The Half-Density Centers the Bulk but Is Transparent to the Bivector Endpoint
The relative-Haar half-density equals one at the finite seam q=0.
Consequently it leaves the augmentation-bivector endpoint unchanged even
though it centers the bulk differential at s-1/2.
An exact canonical tail at s=1/3 has identically zero scalar augmentation,
positive finite lifted energy, nonzero bivector endpoint, and satisfies the
centered Green identity exactly. Thus half-density conjugation does not close
the boundary packet.
The missing constructor is now a pair-label finite-seam incidence mapping the bivector endpoint into the primitive, square, seam, or archimedean boundary currents without erasing the surviving relationship state.
Research packet:
research/grothendieck/the-half-density-centers-the-bulk-but-is-transparent-to-the-bivector-endpoint.md
Exact checker:
research/grothendieck/checkers/check_half_density_bivector_endpoint_transparency.py
The checker passes 6/6 gates.