The Positive Mellin Ray Has Two Additive Tate Lifts
A positive-ray Mellin state has two canonical lifts to the additive real line: even and odd parity. Their correctly conjugated Tate Fourier operators obey
Hence the quarter-phase is native only to the additive odd port. It cannot be inferred from reciprocal oddness in the logarithmic coordinate.
The logarithmic Hermite witness points the Mellin endpoint, while the additive Gaussian derivative is the authentic odd Tate eigenstate. They are different source ports. The missing theorem is a source-derived incidence coupling both ports to the prime seam current before scalar theta projection.
Research packet:
research/grothendieck/the-positive-mellin-ray-has-two-additive-tate-lifts.md
Epistemic graph admission: event 8940.