τ-holomorphy as ω-germ transformer

Once boundary atoms exist, the next burden is not to allow arbitrary maps. The construction must earn a class of admissible transformations from the boundary grammar itself. A τ-holomorphic map is therefore defined as a certified ω-germ transformer: normal-form code with type, tail-stability, and tail-independence, without a prior function graph, Cartesian product, or prior external codomain. The diagonal discipline structurally precludes ordinary function-graph constructions; idempotent collapse to elliptic C is impossible. Its components satisfy split-complex Cauchy – Riemann equations and the hyperbolic wave equation, not the elliptic Laplacian, because j^2=+1. This earns analytic structure without importing complex analysis, and it supplies the admissible-map grammar that Book II will use to derive continuity and topology.