关于 `ntheorem` 和 `amsthm` 中的 `\qedhere` 优化问题 about forum HOT 5 OPEN

\documentclass{article}
\usepackage{amsmath,amssymb}
\usepackage{amsthm}

\begin{document}

\begin{proof} test
  \begin{equation*}
  \begin{aligned}
  \mathbb{E}&\Big[\Big\vert \dfrac{1}{N}\sum\limits^N_{j=1}\varphi(\theta^j,\nu^j)-\displaystyle\int_{\mathbb{T}\times\mathbb{R}}\varphi dF\Big\vert^2\Big]\\[2mm]
  &\leq 2\mathbb{E}\big[\vert\varphi(\theta^j,\nu^j)-\varphi(\bar{\theta}^j,\bar{\nu}^j)\vert^2\big]+2\mathbb{E}\Big[\Big\vert\dfrac{1}{N}\sum\limits^N_{j=1}\varphi(\bar{\theta}^j,\bar{\nu}^j)-\displaystyle\int_{\mathbb{T}\times\mathbb{R}}\varphi dF\Big\vert^2\Big]\qedhere\\[2mm]
  &\leq C\mathbb{E}\big[\vert\theta^j-\bar{\theta}^j\vert^2\big]+2\mathbb{E}\Big[\Big\vert\dfrac{1}{N}\sum\limits^N_{j=1}\varphi(\bar{\theta}^j,\bar{\nu}^j)-\displaystyle\int_{\mathbb{T}\times\mathbb{R}}\varphi dF\Big\vert^2\Big] 
  \end{aligned} \qedhere
  \end{equation*}
\end{proof}

\end{document}

\documentclass{article}
\usepackage{amsmath,amssymb}
\usepackage{amsthm}

\usepackage[pass, showframe]{geometry}

\begin{document}

\begin{proof}
  control group
\end{proof}

\begin{proof} test
  \begin{equation*}
  \begin{aligned}
  \mathbb{E}&\Big[\Big\vert \dfrac{1}{N}\sum\limits^N_{j=1}\varphi(\theta^j,\nu^j)-\displaystyle\int_{\mathbb{T}\times\mathbb{R}}\varphi dF\Big\vert^2\Big]\\[2mm]
  &\leq 2\mathbb{E}\big[\vert\varphi(\theta^j,\nu^j)-\varphi(\bar{\theta}^j,\bar{\nu}^j)\vert^2\big]+2\mathbb{E}\Big[\Big\vert\dfrac{1}{N}\sum\limits^N_{j=1}\varphi(\bar{\theta}^j,\bar{\nu}^j)-\displaystyle\int_{\mathbb{T}\times\mathbb{R}}\varphi dF\Big\vert^2\Big]\\[2mm]
  &\leq C\mathbb{E}\big[\vert\theta^j-\bar{\theta}^j\vert^2\big]+2\mathbb{E}\Big[\Big\vert\dfrac{1}{N}\sum\limits^N_{j=1}\varphi(\bar{\theta}^j,\bar{\nu}^j)-\displaystyle\int_{\mathbb{T}\times\mathbb{R}}\varphi dF\Big\vert^2\Big] 
  \end{aligned} \qedhere
  \end{equation*}
\end{proof}

\end{document}