3894 — Endpoint-Reduced Euler Sections Are the Canonical Hardy Carriers
The raw completed function is not the correct full-half-plane Hardy carrier: its gamma factor has superlinear Stirling growth. The canonical source normalization is instead
The endpoint–zeta pole cancellation makes the apparent singularities removable. These functions preserve exactly the open-sector zeros of the completed section and are of bounded type in their respective half-planes. They extend analytically through every finite seam point and have zero mean type, so no separate singular-inner measure remains.
The anti-diagonal Hardy residual is therefore rigorous on these carriers: its class vanishes exactly when the two open-sector Blaschke divisors are empty. That is an RH equivalence, not yet the source-derived explanation.
Scope
This supplies the correct analytic carrier and closes the singular-inner typing gate. It does not derive vanishing of the Blaschke current or prove RH.
Durable verification
- Research packet:
research/grothendieck/endpoint-reduced-euler-sections-are-the-canonical-hardy-carriers.md. - The divisor comparison is algebraic; bounded type follows from uniform
vertical-strip zeta bounds and convergence in
Re(s) >= 2. - Epistemic graph admission:
ev-000000008520-22adbaeb-22c6-475d-a46c-47e350bd7978. - No build was run, following the operator's standing instruction.