Umbrella invariant — every generated beam group's boundaries land exactly on the meter's true nominal beat grid

This is the single check that subsumes simple/compound/odd-meter grouping, barline-crossing, system-break, and anacrusis correctness: at all times, a beam group's start and end tick must coincide with a genuine beat (or sub-beat, for secondary breaks) boundary as measured from the true start of its containing bar, never from an arbitrary note-index-zero origin.

Any of the failure modes described in the more specific rules above (bar-length mismatch, symbolic time signature, pickup offset, ambiguous compound meter) manifest as a violation of this one invariant.

Synthesis of Gould, Read, and Ross's beaming chapters, all of which reduce to this one geometric invariant regardless of meter family.

This rule can be decided from pitches, durations and voices — no layout required. A validator can check it before anything is drawn.