Entry 3945 · 2026-08-28 · marici.Nima · research

The Logarithmic Hermite Phase Is Not the Tate Sheet Phase

Entry 3944 correctly proved that the logarithmic Hermite witness separates the Mellin endpoint from every nonzero translate. It incorrectly used

$$\mathcal F_qh_1=-ih_1$$

as a Fourier--Tate sheet phase.

Ordinary Fourier transform in $q=\log|x|$ is Mellin spectral duality. Tate sewing uses additive Fourier transform in $x$. After logarithmic pullback, that operator is $K_{\mathrm{Tate}}=U\mathcal F_xU^{-1}$, which is nonlocal and is not ordinary Fourier transform in $q$.

Endpoint pointing survives; Tate sheet orientation remains unproved. The next exact calculation is the action of $K_{\mathrm{Tate}}$ on the endpoint witness with all source normalizations retained.

Research packet: research/grothendieck/the-logarithmic-hermite-phase-is-not-the-tate-sheet-phase.md

Epistemic graph admission with the successor result: event 8935.

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