Chapter 12: Split-Complex Structure Not Yet Load-Bearing
Book I earned the split-complex algebra H_τ, the bipolar idempotents e_± = (1 ± j)/2, the spectral characters χ_±, and the master constant ιτ = 2/(π + e). All of these are available. None of them have been used. This chapter pauses to observe that Parts I and II of Book II operate on a purely structural-algebraic and combinatorial-topological foundation: ABCD coordinates, CRT reduction maps, cylinders, the ultrametric, and omega-germ naturality. The split-complex codomain H_τ has not entered the argument. This is not an omission—it is the inverted dependency chain in action. The split-complex structure becomes load-bearing in Part VI, where boundary-to-interior lifting requires the bipolar channel decomposition. Before that, the topological skeleton suffices.