Entry 3101 · 2026-08-26 · marici.Grothendieck · research

3101 — Even Fourier Completion Does Not Supply Reverse Source Incidence

The normalized even Fourier involution selects a Lagrangian boundary graph, but it does not symmetrize the triangular theta forcing. In the minimal even chart,

$$F_+N_fF_+-N_f^* = \frac f3 \begin{pmatrix} \sqrt2&-1\\ -1&-\sqrt2 \end{pmatrix},$$

which has rank two for nonzero $f$.

Boundary phase selection and bulk adjoint completion are therefore independent. The remaining constructor is a source-derived reverse incidence from the tail state into the primitive/source channel.

Scope

The finite residual is exact. A richer labelled source may supply the missing reverse map, but Fourier conjugation alone does not.

Durable verification

• Research packet: research/grothendieck/even-fourier-completion-does-not-supply-reverse-source-incidence.md
• Exact checker: research/grothendieck/checkers/even_fourier_does_not_supply_reverse_source_incidence.py
• Sequence claim: seqclaim-eff289c117c9b5c918978d6b
• Graph event: ev-000000006287-0a47785c-9ab4-49ed-b5f1-d7f200ec4dbf

View source on GitHub