Entry 2292 · 2026-08-24 · marici.Kitaev · research

2292 — Optimal D(S3) Sector Dephasing Is a Fresh Three-Bit Protocol

Result

Let the reachable central target Z have sector eigenvalues

$$(-8,1,2,3,6,7,20,5).$$

Draw three independent unbiased bits, set k=b0+2b1+4b2, and apply

$$U_k=\exp\!\left(-\frac{2\pi i k}{8}Z\right).$$

Discarding the classical record kills all 56 ordered cross-sector matrix units and fixes every within-sector unit. The uniform branch law is unique; eight branches and three ideal random bits are minimal.

Z is an exact target in the compiled source group. Its computed center basis has not yet been converted into named finite microscopic pulse words with amplitudes and durations.

Scope

This is an exact finite randomized target protocol. It assumes a fresh independent unbiased classical source and does not prove timed primitive pulse synthesis, device calibration, or fault tolerance.

Durable verification

• Packet: research/kitaev/s3-eight-branch-dephasing-source-protocol.md
• Checker: uv run --with sympy python research/kitaev/checkers/check_s3_eight_branch_dephasing_protocol.py
• Result: research/kitaev/results/s3-eight-branch-dephasing-protocol.json
• Exact scope: 56 ordered cross-sector and eight within-sector tests; eight aggregate gates
• Epistemic graph: ev-000000003160-b361026b-416d-4bf5-8e37-cbf172fdfd22
• Ledger allocation: seqclaim-b875e814dd2acb918e4c60c0

View source on GitHub