Model cuts as polylines, not horizontal lines

Page 1 of Engel (Bosse/Partitura) has a boxed VERSE 1 label in the left
margin at the same rows as the preceding system's bass lyric line — ink
on both sides of the page throughout the band, so no horizontal line
separates them. The label belongs to system 2, the lyrics to system 1.

A cut is therefore a polyline spanning the page, two points being the
ordinary straight case. A slice bounded by a non-straight cut is not
rectangular: its image is the region's bounding box with everything
outside made transparent, which composites invisibly on the viewer's
sheet. Masking paints transparency, never white.

CONTEXT.md

@@ -20,9 +20,11 @@ _Avoid_: mode, format
 **Slice**:
 The atomic visual unit of a song — one *system*, one full line of music across
 all voices, typically 4–12 bars with lyrics intact. Same definition as noteman's.
-Structurally, a horizontal region of a page: a page begins as a single slice and
+Structurally, a region of a page bounded above and below by cuts: a page begins
-each cut splits one slice into two, so slices always tile the page with no gaps
+as a single slice and each cut splits one slice into two, so slices always tile
-and no overlap.
+the page with no gaps and no overlap. Rectangular when its cuts are straight,
+and stepped when they are not — the slice image is then its bounding box with
+everything outside the region transparent.
 _Avoid_: segment, strip, row, band
 
 **Discard**:
@@ -76,11 +78,16 @@ living unenforced in two repos, and a score with two codas simply works.
 _Avoid_: link, reference, pointer
 
 **Cut**:
-A horizontal line placed on a page that splits one slice into two. Straight at
+A boundary placed on a page that splits one slice into two. Modelled as a
-first; a later polyline form handles pages where systems slant or interleave.
+**polyline** spanning the page from left edge to right edge, with two points —
-Placement is forgiving — anywhere inside the whitespace gap yields the same
+a straight horizontal line — as the ordinary case. Extra vertices handle the
-output, because trim crops to ink afterwards.
+common publisher habit of printing a section label (`VERSE 1`, `INTRO`) in the
-_Avoid_: split, divider, break
+left margin at the same height as the previous system's lyrics: the cut steps
+above the label on the left and below the lyrics on the right.
+
+Placement along the boundary is forgiving — anywhere inside the whitespace yields
+the same output, because trim crops to ink afterwards.
+_Avoid_: split, divider, break, cut line
 
 **Content rectangle**:
 The region of a page that holds music. Set per PDF, adjustable per page, applied

docs/spec.md

@@ -89,9 +89,24 @@ cuts at the page edges. Modelling a slice as "the region between two cuts" leaks
 page 2 has no header, so it would need an invented top cut whose position depends
 on whether that page happens to have one.
 
-Cut placement is forgiving — anywhere inside the whitespace gap yields the same
+Cut placement is forgiving — anywhere inside the whitespace yields the same
 output, because trim crops to ink afterwards.
 
+**A cut is a polyline, not a line.** Two points — a straight horizontal
+boundary — is the ordinary case and what detection proposes. Extra vertices exist
+because publishers routinely print a section label in the left margin at the same
+height as the *previous* system's lyrics. On page 1 of *Engel* (Bosse/Partitura
+edition), the boxed `VERSE 1` label and the preceding system's bass lyric line
+occupy the same rows: ink is present on both sides of the page throughout that
+band, so no horizontal line separates them. `VERSE 1` belongs to system 2, the
+lyrics to system 1. The cut has to step — above the label on the left, below the
+lyrics on the right.
+
+A slice bounded by a non-straight cut is **not rectangular**. Its image is the
+bounding box of the region, with everything outside the region made transparent.
+That composites invisibly on the viewer's sheet, so nothing downstream needs to
+know. This is also why masking must paint transparency rather than white.
+
 ### Content rectangle
 
 The region of a page that holds music, set per PDF and adjustable per page,