\documentclass{article}
\newtheorem{guess}{conjecture}
\newtheorem{axiom}{subsection Axiom}[subsection]
\newtheorem{axioms}{section Axiom}[section]
\newtheorem{hunch}[guess]{Hunch}

\begin{document}
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\section{First section}
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\begin{guess}Some good conjectures are numbered.\end{guess}
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\begin{guess}Some good conjectures are repeated.\end{guess}
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\begin{hunch} There are no sure-fire hunches. \end{hunch}
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\begin{axiom} All axioms are very dull. \end{axiom}
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\begin{axiom} All axioms are very dull. \end{axiom}
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\begin{axioms} All axioms are very dull. \end{axioms}
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\begin{axioms} All axioms are very dull. \end{axioms}
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\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}
