Hypothesis listing environment for mathematics paper

Question

The problem:

I'm trying to find an appropriate environment for the listing of hypotheses near the beginning of a mathematics research paper. The hypotheses themselves are mostly text, interspersed with display-style mathematics and the occasional equation.

Requirements:

• Each hypothesis should be numbered in the same way that equations are numbered, with the number appearing on the right-hand side of the page (if the standard article class is used)
• The number assigned to a hypothesis should be centred vertically with respect to that hypothesis
• LaTeX should (preferably) handle linebreaks, since each hypothesis is mostly words
• The left-hand margin should be greater than the usual text margin, so that it's inset a little (like with the enumerate environment)

Attempts at solution:

• Using the enumerate environment with the enumitem package gives almost what I want, but the labels appear on the left-hand side of the page, at the beginning of each item. If they were on the right-hand side, and vertically centred, that would probably suffice. Some example code:

  \documentclass{article}
  \usepackage{amsmath,amssymb}
  \usepackage{enumitem}
  
  \begin{document}
  
  \begin{enumerate}[label=(H\arabic*)]
  \item $T>0$ and $\Omega$ is an open, bounded and connected subset of $\mathbb{R}^d$, 
  where $d\in\mathbb{N}$. \label{hyp:domain}
  \item For every $n\in\mathbb{N}$, $\beta_{n}:\mathbb{R}\to\mathbb{R}$ is nondecreasing, Lipschitz continuous 
  with uniform Lipschitz constant $L_\beta > 0$ and satisfies $\beta_{n}(0)=0$.
  There is a function $\beta:\mathbb{R}\to\mathbb{R}$ such that $\beta_{n}\to\beta$ locally uniformly 
  on $\mathbb{R}$. \label{hyp:beta}
  \end{enumerate}
  
  \end{document}
  

• Using a left-aligned array for each hypothesis gives me the correct margins, alignment and numbering, but it just doesn't seem appropriate to use for something that is a list and mostly text. The spacing between lines is wrong and I'm forever having to insert manual linebreaks and \mbox's everywhere. Some example code:

  \documentclass{article}
  \usepackage{amsmath,amssymb}
  \usepackage{geometry}
  
  \begin{document}
  \begin{subequations}
  \begin{align}
  &\begin{array}{l}
  \mbox{$T>0$ and $\Omega$ is an open, bounded and connected subset of $\mathbb{R}^d$, 
  where $d\in\mathbb{N}$.}
  \end{array}\label{hyp:domain} \\ 
  &\begin{array}{l}
  \mbox{For every $n\in\mathbb{N}$, $\beta_{n}:\mathbb{R}\to\mathbb{R}$ is nondecreasing, Lipschitz continuous 
  with uniform} \\
  \mbox{Lipschitz constant $L_\beta > 0$ and satisfies $\beta_{n}(0)=0$.}\\
  \mbox{There is a function $\beta:\mathbb{R}\to\mathbb{R}$ such that $\beta_{n}\to\beta$ locally uniformly 
  on $\mathbb{R}$.}
  \end{array}
  \end{align}
  \end{subequations}
  \end{document}
  

I should point out that the difference in styles of numbering ( (H1), (H2), etc. for the first example, (1a), (1b), etc. for the second example) isn't so important; I'd probably prefer the second style though.

Is the solution to create a custom hypothesis environment (which would be pretty handy for future papers), or is there no middle-ground to be had between my above attempts at solution?

Answer 1

Here's one possibility using tcolorbox. A new hypotheses environment is defined (internally is just a list); inside this environment you use the \Hypo command for each hypothesis; the syntax is

\Hypo[<label>]{<text>}

The code:

\documentclass{article}
\usepackage[many]{tcolorbox}
\usepackage{enumitem}
\usepackage{amsmath,amssymb}
\usepackage{lipsum}

\newcounter{myhypo}
\renewcommand\themyhypo{(H\arabic{myhypo})}

\newtcolorbox{hypo}[1][]{
  breakable,
  enhanced,
  top=0pt,
  bottom=0pt,
  nobeforeafter,
  colback=white,
  boxrule=0pt,
  arc=0pt,
  right=30pt,
  left=20pt,
  outer arc=0pt,
  overlay={
    \node[inner sep=0pt,anchor=east] 
    at (frame.east) 
    {\refstepcounter{myhypo}\themyhypo\label{#1}};
  },
}
\newenvironment{hypotheses}
  {\list{}{\setlength\leftmargin{0pt}\item\relax}}
  {\endlist}
\newcommand\Hypo[2][]{%
  \begin{hypo}[#1]#2\end{hypo}}  

\begin{document}

\lipsum[4]
\begin{hypotheses}
\Hypo[hyp:domain]{%
$T>0$ and $\Omega$ is an open, bounded and connected subset of $\mathbb{R}^d$, 
where $d\in\mathbb{N}$.}

\Hypo[hyp:beta]{%
For every $n\in\mathbb{N}$, $\beta_{n}:\mathbb{R}\to\mathbb{R}$ is nondecreasing, Lipschitz continuous 
with uniform Lipschitz constant $L_\beta > 0$ and satisfies $\beta_{n}(0)=0$.
There is a function $\beta:\mathbb{R}\to\mathbb{R}$ such that $\beta_{n}\to\beta$ locally uniformly on $\mathbb{R}$.}

\Hypo[hyp:test]{%
A short hypothesis.}
\end{hypotheses}
As we see from hypotheses~\ref{hyp:domain}, \ref{hyp:beta} and~\ref{hyp:test}...

\end{document}

The result:

I used

\renewcommand\themyhypo{(H\arabic{myhypo})}

to get (H1), (H2),... but you can get any other numbering schema by changing this redefinition.

Answer 2

I know I'm like 3 years late but since this question still shows in Google, I will add my answer for completeness.

As I didn't want to use any extra packages (especially one such as tcolorbox which has a lot of unwanted fuzz, at least to me); I hacked together a solution using tabular environments. Please note that I don't know the efficiency of this, what with my Master Thesis having a few hypotheses (4 or so) there is no noticeable compilation overhead, but I don't know what would happen with a text with, say, 100 hypotheses.

\documentclass{article}

\usepackage{amsmath,amssymb} % needed for math
\usepackage{array} % needed for the 'm' column type in tabular

\newcounter{hypocounter}
\renewcommand\thehypocounter{(H\arabic{hypocounter})} % this produces '(H1)'
                                                      % when referencing
\setcounter{hypocounter}{0}

\newenvironment{hypothesis}{
\refstepcounter{hypocounter}
\begin{center}
\begin{tabular}{m{0.75\linewidth}c} % adjust '0.75' to preferred width
}{&\thehypocounter\end{tabular}\end{center}}

\begin{document}

This is some text.

\begin{hypothesis}
\label{hyp:one}
$T>0$ and $\Omega$ is an open, bounded and connected subset of $\mathbb{R}^d$, 
where $d\in\mathbb{N}$.
\end{hypothesis}

This is a reference to hypothesis \ref{hyp:one}.

\begin{hypothesis}
For every $n\in\mathbb{N}$, $\beta_{n}:\mathbb{R}\to\mathbb{R}$ is nondecreasing, Lipschitz continuous 
with uniform Lipschitz constant $L_\beta > 0$ and satisfies $\beta_{n}(0)=0$.
There is a function $\beta:\mathbb{R}\to\mathbb{R}$ such that $\beta_{n}\to\beta$ locally uniformly on $\mathbb{R}$.
\end{hypothesis}

\begin{hypothesis}
\label{hyp:three}
A short hypothesis.
\end{hypothesis}

Another reference to the last hypothesis: \ref{hyp:three}.

\end{document}

Which procuces this: