zref-perpage doesn't work with theorem-like environments

Question

I am trying to use the zref-perpage package to number theorem-like enviroments and equations by page. Unfortunately, it doesn't work well. In this first example, we see that the second thm appears on the 2nd page, but its counter is 1.2 instead of 2.1. The equation numbers come out OK.

\documentclass{amsart}
\usepackage[textheight=1in]{geometry} 
\usepackage{zref-perpage}

\newtheorem{thm}{Theorem}
\zmakeperpage{thm}

\renewcommand{\thethm}{\thezpage.\arabic{thm}}
\zmakeperpage{equation}
\renewcommand{\theequation}{\thezpage.\arabic{equation}}

\begin{document}

\begin{thm}
  We have
  \begin{equation}
    \int_1^e\frac1x = 1
  \end{equation}
\end{thm}

\begin{thm}
  We have
  \begin{equation}
    \int_1^e\frac1x = 1
  \end{equation}

  \begin{equation}
  \int_1^e\frac1x = 1
  \end{equation}
\end{thm}

\end{document}

In the second example, the only change I make is I increase the textheight from 1 in to 1.5 in. This makes the second thm begin on the first page but finishes on the second page. As you can see, this time the equation counter gets messed up: the second equation is on the 2nd page, but it gets the label 1.3, so as if it was on page 1.

\documentclass{amsart}
\usepackage[textheight=1.5in]{geometry} 
\usepackage{zref-perpage}

\newtheorem{thm}{Theorem}
\zmakeperpage{thm}

\renewcommand{\thethm}{\thezpage.\arabic{thm}}
\zmakeperpage{equation}
\renewcommand{\theequation}{\thezpage.\arabic{equation}}

\begin{document}

\begin{thm}
  We have
  \begin{equation}
    \int_1^e\frac1x = 1
  \end{equation}
\end{thm}

\begin{thm}
  We have
  \begin{equation}
    \int_1^e\frac1x = 1
  \end{equation}

  \begin{equation}
  \int_1^e\frac1x = 1
  \end{equation}
\end{thm}

\end{document}

At the suggestion of @christian, in the following example I only use article and, with textheight=.9in, the second thm is on the 2nd page, but the thm counter shows 1.2 instead of 2.1.

\documentclass[letterpaper]{article}
%\usepackage{mdframed}
\usepackage[textheight=.9in]{geometry} 
\usepackage{zref-perpage}

\newtheorem{thm}{Theorem}
\zmakeperpage{thm}

\renewcommand{\thethm}{\thezpage.\arabic{thm}}
\zmakeperpage{equation}
\renewcommand{\theequation}{\thezpage.\arabic{equation}}

\begin{document}

\begin{thm}
  We have
  \begin{equation}
    \int_1^e\frac1x = 1
  \end{equation}
\end{thm}

\begin{thm}
  We have
  \begin{equation}
    \int_1^e\frac1x = 1
  \end{equation}

  \begin{equation}
  \int_1^e\frac1x = 1
  \end{equation}
\end{thm}

\end{document}

This example shows that the perpage package doesn't work either.

\documentclass[letterpaper]{article}

\usepackage[textheight=.9in]{geometry} 
\usepackage{perpage}

\newtheorem{thm}{Theorem}
\let\origthethm\thethm
\MakePerPage{thm}
\renewcommand{\thethm}{\theperpage.\origthethm}

\let\origtheequation\theequation
\MakePerPage{equation}
\renewcommand{\theequation}{\theperpage.\origtheequation}

\begin{document}

\begin{thm}
  We have
  \begin{equation}
    \int_1^e\frac1x = 1
  \end{equation}
\end{thm}

\begin{thm}
  We have
  \begin{equation}
    \int_1^e\frac1x = 1
  \end{equation}

  \begin{equation}
  \int_1^e\frac1x = 1
  \end{equation}
\end{thm}

\end{document}

Answer 1

Environment equation, redefined by package amsmath, increments the equation counter before the math is started. Thus, it happens that there is a page break between the counter setting and the displayed math equation. The former is the place, where the label is set to get the page number.

Workarounds:

• Putting a minipage around to prevent the page break:

  \noindent
  \begin{minipage}{\linewidth}
    \begin{equation}...\end{equation}
  \end{minipage}
  

• Redefinition of \equation to move \incr@eqnum, which calls \refstepcounter{equation}, to a later place:

  \makeatletter
  \renewcommand*{\equation}{% amsmath version
    \nobreak
    \mathdisplay@push
    \st@rredfalse
    \global\@eqnswtrue
    \mathdisplay{equation}%
    \incr@eqnum
  } 
  \makeatother