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\documentclass{article}
\newtheorem{guess}{conjecture}
\newtheorem{axiom}{subsection Axiom}[subsection]
\newtheorem{axioms}{section Axiom}[section]
\newtheorem{hunch}[guess]{Hunch}
\begin{document}
Blippity, blah blah blah blah, blippity blah blah blah.
Blippity, blah blah blah blah, blippity blah blah blah.
Blippity, blah blah blah blah, blippity blah blah blah.
\section{First section}
Blippity, blah blah blah blah, blippity blah blah blah.
Blippity, blah blah blah blah, blippity blah blah blah.
Blippity, blah blah blah blah, blippity blah blah blah.
\begin{guess}Some good conjectures are numbered.\end{guess}
Blippity, blah blah blah blah, blippity blah blah blah.
Blippity, blah blah blah blah, blippity blah blah blah.
Blippity, blah blah blah blah, blippity blah blah blah.
\begin{guess}Some good conjectures are repeated.\end{guess}
Blippity, blah blah blah blah, blippity blah blah blah.
Blippity, blah blah blah blah, blippity blah blah blah.
Blippity, blah blah blah blah, blippity blah blah blah.
\begin{hunch} There are no sure-fire hunches. \end{hunch}
Blippity, blah blah blah blah, blippity blah blah blah.
Blippity, blah blah blah blah, blippity blah blah blah.
Blippity, blah blah blah blah, blippity blah blah blah.
\begin{axiom} All axioms are very dull. \end{axiom}
Blippity, blah blah blah blah, blippity blah blah blah.
Blippity, blah blah blah blah, blippity blah blah blah.
Blippity, blah blah blah blah, blippity blah blah blah.
\begin{axiom} All axioms are very dull. \end{axiom}
Blippity, blah blah blah blah, blippity blah blah blah.
Blippity, blah blah blah blah, blippity blah blah blah.
Blippity, blah blah blah blah, blippity blah blah blah.
\begin{axioms} All axioms are very dull. \end{axioms}
Blippity, blah blah blah blah, blippity blah blah blah.
Blippity, blah blah blah blah, blippity blah blah blah.
Blippity, blah blah blah blah, blippity blah blah blah.
\begin{axioms} All axioms are very dull. \end{axioms}
Blippity, blah blah blah blah, blippity blah blah blah.
Blippity, blah blah blah blah, blippity blah blah blah.
Blippity, blah blah blah blah, blippity blah blah blah.
\subsection{First subsection}
\begin{guess}Some good conjectures are numbered.\end{guess}
\begin{guess}Some good conjectures are repeated.\end{guess}
\begin{hunch} There are no sure-fire hunches. \end{hunch}
\begin{axiom} All axioms are very dull. \end{axiom}
\begin{axiom} All axioms are very dull. \end{axiom}
\section{Second section}
\begin{guess}Some good conjectures are numbered.\end{guess}
\begin{guess}Some good conjectures are repeated.\end{guess}
\begin{hunch} There are no sure-fire hunches. \end{hunch}
\begin{axiom} All axioms are very dull. \end{axiom}
\begin{axiom} All axioms are very dull. \end{axiom}
\subsection{Second subsection}
\begin{guess}Some good conjectures are numbered.\end{guess}
\begin{guess}Some good conjectures are repeated.\end{guess}
\begin{hunch} There are no sure-fire hunches. \end{hunch}
\begin{axiom} All axioms are very dull. \end{axiom}
\begin{axiom} All axioms are very dull. \end{axiom}
\end{document}
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