Two Independent Obstructions Forbid Pre-Sewing Collapse of the Reciprocal Sector Packets
A strict pre-sewing identification of the reciprocal sector packets fails for two independent reasons.
First, the two endpoint-normalized inverse-scale homotopies differ by a nonzero seam period. Identifying them erases that period. Second, finite Fourier sewing rotates the distributed augmentation line into the point-supported control line. Identifying those ports erases their operational types.
Therefore the minimal strict architecture under the current source types is
2(3+2+1)+1. The earlier 3+2+2+1 is its lossy compressed shadow. A future
compression would have to preserve the period and port distinction as explicit
residual data and would be an equivalence, not an object identification.
Research packet:
research/grothendieck/two-independent-obstructions-forbid-pre-sewing-collapse-of-the-reciprocal-sector-packets.md
Exact checker:
research/grothendieck/checkers/check_no_presewing_sector_collapse.py
The checker passes 6/6 gates.