The derivation produces closure at three scales. Each scale recapitulates the same structural logic — act, condition, structure; underdetermination; forced resolution — but operates on a different domain.
Unit closure (step 3): Sustaining mediates between Relating and Relation, producing Self-coherence and Closure. The unit maintains itself through its own activity. Mathematically: a closure operator on with fixed points forming a poset.
Field closure (step 7): Inter-unit relating and Field-integrating produce Mutual form and Field form. Multiple units cohere locally and globally. Mathematically: two commuting nuclei on a complete Heyting algebra, with orthogonal factorization.
Grand closure (step 18): Profiles reconstruct the full tower; the tower produces Profiles. The derivation is at its fixed point. Mathematically: the self-containment theorem .
The three scales are not imposed as an organizational scheme. They emerge because the same structural demand — what holds this together? — recurs at each level, and its resolution at each level exposes the next. This is Recursive domain unfolding: each closure reveals the next domain that must be formalized.
The recurring pattern at all three scales is Residuation — the adjunction between complementary operations that governs the interplay at each level.
See Relational Closure Operators for the mathematical treatment.