math tagging produces misaligned footnote below equation

[John02139]

\DocumentMetadata 
{
	testphase={phase-III,math},
	pdfstandard = a-4,
	pdfversion  = 2.0,
	lang		= en-US,
}

\documentclass[11pt]{article}
\usepackage[letterpaper,margin=1in]{geometry} 
\usepackage{lipsum}

\begin{document}
K. O. Friedrichs introduced the following model equation to explain boundary layers\footnote{In Friedrich's 1941 lecture notes on fluid dynamics, the forcing function is a constant. Other reports have cited other forcing functions, including this one and $g'(x)$. He seems to have used this equation often with various forcing functions. Prandtl reportedly used $\varepsilon y''+y'+y = 0$ a decade earlier.}:
\begin{equation}
\varepsilon \frac{d^2 y}{dx^{2}} + \frac{dy}{dx} = 1+2x \qquad \textrm{with } y(0) = 0 \textrm{ and } y(1) = 1
\end{equation}
Note that $y = y(x,\varepsilon)$.  As $\varepsilon\to 0$, the highest derivative is lost: the equation becomes first order and cannot meet two boundary conditions.  This fact leads to a boundary layer at one side of the domain.

\lipsum[1-5]

A perturbation expansion in $f(\varepsilon)$ for $f\to 0$ is\begin{equation}
y(z,\varepsilon) = Y_{0}(z) + f Y_{1}(z) + f^{2} Y_{2}(z) + \cdots
\end{equation}

\end{document}

With math tagging:

Without math tagging:

[u-fischer]

hm, I think the logic to reinsert \belowdisplayskip after the tagging code is not right. We should ensure that there is no negative skip before a possible breakpoint.

\DocumentMetadata 
{
	testphase={phase-III,math},
	pdfstandard = a-4,
	pdfversion  = 2.0,
	lang		= en-US,
}

\documentclass[11pt]{article}
\usepackage[letterpaper,margin=1in]{geometry} 
\usepackage{lipsum}
\ExplSyntaxOn\makeatletter
\cs_set_protected:Npn \__math_tag_dollardollar_display_end: 
  {
    \para_raw_end:
    \tagpdfparaOn
    \l__math_tmpa_skip \lastskip
    \tag_socket_use:n{math/display/formula/end}    
    \penalty 10000
    \skip_vertical:n { -\l__math_tmpa_skip  } % negate the negative belowdisplayskip
    \penalty \postdisplaypenalty
    \skip_vertical:n { -\l__math_tmpa_skip  } % reinsert it 
  \@doendpe             % this has no \end{...} to take care of it
}
\ExplSyntaxOff\makeatother

\begin{document}
K. O. Friedrichs introduced the following model equation to explain boundary layers\footnote{In Friedrich's 1941 lecture notes on fluid dynamics, the forcing function is a constant. Other reports have cited other forcing functions, including this one and $g'(x)$. He seems to have used this equation often with various forcing functions. Prandtl reportedly used $\varepsilon y''+y'+y = 0$ a decade earlier.}:
\begin{equation}
\varepsilon \frac{d^2 y}{dx^{2}} + \frac{dy}{dx} = 1+2x \qquad \textrm{with } y(0) = 0 \textrm{ and } y(1) = 1
\end{equation}
Note that $y = y(x,\varepsilon)$.  As $\varepsilon\to 0$, the highest derivative is lost: the equation becomes first order and cannot meet two boundary conditions.  This fact leads to a boundary layer at one side of the domain.

\lipsum[1-5]

A perturbation expansion in $f(\varepsilon)$ for $f\to 0$ is\begin{equation}
y(z,\varepsilon) = Y_{0}(z) + f Y_{1}(z) + f^{2} Y_{2}(z) + \cdots
\end{equation}

\end{document}

@FrankMittelbach does that look correct?

[FrankMittelbach]

Wrong sign on the reinsert?

[u-fischer]

No the sign is fine. The first equation in the document shows that (as wanted) first a negative glue is inserted and then the double positive to compensate:

...\penalty 10000
...\glue(\belowdisplayskip) -11.0 plus -3.0 minus -6.0
...\penalty 0
...\glue 22.0 plus 6.0 minus 12.0

but after the second equation the compensation is lost at the page break:

...\penalty 10000
...\glue(\belowdisplayskip) -11.0 plus -3.0 minus -6.0
...\glue 10.0 plus 4.0 minus 2.0
...\kern-3.0

With my fix one gets there

...\penalty 10000
...\glue(\belowdisplayskip) -11.0 plus -3.0 minus -6.0
...\penalty 10000
...\glue 11.0 plus 3.0 minus 6.0
...\glue 10.0 plus 4.0 minus 2.0
...\kern-3.0

which in the sum is the same what you get without math tagging:

...\glue 10.0 plus 4.0 minus 2.0
...\kern-3.0

[FrankMittelbach]

I realized that by now. yes your code is correct. first we have to get back to the same position before belowskip is is added (without a break point) and then we have to insert postpenalty and the real belowskip, so yes your adjust is the right one. I make an update.