The Doubled Tail Needs Diagonal Control Sewing Before Evans Evaluation
The constructible-rank obstruction has been applied to the source-derived tail ODE
After imposing decay at infinity, one sheet has a rank-one solution module:
Two unsown sheets therefore have independent amplitudes (c_+,c_-) and a
rank-two pre-Evans module. Every scalar Evans row on that module has a nonzero
kernel. The reciprocal completion must identify the two controls as one source
preparation, minimally through c_+=c_-. This diagonal pullback reduces the
module to rank one before scalar evaluation.
The repair is necessary but not RH-bearing by itself. On the sewn line the
Evans coefficient is F_+(s)+F_-(s), namely the completed scalar transform
whose nonvanishing is at issue. Control sewing correctly types the spectral
problem; it cannot prove its answer.
This gives the multi-tower coherence cell an exact role: it identifies the two transport towers as actions on one input preparation. Without it, scalar zero exclusion is algebraically impossible. With it, the remaining work is an independently derived off-seam constraint on the rank-one Evans coefficient.
Research packet:
research/grothendieck/the-doubled-tail-needs-diagonal-control-sewing-before-evans-evaluation.md
Exact checker:
research/grothendieck/checkers/check_doubled_tail_control_sewing_rank.py
The checker passes 8/8 exact tests.