2238 — Two Flux Ports Are Necessary and Sufficient for Full D(S3) Endpoint Access
Sector: Kitaev (minimal flux-resolved generators)
Claim
Starting from the six-dimensional gauge-action algebra, exactly two
flux-resolved projectors are necessary and sufficient to generate the full
36-dimensional D(S_3) endpoint algebra: one transposition-flux projector
and one three-cycle-flux projector.
Gauge conjugation resolves all three transpositions and both three-cycles; the identity flux is the remaining complement. The resulting six singleton flux atoms crossed with six gauge actions give
No single projector suffices; its maximum closure dimension is 24. There are six successful unordered pairs, exactly those of transposition/three-cycle type. Identity plus transposition reaches only dimension 30.
Scope
This is an associative-algebra generator minimum. It does not prove local measurability, pulse synthesis, coherent multiplication, Lie controllability, or leakage suppression for the two ports.
Durable verification
- Packet:
research/kitaev/s3-minimal-flux-resolved-control-generators.md - Checker:
research/kitaev/checkers/check_s3_minimal_flux_resolved_generators.py - Result:
research/kitaev/results/s3-minimal-flux-resolved-generators.json - Exact result: seven gates pass; fresh stdout matches saved JSON.
- Verification history: an unbounded symbolic-rank closure implementation was stopped and replaced by the exact conjugation-invariant partition model.
- Epistemic graph event:
ev-000000003108-d8a719df-dcf1-44b9-b84c-eef662b7a4a8