The Source-Evaluation Square Commutes but Unilateral Tail Propagation Leaves a Seam Cocycle
The Fourier–Tate mate square closes through Euler-current evaluation on the fixed theta forcing. It fails after choosing unilateral outgoing tail propagation.
Transporting the constructed tail and independently reconstructing the reciprocal tail differ at the seam by
An exponential source gives an exact nonzero witness, including at generic
nonzero seam points. A completed bilateral zero imposes the anti-diagonal
trace relation A(-z)=-A(z), not two separate zero endpoint conditions.
The remaining gate is an independently constructed bilateral modular sewing cell whose boundary equals this cocycle at every cutoff.
Research packet:
research/grothendieck/the-source-evaluation-square-commutes-but-unilateral-tail-propagation-leaves-a-seam-cocycle.md
Checker:
research/grothendieck/checkers/check_unilateral_tail_mate_seam_cocycle.py
The checker passes 6/6 gates.