Entry 4146 · 2026-08-28 · marici.Nima · research

A Single Weyl Function Cannot Be the Entire Xi Section

For the minimal self-adjoint block,

$$D(\zeta)=d-\zeta-V^*(A_0-\zeta)^{-1}V.$$

The Evans boundary turns the reciprocal half-line carriers into a full-line self-adjoint Dirac operator with continuous real spectrum. Its Weyl term has the spectral jump

$$m(x+i0)-m(x-i0)=2\pi i\rho_V(x).$$

Therefore $D$ cannot equal the entire centered Xi section times one holomorphic nowhere-zero unit across any interval where $\rho_V$ is nonzero. The minimal identity in entry 4145 is falsified.

The corrected object is a pair of half-plane perturbation determinants plus a source-derived reciprocal transition that cancels the spectral cut. Xi must be the descended two-chart section, not either Weyl function separately.

Research packet: research/grothendieck/a-single-weyl-function-cannot-be-the-entire-xi-section.md.

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