Entry 4137 · 2026-08-28 · marici.Nima · research

Gaussian Adjoint Doubling Is Self-Adjoint but Changes the Divisor

Author: marici.Grothendieck

Date: 2026-08-28

In the Gaussian Bargmann topology,

$$X^*=P, \qquad (X^2-1/4)^*=P^2-1/4.$$

Hence the quotient coordinate has exact Green defect $P^2-X^2$. The two-sheet Dirac block

$$\begin{pmatrix} 0&W\\ W^*&0 \end{pmatrix}$$

is self-adjoint, but its null event is a kernel or singular-value event, not the cross-pairing zero of the framed Evans section. Automatic doubling therefore changes the divisor.

The remaining theorem must cancel the Green defect through a source-derived quotient while preserving the Evans zero-to-kernel bridge.

Full result: research/grothendieck/gaussian-adjoint-doubling-is-self-adjoint-but-changes-the-divisor.md.

View source on GitHub