Fine-grain numbered elements/theorems

numbering.tex

\usepackage{amsthm}
\usepackage{cleveref}
\usepackage{etoolbox}


\newcounter{everythingcnt}
\newcounter{Heverythingcnt}  % the corresponding counter for hyperref
\providecommand{\lfstyle}[1]{#1} % \lfstyle is the command for lining figures in many font packages. If there's none, we use an empty one

\makeatletter
% Assuming that we will never skip levels (e.g. opening a subsection before opening
% a section of a chapter, we can infer the current level of structures by looking
% at which level counter is 0.
\newcommand{\currentLevel}{%
  \ifnum\c@section=0 %
  \thechapter
  \else
  \ifnum\c@subsection=0 %
  \thesection
  \else
  \ifnum\c@subsubsection=0 %
  \thesubsection
  \else
  \thesubsubsection
  \fi
  \fi
  \fi
}
\newcommand{\currentLevelH}{%
  \ifnum\c@section=0 %
  \theHchapter
  \else
  \ifnum\c@subsection=0 %
  \theHsection
  \else
  \ifnum\c@subsubsection=0 %
  \theHsubsection
  \else
  \theHsubsubsection
  \fi
  \fi
  \fi
}

\newcommand{\setupeverythingcnt}{%
  \setcounter{everythingcnt}{0}%
  \renewcommand*{\theeverythingcnt}{\currentLevel\textasteriskcentered\arabic{everythingcnt}}%
  \renewcommand*{\theHeverythingcnt}{\currentLevelH.\arabic{everythingcnt}}%
}

% Whenever enters a new leve, the element counter is reset and its format is updated.
\apptocmd{\@sect}{\setupeverythingcnt}{}{}%

\setupeverythingcnt

\makeatother

\newlength{\elementspace}
%\setlength{\elementspace}{10pt plus 6pt minus 4pt}
\setlength{\elementspace}{10pt plus 6.675pt}

\newtheoremstyle{mytheorem}% 〈name〉
  {\elementspace}% 〈Space above〉
  {\elementspace}% 〈Space below〉
  {\thfamily}% 〈Body font〉
  {}% 〈Indent amount〉
  {\bfseries}% 〈Theorem head font〉
  {.}% 〈Punctuation after theorem head〉
  {.5em}% 〈Space after theorem head
  {{\normalfont\bfseries\lfstyle\thmnumber{#2} \thmname{#1}}\thmnote{\normalfont \ (#3)}}% 〈Theorem head spec (can be left empty, meaning ‘normal’)
%  {\llap{\thmname{#1}\hspace{2em}}\thmnumber{#2}\thmnote{ \normalfont(#3)}}% 〈Theorem head spec (can be left empty, meaning ‘normal’)

\newtheoremstyle{mydefinition}% 〈name〉
  {\elementspace}% 〈Space above〉
  {\elementspace}% 〈Space below〉
  {}% 〈Body font〉
  {}% 〈Indent amount〉
  {\bfseries}% 〈Theorem head font〉
  {.}% 〈Punctuation after theorem head〉
  {.5em}% 〈Space after theorem head
%  {(\thmnumber{#2}) \thmname{#1}\thmnote{ \normalfont(#3)}}% 〈Theorem head spec (can be left empty, meaning ‘normal’)
  {{\normalfont\bfseries\lfstyle\thmnumber{#2} \thmname{#1}}\thmnote{\normalfont \ (#3)}}% 〈Theorem head spec (can be left empty, meaning ‘normal’)

\newtheoremstyle{basic}% 〈name〉
  {\elementspace}% 〈Space above〉
  {\elementspace}% 〈Space below〉
  {}% 〈Body font〉
  {}% 〈Indent amount〉
  {\bfseries}% 〈Theorem head font〉
  {.}% 〈Punctuation after theorem head〉
  {.5em}% 〈Space after theorem head
  {{\normalfont\bfseries\lfstyle\thmnumber{#2}}\thmnote{\normalfont \ ({#3})}}% 〈Theorem head spec (can be left empty, meaning ‘normal’)
  %{{\normalfont\bfseries\lfstyle\thmnumber{#2}}}% 〈Theorem head spec (can be left empty, meaning ‘normal’)


\theoremstyle{mytheorem}
\newtheorem{theorem}[everythingcnt]{Theorem}

\theoremstyle{mydefinition}
\newtheorem{definition}[everythingcnt]{Definition}
\newtheorem{example}[everythingcnt]{Example}
\newtheorem{axiom}[everythingcnt]{Axiom}
\newtheorem{remark}[everythingcnt]{Remark}
\newtheorem{notation}[everythingcnt]{Notation}
\newtheorem{convention}[everythingcnt]{Convention}
\newtheorem{terminology}[everythingcnt]{Terminology}
\newtheorem{corollary}[everythingcnt]{Corollary}
\newtheorem{lemma}[everythingcnt]{Lemma}
\newtheorem{conjecture}[everythingcnt]{Conjecture}
\newtheorem{proposition}[everythingcnt]{Proposition}

\theoremstyle{basic}
\newtheorem{element}[everythingcnt]{Element}

\crefname{element}{}{}
\Crefname{element}{}{}

Test.tex

\documentclass{article}

\input{numbering.tex}

\begin{document}

\section{Introduction}

\begin{element}
Hello
\end{element}

\subsection{World}
\begin{element}
Hello
\end{element}

\begin{element}
Again
\end{element}

\end{document}