[latexrefman] node \par

[Karl Berry]

    ``horizontal mode'' and ``unrestrcited horizontal mode'' are
    synonyms. Simlarly ``vertical mode'' and `\outer vertical mode''. The
    latters are just as opposed to restrcited horizontal mode, resp. inner
    vertical mode.

Yes.

LaTeX's renaming of TeX's modes is one of the most irritating and
unnecessary things done by Lamport, IMHO. It's just a constant source of
confusion, as far as I can see.  I've never looked at what's said in
latex2e.texi about them. I don't doubt additional clarity would be welcome.

    @dfn{Paragraph mode} is what @LaTeX{} is in when processing ordinary
    text.  It breaks the input text into lines and breaks the lines into
    pages.

Well, "paragraph mode" is simply an unclarity introduced by Lamport. It
is true that the default operation of (La)TeX is to read words, break
them into lines of paragraphs, and break the lines into pages, which is
what he's trying to describe. However, this conflates what's really
going on, which is two different things, as you say: horizontal mode
(words into paragraphs) and vertical mode (lines into pages). So as soon
as you get beyond the most superficial level of understanding how TeX
works, it just makes things things to speak of this "paragraph mode".

However, since Lamport described it this way, it is hard to say what to
do in latex2e.texi.

    paragraph line breaking process

It's not during the breaking-words-into-paragraphs per se, but then the
line breaks have been chosen and the lines are being added to the page
(aka "main vertical list").

    TeX keeps track of the potential good break points positions.

When a paragraph is broken into lines, each line is a potential point
for a page break. More generally, most items added in vertical mode are
potential page breaks.

    Then, is there some way to retrieve explicitely these good positions

Not at the TeX level (except maybe in LuaTeX), but TeX will output every
potential page break in the log file if you ask it (% lines and %%
lines). The TeXbook goes into quite some detail about this.

(I suspect you already know all this, but )
    https://github.com/olpa/tex/issues/6

To get a page break in the middle of a tall cell, you somehow have to
make the contents of that cell be at the top level of the page (again,
the "main vertical list"). That would mean unhboxing the line and
unvboxing the cell, I'm guessing. It sounds pretty impossible.

In LuaTeX, it may be possible to play around with the boxing after the
table is built and then trigger the page builder, but I don't actually
know. --best, karl.