分页符上的框/行的转换

Question

情况：目前，我实现了一个定理环境，其左侧有一条灰线（目前该实现应该不太相关）。示例见下文。我对结果非常满意，但想优化分页行为。

希望：如果线条断开，我希望线条呈现“淡入淡出过渡”（作为环境继续的视觉指示）。因此线条可能会变得更加透明，或者可能会过渡为虚线。

总的来说，我对这种用于框和框架的“转换”很感兴趣。我对用于生成线/框/框架的包没有任何偏好，并且对任何与定理环境配合良好的解决方案都感到高兴。

Answer 1

像这样？

\documentclass{article}
\usepackage[most]{tcolorbox}
\usepackage{mathtools}
\usepackage{lipsum}

\newtcbtheorem[auto counter]{PeterTheorem}{Theorem}%
{theorem style=plain, enhanced, breakable, 
empty,
coltitle=black, 
fonttitle=\upshape\scshape,
boxrule=0.0pt,
overlay unbroken={\fill[gray](frame.north west)rectangle ([xshift=1.5mm]frame.south west);},
overlay first={\fill[top color=gray, bottom color=white](frame.north west)rectangle ([xshift=1.5mm]frame.south west);},
overlay last={\fill[top color=white, bottom color=gray](frame.north west)rectangle ([xshift=1.5mm]frame.south west);},
overlay middle={\fill[top color=white, bottom color=white, middle color=gray](frame.north west)rectangle ([xshift=1.5mm]frame.south west);},
}{theo}


\begin{document}

\lipsum[1-4]

\begin{PeterTheorem}{}{theo1-3}%
Consider the n.n.f. Insing model on $Z^d,\ d\geq 1$. There exists acritical inverse temperature $\beta_c=\beta_c(d) \in[0,\infty]$, such that the Ising undergoes a \emph{sharp} ferromagnetic phase transistion at $\beta_c$:
\begin{equation*}
(\sigma_0)^+_{\beta;\Lambda_n}
\begin{cases}\leq e^{-cn} & $for$\ \beta<\beta_c\ $with$\ c=c(\beta)>0\\
\geq \sqrt{1-(\beta_c/\beta)^2} & $for$\ \beta\geq \beta_c \end{cases}
\end{equation*}
uniformly in $n\geq0$, where $\Lambda_n:=Z^d\cap[-n,n]^d$ denotes the box of size $n$ around the origin. Moreover, for\ $d\geq2$, the phase transition is \emph{non-trivial}, meaning that $0<\beta_c<\infty$.
\end{PeterTheorem}

\end{document}