The Resolvent Homotopy Realizes the Third Sector and Its Two Directed Faces
The direct tail, second-order resolvent homotopy, and reciprocal tail form three analytic sectors:
Their two source-local faces are exact:
Endpoint evaluation supplies the shared mate cell. A direct two-sector scalar
comparator depends on the source, whereas these two differential faces are
universal. Thus the outer 3+2+1 skeleton is proved.
The operator's 3(3+2+1)+2+1 proposal is reduced to lifting the complete
primitive, square, connected, seam, and archimedean packet onto the new
homotopy sector and verifying both grade-preserving faces.
Research packet:
research/grothendieck/the-resolvent-homotopy-realizes-the-third-sector-and-its-two-directed-faces.md
Checker:
research/grothendieck/checkers/check_three_sector_resolvent_incidence.py
The checker passes 5/5 gates.