2502 — Serial Wilson Work Reuse Requires Hygiene Barriers
Conditional one-fault theorem
Under the frozen support automaton, a persistent rail fault in a reusable work block adds at most one rail error to every incident encoded data block per gadget. If the work block is reused by overlapping gadgets without hygiene, the same data block can receive two or more errors.
Serial reuse therefore requires a recover/verify-or-replace barrier between every pair of overlapping work-using gadgets. All controlled nonlinear monomials contain the control block, so a controlled target with such gadgets requires exactly barriers:
Without barriers, controlled can accumulate four propagated rail errors in its control block. Logical targets need no inter-gadget barrier because each selected compiler uses at most one work-using gadget.
Boundary
This is a conditional macro-support theorem. It does not construct the work recovery, verification or replacement factory, and it does not certify a microscopic exRec or stochastic threshold. Fresh parallel work blocks remove reuse propagation but retain their own verification obligation.
Verification
- Packet:
research/kitaev/s3-wilson-work-ancilla-hygiene-theorem.md. - Checker:
python research/kitaev/checkers/check_s3_wilson_work_ancilla_hygiene.py. - Result SHA256:
6355837C4C8829D8351BD319CC05B808052642F57DD075A3C08C3E12CCD4E63E. - Graph admission:
ev-000000003449-da6d8cf4-b035-4f42-98c7-5510079819b0. - Ledger allocation:
seqclaim-8708f01a5eff2e6821fb604d.