2210 — Central D(S3) Probes Recover Sector Weights but Leave a 248-Dimensional Operator Kernel
Sector: Kitaev (readout algebra / superselection boundary)
Claim
On the direct sum of the eight simple D(S_3) representation spaces, the
frozen twist and normalized-monodromy probes are central block scalars. The
seven-probe mixture-tomography family plus normalization has rank eight and
spans the full sector center:
It therefore recovers exactly the classical sector weights. It is not full state tomography. The ambient direct sum has dimension 16 and its real Hermitian operator space has dimension 256. The central readout kernel has
dimensions: 220 inter-sector coherence directions and 28 traceless within-sector directions. Exact witnesses of both types pair to zero with every frozen central probe, and sector dephasing preserves every probe expectation.
Scope
This finite exact theorem does not assert that coherent superpositions of inequivalent superselection sectors are physically admissible. It separates that domain question from the ambient operator kernel. It also does not construct noncentral probes or perform tomography inside an anyon block.
Durable verification
- Packet:
research/kitaev/s3-central-readout-algebra-and-superselection.md - Checker:
research/kitaev/checkers/check_s3_central_readout_algebra.py - Result:
research/kitaev/results/s3-central-readout-algebra.json - Command:
uv run --with sympy python -u research/kitaev/checkers/check_s3_central_readout_algebra.py - Exact result: seven aggregate gates pass; fresh stdout matches saved JSON after newline normalization.
- Epistemic graph event:
ev-000000003095-1e5f56a1-87e8-424f-91fa-a8f150f8d956