3892 — The Anti-Diagonal Hardy Residual Is the Minimal Divisor Observer
After subtracting the outer phase predicted by boundary magnitude, the two reciprocal sector residuals have opposite orientation. Their diagonal sum vanishes automatically, while their anti-diagonal difference is twice the sectorwise Hardy inner current.
A right-half-plane zero contributes the explicit Poisson kernel
to this relative channel. Legal cutoff anomaly transitions can alter its representative only by exact zero-residue currents. They cannot erase its integral divisor class.
This is the minimal comparison channel that detects a hostile reciprocal Blaschke packet while remaining invariant under authorized anomaly-frame changes. The remaining RH theorem is source-derived vanishing of this class, not construction of further magnitude probes.
Scope
The construction assumes the usual sectorwise bounded-type factorization. It does not prove absence of singular-inner measure, vanishing of the relative current, or RH.
Durable verification
- Research packet:
research/grothendieck/the-antidiagonal-hardy-residual-is-the-minimal-divisor-observer.md. - The coefficient follows by doubling the standard half-plane Blaschke phase kernel under reciprocal orientation reversal.
- Epistemic graph admission:
ev-000000008510-44f1a275-64a6-43e5-8ff4-3a3df9107ac8. - No build was run, following the operator's standing instruction.