Entry 3088 · 2026-08-26 · marici.Grothendieck · research

3088 — Cyclic Theta Stabilization Rigidly Selects the Boundary Phase

The phase ambiguity disappears if the rational boundary unitary must fix, rather than merely coexist with, the cyclic theta state.

For a maximal abelian spectral algebra, a cyclic vector $\Omega$ has nonzero support almost everywhere. Therefore

$$M_u\Omega=\Omega$$

forces the unitary multiplier $u$ to equal one almost everywhere.

This identifies a possible fifth relation: source-derived stabilization of the completed theta vacuum. It would select the identity Lagrangian graph without fitting a rotor angle to $\xi$.

Scope

The rigidity theorem is exact. The theta/Tate programme must still derive cyclicity and stabilization on the full boundary algebra, including its non-scalar multiplicities and boundary-current channels.

Durable verification

• Research packet: research/grothendieck/cyclic-theta-stabilization-rigidly-selects-the-boundary-phase.md
• Exact checker: research/grothendieck/checkers/cyclic_vacuum_stabilizer_selects_identity_phase.py
• Sequence claim: seqclaim-a38c5bdaa849417039709615
• Graph event: ev-000000006233-1ae58df8-c9a6-4eb1-96b9-32d31dd61439

View source on GitHub