visual: mid-formula `\displaystyle` is ignored, and `\cfrac` is typeset as `\frac`

[d-q222]

Two separate math-style bugs, filed together because one repro exposes both and they are likely the same style-tracking code.

Found by visual comparison of rendered pages against pdflatex.

Minimal repro

\documentclass{article}
\usepackage{amsmath}
\begin{document}
A: leading displaystyle: $\displaystyle\sum_{d\mid n}\varphi(d)$.

B: mid-formula displaystyle: $L(n)=\displaystyle\sum_{d\mid n}\varphi(d)$.

C: mid-formula prod: $m=\displaystyle\prod_{k=1}p_k$.

D: no displaystyle: $\sum_{d\mid n}\varphi(d)$.

E: cfrac: $[3,5,2,3]=3+\cfrac{1}{5+\cfrac{1}{2+\cfrac{1}{3}}}$.

F: frac: $[3,5,2,3]=3+\frac{1}{5+\frac{1}{2+\frac{1}{3}}}$.

G: display cfrac:
\[ 3+\cfrac{1}{5+\cfrac{1}{2+\cfrac{1}{3+\cfrac{1}{4}}}} \]
\end{document}

Oracle: /Library/TeX/texbin/pdflatex, TeX Live 2026; Package: amsmath 2025/07/09 v2.17z confirmed in the .log. \cfrac is amsmath's; \displaystyle is plain TeX.

Bug 1 — \displaystyle is honoured only as the first token of the formula

line	pdflatex	FlashTeX
A $\displaystyle\sum...$	big ∑, limits below	big ∑, limits below — ok
B $L(n)=\displaystyle\sum...$	big ∑, limits below	small ∑, limits at the side — wrong
C $m=\displaystyle\prod...$	big ∏, limits below	small ∏, limits at the side — wrong
D $\sum...$ (no \displaystyle)	small ∑, limits at side	small ∑, limits at side — ok

Measured inside FlashTeX's own output (page.get_texttrace(), glyph widths):

• A: ∑ glyph 3074, width 14.39 pt (display variant)
• B: ∑ glyph 3060, width 10.52 pt
• D: ∑ glyph 3060, width 10.52 pt

B and D are byte-for-byte the same size, i.e. the \displaystyle in B had no effect at all. pdflatex renders B the same as A.

Bug 2 — \cfrac is typeset as \frac

\cfrac must keep every level of a continued fraction at the same (display) size. FlashTeX shrinks each nesting level exactly as \frac does, so a three- or four-level continued fraction ends up unreadably small.

Lines E and F prove it directly: FlashTeX's \cfrac output is indistinguishable from its own \frac output, while pdflatex renders them very differently. Line G shows the same in a display.

Why the numeric checks missed both

Neither changes the extracted text, and FlashTeX emits no diagnostic for either. They only change glyph sizes and vertical extents.

Corpus occurrences

• \displaystyle: /Users/dqi26/ross/set11/set11.tex:115 ($L(n) = \displaystyle\sum_{d \mid n} \varphi(d)$) and :145–146 ($m = \displaystyle\prod_{k=1} p_k^{e_k}$). Both on page 1 of set11; line 109 in the same file has \displaystyle leading and renders correctly, which is the tell.
• \cfrac: /Users/dqi26/ross/set3/set3.tex:208, 238, 241, 245, 248. Page 3 of set3 is the clearest side-by-side — the oracle's nested fractions are full height, FlashTeX's collapse to a few points tall.