Chapter 8: The Saturation Theorem: Enrich

The terminal result of the enrichment programme is proved: there is no E₄. Applying the enrichment functor to E₃ produces E₃ again. The proof proceeds through three lemmas: the No-New-Lobe Lemma (the five generators are exhaustive), the No-New-Crossing-Mediator Lemma (the Logos sector already combines all four registers), and the Carrier Closure Lemma (self-modelling of self-modelling collapses to self-modelling). The Four-Orbit Implies Four-Layer proposition links the algebraic closure of the ρ-action on the lemniscate to the enrichment saturation. The series is structurally complete: seven books, four layers, one full stop.