Math boxes and invisible layout

Math keeps logical dimensions separate from drawing bounds. Phantom, smash, and lap deliberately change one without changing the other.

Command	Dimensions	Ink
`\phantom{…}`	Keep width, height, and depth.	Hidden.
`\hphantom{…}`	Keep horizontal advance only.	Hidden.
`\vphantom{…}`	Keep height and depth only.	Hidden.
`\smash{…}`	Keep advance; suppress height and depth.	Retained.
`\smash[t]{…}` / `\smash[b]{…}`	Suppress only height / depth.	Retained.
`\mathrlap{…}` / `\mathllap{…}` / `\mathclap{…}`	Zero advance; retain height and depth.	Right of / left of / centered on the insertion point.

The direct elements are Phantom, Smash, and Lap. A lap has zero advance; a negative kern actually moves the next atom backward. Physical boxes remain nonnegative even when a sequence's total advance is negative. Nested explicit colors and backgrounds cannot make phantom ink reappear.

Suppressed dimensions stay suppressed when the expression is put in a math row or prose line. Ink survives in the fragment's independent bounds. Give an explicit SVG enough padding; its viewport still clips overhang. The comparison script includes this ink when rasterizing, including leading laps.

Frames, cancellation, and position

Enclose supplies frames, background colors, diagonal cancellation, and strikeout. TeX supports \boxed, \fbox, \colorbox, \fcolorbox, \cancel, \bcancel, \xcancel, and text-mode \sout. Frames add padding and preserve the body's baseline. Cancellation retains the original logical box and draws its lines over the body.

\rule[shift]{width}{height} draws a filled rectangle with its bottom at shift above the baseline. Positive and negative shifts are supported; a nonpositive width or height has no ink. Its direct counterpart is MathRule. TeX point dimensions keep their size in script styles; TeX em/ex dimensions use the local text size.

RaiseBox changes an operand's position relative to the baseline; VCenter centers it on the math axis. \hbox{…} is a literal text box with optional $…$ math, useful inside \raisebox and \vcenter.

Pmb overprints an operand to simulate bold while retaining its advance. Real bold font commands are covered in math fonts and macros. Exotic \phase, \angl, and \angln enclosures remain unsupported.

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