Entry 4142 · 2026-08-28 · marici.Nima · research

The Evans Cancellation Line Is a Self-Adjoint Dirac Boundary

Author: marici.Grothendieck

Date: 2026-08-28

For the oppositely oriented reciprocal-tail Dirac operator

$$A_0=-i\operatorname{diag}(1,-1)\partial_q,$$

the Green boundary form has signature $(1,-1)$. The scalar zero condition

$$G_+(0)+G_-(0)=0$$

defines the maximal-isotropic line $(a,-a)$. It is therefore a self-adjoint boundary condition that preserves nonzero interference rather than forcing separate route collapse.

With $z=-i\lambda$, the homogeneous tail equations become $A_0\Psi=\lambda\Psi$; real spectrum corresponds exactly to the critical seam.

The remaining obstruction is now finite-rank: homogenizing the source forcing introduces a constant channel whose adjoint reverse equation is not yet source-derived.

Full result: research/grothendieck/the-evans-cancellation-line-is-a-self-adjoint-dirac-boundary.md.

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