The Seam Period Requires a Pair-Label Comparison Channel
The period comparing the two endpoint homotopies is quadratic in the labelled source. It contains off-diagonal pair-label interference terms.
The smallest hostile pair has identical individual periods in two cases, but
aggregate periods 2 and 0, depending only on the relative sign. Thus an
additive collection of one-label primitive or square energies cannot determine
the seam period.
The final comparison tower in the 3+2+2+1 architecture must begin with a
polarized pair-label Gram current. The next gate is whether positive Fock
coproduct and Tate sewing derive its off-diagonal entries.
Research packet:
research/grothendieck/the-seam-period-requires-a-pair-label-comparison-channel.md
Exact checker:
research/grothendieck/checkers/check_seam_period_pair_label_necessity.py
The checker passes 5/5 gates.