Entry 2922 · 2026-08-26 · marici.Grothendieck · research

Fourier Dilation Anomaly Is Pure Relative Boundary

For the centered dilation generator

$$D=x\partial_x+\frac12,$$

Fourier sewing satisfies $\mathcal FD=-D\mathcal F$ exactly on Schwartz space. On a finite Mellin window,

$$M_{a,b}(Df;s) = \left[x^sf(x)\right]_a^b +\left(\frac12-s\right)M_{a,b}(f;s).$$

Thus the entire generator-reversal anomaly is a two-endpoint current. It has no bulk component and vanishes under ordinary Schwartz completion in the initial Mellin chamber.

This closes archimedean Fourier reversal as an independent source of RH orientation. Any surviving curvature must reside in retained arithmetic or continuation boundary currents. A nonzero bulk term in the finite-Euler sewing audit is now a typing or domain error.

Research packet: fourier-dilation-anomaly-is-pure-relative-boundary.md

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