closure-check

name	closure-check
description	Gate whether a working set of atoms/clusters is closed under dependency edges (OPEN lists crossings). Use after organize-work when the border must be a real min-cut. Not organize-work. Not architecture-design.

Closure Check

Input: working set W of atoms/clusters + the coupling/dependency edges among them (including edges that touch atoms outside W).
Output: CLOSED or OPEN. If OPEN: the exact outside atoms that must be admitted (or inside atoms that must be excluded).

Do this

1. Take W and the full edge list as given. Do not re-cluster.
2. Find every edge with one end in W and one end outside W whose weight/meaning is a true dependency (must exist / changes together), not a soft mention.
3. If no such edge exists → CLOSED. Emit CLOSED and stop.
4. If any such edge exists → OPEN. Emit:
   • each crossing edge
   • the outside atom to admit (or the inside atom to drop) to remove the cross
5. Do not enlarge W yourself unless asked. Hand the OPEN set back to organize-work to re-partition.

Do not

• Invent edges.
• Pass a border that still has a hard dependency across it.
• Re-run the whole organize-work ritual inside this skill.