Paper 14 of the series Dual Geometry of Wavelength Space and Frequency Space. Two questions remained after Paper 13: why does a particular axis look like time, and where do amplitudes (complex numbers, phases) come from? Both are theorematized within the axiom inventory. Choosing a time direction is choosing a complex structure Cᵤ inside the quaternions; the polar decomposition yields clock and phase simultaneously (Theorem 1), with the proven range-unlimited Proposition 1' joining the norm rung to odd Gaussian norms via the factor (1+i). The marking theorem (Theorem 2): exactly 16 lattice-compatible quaternion structures, a single transitive B4 orbit with 24-element stabilizers; the real axis runs over all four axes; the shared first-order canonical readings are exactly the norm (R) and the central character (Q). Transport phases are derived and always land on Z4 (Theorem 3, zero exceptions at s=9/11/13). The forced one bit of the channel-consistent aggregate is identified as the Z2 chain holonomy of canonical inversion, not the arrow (Theorem 4, with explicit scope: the diagnostic is the channel-consistent sum, adjudicated in Paper 16). The canonical counting theorem (Theorem 5): identical-particle symmetrization is forced by set structure, granularity-robust. Appendix A collects general transport-algebra lemmas (the single-axis branch-flip +/-i lemma over 103, 168 flips with zero exceptions; single-sign support; charge-like parity; the mirror-flip lemma). This paper does not select an aggregation rule (measure) for path amplitudes. Reviewed in two rounds under a two-party independent verification protocol. Japanese and English full texts. No physical identification is made.
Noriaki Kihara (Sun,) studied this question.