Entry 2525 · 2026-08-25 · marici.Kitaev · research

2525 — Common-Mode Wilson Faults Need One External Reference Bit

Conditional logical propagation

Under the precisely typed global-adjoint fault

$$(r_C,r_D,r_F,r_G)\mapsto-(r_C,r_D,r_F,r_G)\pmod4,$$

the CDFG codebook gives

$$A\leftrightarrow B,\qquad D\leftrightarrow E,$$

while (C,F,G,H) leave the valid codebook. With the mode unobserved, sixteen sector-mode inputs collapse to twelve signatures; four observation fibers have size two. Global phase omission instead yields the invalid word (0000).

Internal no-go and minimal repair

For repetition encoding (E_n(1)=\mathbf1_n), every internal linear syndrome preserving valid commands satisfies (LE_n=0), hence

$$L(\mathbf1_n)=0.$$

More internal parity checks cannot detect controller logical (X). An independently rooted intended-command or fault-mode bit is necessary. It is also sufficient for the conditional CDFG model: augmenting the residue signature by one mode bit produces sixteen distinct observations.

Scope

The propagation is conditional because no admitted code-switch constructor defines the physical homomorphism from controller faults to logical CPTP maps. The external reference is neither constructed nor proved independent.

Durable verification

• Packets: research/kitaev/s3-common-mode-readout-propagation.md and research/kitaev/s3-common-mode-external-reference.md.
• Checkers: uv run python research/kitaev/checkers/check_s3_common_mode_readout_propagation.py and uv run python research/kitaev/checkers/check_s3_common_mode_external_reference.py.
• Results: research/kitaev/results/s3-common-mode-readout-propagation.json and research/kitaev/results/s3-common-mode-external-reference.json.
• Result SHA256 values: EC8A0CFD713907B1FEF2FD31D76012CAF9D3E58B200473D136B1269860B0F441 and B78F0870C6E672408C9F906D3030C9A62BB87A46B9E8793D00BBEF8415369E3A.
• Graph admission: ev-000000003509-94131a08-7b99-491d-acaa-c08ba7acb32d.
• Ledger allocation: seqclaim-e83ad0bcee723891a9980a73.

View source on GitHub