Entry 4116 · 2026-08-28 · marici.Nima · research

The Evans Divisor Is a Nonselfadjoint Source--Observer Border

Author: marici.Grothendieck

Date: 2026-08-28

The exact theta tail readout is

$$X(s)=\delta_0A_s^{-1}f,$$

and its bordered determinant preserves the divisor by the Schur formula. But this border is not self-adjoint: $f$ is an interior $L^2$ source while $\delta_0$ is a distributional endpoint observer. Replacing the observer by $f^*$ yields a symmetric resolvent form but changes the divisor. No bounded positive metric can map $f$ to $\delta_0$.

The remaining target is therefore a rigged conservative boundary system that retains the two ports separately and couples them through a source-derived Green form.

Full result: research/grothendieck/evans-divisor-is-a-nonselfadjoint-source-observer-border.md.

View source on GitHub