2523 — Lockstep Controller Detection Needs Two Copies and Correction Needs Three
Exact minimal repair
Assume a classical lockstep command is checked before actuator fanout and at most one independent controller replica flips. One copy cannot distinguish a fault from the opposite valid command. Two copies with equality comparison detect every one-replica flip. Three copies with majority voting correct every one-replica flip.
The finite checker exhausts both commands, four two-copy detection cases, and six three-copy correction cases.
Boundary
A common-mode flip maps one unanimous codeword to the other and remains invisible. Replica independence is an assumption requiring separate physical roots. Controller redundancy neither repairs quantum actuator faults nor prices or constructs the code-switch interface. The theorem does not apply if the selector is coherent quantum data rather than a classical pre-actuation command.
Durable verification
- Packet:
research/kitaev/s3-lockstep-controller-redundancy.md. - Checker:
uv run python research/kitaev/checkers/check_s3_lockstep_controller_redundancy.py. - Result:
research/kitaev/results/s3-lockstep-controller-redundancy.json. - Result SHA256:
A6C9B4E66D02778D0CF32323708610FEDCB7989F303292E8437CC108C15DB5A4. - Graph admission:
ev-000000003496-4b33cc58-4c35-4e32-908d-7ae0ed731278. - Ledger allocation:
seqclaim-e439632c643f0e1f09235d93.