A slur spanning a system break must draw a partial curve on each system

Same principle as ties: a slur whose notes fall on different engraved systems is drawn as two segments, never simply omitted.

Gould ('Slurs across a system break') explicitly documents the two-segment convention; Ross and Dorico/LilyPond all auto-split system-crossing slurs identically to ties.

This rule needs the notated content and the rendered result together — the score says what should happen, the page says whether it did.