The Relative Mapping-Cone Green Lemma Forces the Centered Real Part to Vanish
The direct and reciprocal sector Green identities have opposite spectral and boundary orientations. If the final seam mate identifies their full typed energy, endpoint, and forcing packets, adding the identities gives
For finite strictly positive relationship energy, this forces the centered real part to vanish.
The finite algebraic confinement theorem is complete. Its theta/Tate application now depends precisely on the source-derived full-packet mate, retention of primitive/square/archimedean channels, zero-to-state admissibility, and completion stability.
Research packet:
research/grothendieck/the-relative-mapping-cone-green-lemma-forces-the-centered-real-part-to-vanish.md
Exact checker:
research/grothendieck/checkers/check_relative_mapping_cone_green_lemma.py
The checker passes 5/5 gates.