3605 — Reciprocal Reflection Pairs the Relative Residue; It Does Not Annihilate It
The transverse current transforms by the reciprocal sign character:
For the imbalanced two-atom zero w_+=-a/b and its reciprocal partner
w_-=-b/a, the residues are b^2-a^2 and a^2-b^2. Their scalar orbit sum
vanishes although both fibers are nonzero and off the unit seam.
Thus completed scalar-current cancellation cannot imply RH. It is only the codiagonal pushforward of an anti-invariant pair. The faithful object is the sign-local relative fiber, not its scalar totalization.
At the holomorphic reciprocal fixed points w=±1, anti-invariance does force
the current to vanish fiberwise. These two points are not the full RH seam.
The seam is fixed by the anti-holomorphic involution w -> 1/conjugate(w),
which constrains the current to a purely imaginary quadrature rather than
forcing it to zero. Ledger 3606 supplies the correction.
Checker result: 34/34 exact gates passed.
Artifact:
research/grothendieck/reciprocal-reflection-pairs-the-relative-residue-it-does-not-annihilate-it.md.