid{rrxiv-paper-euclid-elements}
\rrxivversion{v1}
\rrxivprotocolversion{0.1.0}
\rrxivlicense{CC-BY-4.0}
\rrxivtopics{math.HO,math.MG,math.NT,history-of-mathematics,reproducibility}

\title{Euclid's \emph{Elements}, encoded as an rrxiv paper}
\author{Blaise Albis-Burdige \and Claude \\
        \small {(translation after Heath, 1908; encoding new, CC-BY-4.0)}}
\date{\today}

\begin{document}
\maketitle

\begin{abstract}
We publish a complete, machine-readable rendering of Euclid's
\emph{Elements} as an rrxiv paper. All thirteen books are encoded:
every definition, postulate, common notion, and proposition is
registered as an addressable rrxiv \texttt{claim}, and every proof
is encoded as a sequence of explicit \texttt{depends\_on} edges to
earlier claims. The encoding produces 465 propositions, 109
definitions, 5 postulates, and 5 common notions, connected by over a
thousand \texttt{depends\_on} edges --- the full reasoning DAG of
the \emph{Elements} is queryable through the rrxiv API.

The encoding serves three purposes: (i)~it dogfoods the rrxiv schema
on a finite, dependency-rich corpus that has been studied for two
thousand years; (ii)~it provides a working reproducibility
demonstration --- every proposition is provable from claims that the
rrxiv graph can enumerate, terminating in the five postulates and
five common notions; and (iii)~it gives agent harnesses a canonical
proof corpus to retrieve over.

Books~I, II, and III are written in full Heath-density prose with
TikZ figures for the canonical constructions (I.1, I.5, I.32, I.47,
II.4, II.11, II.14, III.20, III.31, III.36). Books~IV through XIII
carry the full statement + dependency-edge DAG with condensed proof
sketches; rendering them at Heath density is a long-running editorial
project, and PRs at \url{https://github.com/random-walks/rrxiv-paper-euclid-elements}
are welcome. The translation follows Heath (1908, public domain) with
light modernisation; the rrxiv encoding is released under CC-BY-4.0.
\end{abstract}

% ---- Front matter: postulates + common notions + Book I definitions ----
\input{postulates}
\input{common-notions}
\input{definitions}

% ---- Books ----
\input{books/book01}
\input{books/book02}
\input{books/book03}
\input{books/book04}
\input{books/book05}
\input{books/book06}
\input{books/book07}
\input{books/book08}
\input{books/book09}
\input{books/book10}
\input{books/book11}
\input{books/book12}
\input{books/book13}

\end{document}