Global Character Descent Selects One Tate Parity Channel
The even and odd archimedean Tate lifts are a genuine local double, but not two global channels of the Riemann zeta source. The trivial idele-class character forces even archimedean parity. Sign at infinity is nontrivial on unless finite character data compensate it.
Therefore the local identity
does not yet constrain zeros of the globally even zeta section. The odd port can return only through a globally compatible character family or an explicit source-derived boundary incidence that compensates its parity.
This is the first real obstacle after deriving the native Tate Hankel operator: local parity and global character descent are different rungs.
Research packet:
research/grothendieck/global-character-descent-selects-one-tate-parity-channel.md
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