Chapter 33: Evolution Operator and Causal Arrow

the relevant chapter proved the Mutual Determination Theorem: five descriptions of holomorphic data are canonically equivalent. This chapter puts the equivalence to work. The ω-germ description (G) provides a natural notion of transport along the primorial tower: given holomorphic data at stage n, the BndLift_n operator (II.D36, the relevant chapter) propagates it to stage n+1. We define the evolution operator E_{n → m} as the composition of successive lifts. The B/C asymmetry from Prime Polarity (I.T05, Book I) breaks the symmetry of this propagation and selects a preferred direction: forward along the tower (increasing stage number, increasing refinement depth). This preferred direction is the causal arrow. The causal arrow is structural—it arises from the asymmetry between the γ-orbit (exponent, B-channel) and the η-orbit (tetration, C-channel), which distinguishes forward propagation from backward propagation. We prove the main result of the chapter: B/C asymmetry implies a time-like direction (II.T28). Elliptic holomorphy (i² = -1) has no such asymmetry and no causal arrow. The chapter connects back to the wave-type causal structure of the relevant chapter and provides the dynamical content that the Mutual Determination Theorem (II.T27) left implicit.