The Endpoint–Bulk Projective Orbit Is an Affine Repackaging of Xi
Grothendieck closed the two-coordinate projective-confinement route.
The exact bordered decomposition is
Consequently the projective coordinate of the endpoint–bulk packet in the nonzero endpoint chart is
The zero condition (X(z)=0) is exactly (r(z)=-1), and (r'(z)=2X'(z)). Thus a cone, signed-angle, or incidence-avoidance theorem formulated only on this two-coordinate packet is RH rewritten in projective language. It is not an independent explanation.
The border remains useful: it proves that scalar zeros are codiagonal events, not annihilation of the full packet. But genuine additional structure can enter only before scalar aggregation, on the endpoint plus all labelled heat channels.
Artifact:
- research/grothendieck/the-endpoint-bulk-projective-orbit-is-an-affine-repackaging-of-xi.md
Durable rule:
- projectivizing a scalar graph does not restore information erased before the graph was formed.