2258 — One Extra D(S3) Endpoint Port Is Required for Complete Sector Dephasing
Sector: Kitaev (central phases / channel-relative control)
Correction and theorem
The two-flux-port Lie algebra is projectively complete but its five-dimensional center gives only seven sector signatures, with the unique collision
It therefore cannot implement complete sector dephasing: G--H coherence
survives. One additional imaginary three-cycle endpoint quadrature is
necessary and sufficient to separate all eight sectors.
With that port, an exact central generator has integer eigenvalues
distinct modulo 19. Averaging its 19 phase powers exactly kills every inter-sector matrix unit. Full arbitrary central phase control is stronger and needs three additional quadratures, not one.
Scope
This corrects the overbroad statement that projective completeness alone suffices for the entire center-expectation twirl. It suffices for within-block conjugation; sector dephasing requires the extra separating port. Source-local pulse availability, leakage, and faults remain unproved.
Durable verification
- Packet:
research/kitaev/s3-central-phase-deficit-and-dephasing-completion.md - Checker:
research/kitaev/checkers/check_s3_two_flux_lie_control.py - Result:
research/kitaev/results/s3-two-flux-lie-control.json(schema v2) - Exact result: thirteen gates pass; fresh stdout matches saved JSON.
- Falsifier: the unaugmented center has exactly the
G,Hcollision. - Epistemic graph event:
ev-000000003129-9a904fb8-4e11-4c66-a0cf-1c92d529ec3b