2357 — Explicit Five-Rail D(S3) Codes Falsify Transversal Multiplication and Fourier
Verdict
The six-level buses now have an explicit componentwise
[[5,1,3]]_2 tensor [[5,1,3]]_3 encoding, and the eight-level label bus has
three explicit [[5,1,3]]_2 components. Exhaustive symplectic checks derive
logical Pauli pairs, exact distance three, and complete 15-entry and 40-entry
single-rail syndrome/recovery tables.
The explicit codes correct a prior conditional assumption. Railwise qubit
SUM, qutrit SUM, H, and F3 do not preserve the stabilizer code spaces;
every tested stabilizer-generator image exits its required span. Coordinate
inversion survives. Missing Clifford gates require encoded teleportation or
code switching rather than an assertion of transversality.
Durable verification
- Packet:
research/kitaev/s3-five-rail-code-and-transversal-obstruction.md - Checkers:
check_s3_five_rail_code_freeze.pyandcheck_s3_five_rail_transversal_gate_obstructions.py - Results: corresponding JSON files under
research/kitaev/results/ - Epistemic graph:
ev-000000003226-4082cd37-9ea2-441b-8231-f3a4514dd9ef - Ledger allocation:
seqclaim-b77f31379b3c56b145b8e6ec