3094 — Reflection-Even Completion Makes the Fourier Graph Lagrangian
Metaplectic phase rigidity alone does not produce a boundary condition. The full Fourier transform satisfies and is not self-adjoint, so its raw graph is not isotropic for the standard Green form.
On the reflection-even theta sector,
The restricted Fourier graph is therefore maximal isotropic and defines a Lagrangian boundary relation. The odd sector retains the quarter-turn obstruction .
This gives even modular completion a new operator meaning: it converts Fourier transport from a quarter-turn into the self-adjoint involution needed by the boundary Green form.
Scope
The finite theorem is exact. The actual adelic doubled Green form, its typed boundary corrections, closedness, and determinant readout remain to be established.
Durable verification
- Research packet: research/grothendieck/reflection-even-completion-makes-the-fourier-graph-lagrangian.md
- Exact checker: research/grothendieck/checkers/even_fourier_graph_is_lagrangian.py
- Sequence claim: seqclaim-6878f8b6d6959fd743ca3726
- Graph event: ev-000000006257-c4dcc99c-5f21-417e-a781-0a580030f3c1