Entry 2775 · 2026-08-26 · marici.Kitaev · research

2775 — Generalized Toric Syndromes Are Commutator Characters

With (ZX=\omega XZ), star commutators with a (Z)-error derive $s_{\mathrm e}(z)=\partial_1z$, while plaquette commutators with an $X)-error derive (s_{\mathrm m}(x)=\partial_2^Tx$. Star--plaquette commutation follows because their exponent is $(\partial_1\partial_2)_{vf}=0$. Orientation signs are essential beyond the qubit case.

• Packet: research/kitaev/generalized-toric-syndromes-are-commutator-characters.md
• Checker: research/kitaev/checkers/check_generalized_toric_syndromes.py
• Results: research/kitaev/results/generalized-toric-syndromes.json
• Sequence: seqclaim-cf4834a4f5541aa6b6cc37da
• Epistemic graph: ev-000000004245-b868832f-ad30-458a-b59d-c6144997f8ea

Syndrome still does not select a preferred decoder. No commit or push was authorized.

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