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docs: move the VLE physics equations to the example page; fix a grammar slip - #3

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Aug 7, 2026
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docs: move the VLE physics equations to the example page; fix a grammar slip#3
adowling2 merged 1 commit into
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Two small documentation improvements, no code changes.

Move the example's physics to the example page. The Theory page ended with a section
stating extended Raoult's law (Eq 10), the Gibbs–Duhem relation (Eq 11), and the SI-4
McCabe–Thiele column closures. Those are properties of the case study, not of the method —
bits_for_gaps never sees them; it only ever sees the black-box activity coefficient. They
now live on the VLE/distillation example page as "The governing equations", directly after
"The physics", so each equation sits beside the component it describes. The Theory page
keeps a short cross-reference so the material is still discoverable.

Grammar. "which matters most exactly when data is scarce" → "data are scarce".

Verified: sphinx-build -W clean, and both equations plus the corrected sentence confirmed
in the rendered HTML.

🤖 Generated with Claude Code

…re scarce"

- index.md: "data is scarce" -> "data are scarce" ("data" as a plural noun).
- Move "The example: extended Raoult's law and Gibbs-Duhem" off the Theory page and
  onto the VLE/distillation example page as "The governing equations", placed right
  after "The physics" so Eqs (10)/(11) and the SI-4 column closures sit next to the
  four components they describe. The Theory page is now purely about the method, and
  keeps a short cross-reference explaining that the example's thermodynamics lives on
  the example page because bits_for_gaps never sees it -- only the black-box activity
  coefficient.

sphinx-build -W clean; both equations and the typo fix verified in the rendered HTML.

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
@adowling2
adowling2 merged commit aa97d8f into main Aug 7, 2026
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