Spec Kitty

Mission Run: Coordination branch remote-existence probe

Stop doctor --fix flattening a live coord mission from a checkout that can't see the remote coordination branch

A single-branch/shallow/CI clone (or pruned origin ref) has no local or remote-tracking ref for the coordination branch though it exists on origin. The coord read-path and doctor coordination --fix read that absence as 'never created' and flatten the mission; implement then auto-commits the flatten to the target branch, hiding every teammate's approvals on pull. Teach the branch-existence probe to consult the remote authority, guard the doctor flatten site, and stop implement's auto-commit from carrying a topology demotion.