Chapter 30: Split-Complex Codomain with Calibration

Parts I–V built the infrastructure of Book II without making the split-complex codomain H_τ load-bearing. The bipolar scalars (I.D20, Book I) were present from the prologue, but they carried no numerical content: e_± = (1 ± j)/2 were algebraic idempotents without concrete geometric meaning. Part V changed this. π calibrates angular periods (II.T22, the relevant chapter), e calibrates radial growth (II.T23, the relevant chapter), j replaces i as the bipolar unit (II.T24, the relevant chapter), and ι_τ = 2/(π + e) couples the two measurement systems (II.T25, the relevant chapter). This chapter restates the split-complex codomain with these four constants installed. The result is H_τ^cal: the calibrated split-complex codomain. The idempotents e_± acquire geometric meaning as projections onto angular–growth sectors, and the ω-germ transformers become valued in a codomain that carries numerical content. Part VI builds on this calibrated codomain; every subsequent construction in Chapters – uses the constants π, e, j, ι_τ through the lens of H_τ^cal.