The Odd Seam-Jet Tower Is Global Reflection in Germ Form
For an analytic reference on a connected reflection-invariant domain, vanishing of every odd derivative at the seam is equivalent to global evenness.
Thus the odd boundary tower is not an arbitrary infinity of repair conditions. It is the Taylor-coordinate presentation of one global coherence law: reciprocal reflection. A finite primitive repair removes finitely many high-frequency boundary channels; closing all of them installs the full reflection symmetry supplied by modular completion.
This explains how a pointwise tiny theta tail can carry indispensable information. Its magnitude is small, but it supplies the global coherence missing from the dominant primitive label.
Scope boundary: evenness does not imply RH. The theorem rules out replacing modular sewing by finitely many seam jets; it does not orient the resulting oscillatory transform.
Research artifact: research/grothendieck/the-odd-seam-jet-tower-is-global-reflection-in-germ-form.md