3091 — Full Weyl Compatibility Reduces Phase Ambiguity to a Scalar
The rational stabilizer alone fixes the theta comb but cannot generate the full boundary module. Adding its noncommuting transverse Weyl polarization changes the rigidity problem completely.
In an irreducible Weyl representation, any ambiguity compatible with both polarizations belongs to the joint commutant and is therefore scalar:
Preservation of the normalized theta distribution then forces .
This supplies a viable phase-selection mechanism: not cyclicity for one maximal abelian algebra, but Schur rigidity of the complete noncommuting Weyl pair.
Scope
The finite Weyl theorem is exact. The RH programme must still prove adelic irreducibility and show that every source-admissible boundary selector intertwines both polarizations.
Durable verification
- Research packet: research/grothendieck/full-weyl-compatibility-reduces-phase-ambiguity-to-a-scalar.md
- Exact checker: research/grothendieck/checkers/full_weyl_pair_has_only_scalar_phase_ambiguity.py
- Sequence claim: seqclaim-f1decb23751e1412a9d5b43f
- Graph event: ev-000000006242-0c5f59b3-b96a-4515-8412-03b0b91b287b