Chapter 8: ABCD Structure Replaces Quaternions

The 1st Edition of Book II proposed a quaternionic interior structure: three imaginary units i, j, k satisfying i² = j² = k² = ijk = -1 as the algebraic skeleton of the four-dimensional interior. This chapter explains why quaternions are not earned and why the ABCD coordinate structure—with its four canonical rays and split-complex algebra—provides the correct replacement. The quaternion algebra ℍ requires three anticommuting imaginary units; τ provides only j (from polarity) and the identity. Two units, not three. Holomorphy in τ is not derived from a tangent-bundle complex structure J but is primitive: it arises from omega-germ coherence (Book I, Part XII). The four ABCD rays give holomorphic rigidity without importing quaternionic algebra.