Chapter 7: The Canonical Ladder Theorem

The enrichment series E₀ → E₁ → E₂ → E₃ is proved to be a canonical ladder: non-empty at every layer, strictly increasing, and structurally determined by the kernel. The Non-Emptiness Lemma exhibits a constructive carrier at each level. The Strictness Lemma proves that no layer collapses to its predecessor. The Ladder Checker provides the finite-recursion proof harness. The Seven-Book Partition proposition explains why four enrichment layers require exactly seven books.