WHAT: the D∞ notation — the ⟨parts | Ω⟩ shape every durable teaching, framework, plan, and joke has — plus the three operators over it (FACTOR, ADJOIN, CHRISTEN) and the `dinf` CLI that makes the missing-closure defect machine-catchable. WHEN: when stuck; when a plan feels like unjoined parts; when two frames are fighting; when writing any rule, skill, or explanation that must be understood once rather than re-derived per case; when a loop has no stop condition.