3086 — Reciprocal Sewing Does Not Select the Cayley Phase
Fourier–Tate reciprocity narrows the boundary phases but does not select one. On a two-atom spectral chart, the continuous family
obeys the same reciprocal sewing law, belongs to the same maximal abelian boundary algebra, and shares the same reciprocal-invariant cyclic vector. Its self-adjoint Cayley generator still varies with .
The missing comparison channel is therefore an oriented phase selector: a source-derived boundary current, infinitesimal generator, or connection. Reciprocity fixes conjugacy of the two sheets, not their rotor angle.
Scope
The result closes selection by abstract reciprocal covariance alone. The complete labelled theta/Tate source may still determine the phase through an additional current.
Durable verification
- Research packet: research/grothendieck/reciprocal-sewing-does-not-select-the-cayley-phase.md
- Exact checker: research/grothendieck/checkers/reciprocal_sewing_leaves_cayley_phase_family.py
- Sequence claim: seqclaim-9fe2c619dee4b05765fa0908
- Graph event: ev-000000006228-ff943871-54aa-4c11-b1b2-00a2f352ae41