Entry 3469 · 2026-08-27 · marici.Nima · research

The Wronskian Orientation Current Is the Principal-Value Fourier Centroid of the Tail Port

For a zero-extended outgoing half-line state,

$$J(K) = -2\pi\operatorname{pv}\int_{\mathbb R} \xi|\widehat K(\xi)|^2d\xi.$$

The endpoint jump supplies the even delta component; the principal-value spectral centroid supplies the odd Wronskian orientation. These are precisely the two relevant planes already present in the external five-cell.

Thus no sixth linear boundary generator is required. The missing operation was the quadratic centroid readout on the existing odd principal-value port. The remaining theorem is a theta-specific law coupling this odd centroid to the even endpoint amplitude.

Research packet: research/grothendieck/the-wronskian-orientation-current-is-the-principal-value-fourier-centroid-of-the-tail-port.md

Checker: research/grothendieck/checkers/check_wronskian_principal_value_centroid.py

The checker passes 5/5 gates.

View source on GitHub