2290 — The D(S3) Within-Block Twirl Is Explicit but Timed Primitive Words Remain Open
Result
The six nontrivial blocks (C,D,E,F,G,H) admit the explicit sequential Weyl
twirl with branch counts
Uniform independent draws exactly depolarize all 34 nontrivial-block matrix units. There are 34 branch choices across the stages, 20,736 unitaries in the flattened ensemble, and ideal entropy
Every branch target is projectively reachable because the compiled source Lie algebra contains every block's special-unitary algebra. Global phases are irrelevant to the conjugation channel.
The Lie-rank certificate does not itself provide finite primitive pulse words, amplitudes, durations, or geometric schedules. The channel-target protocol is explicit; the timed microscopic pulse protocol remains open.
Scope
This entry proves a finite randomized target protocol and exact group-level reachability. It does not assert a constructive optimal-control solution or device execution.
Durable verification
- Packet:
research/kitaev/s3-within-block-twirl-protocol-and-pulse-gap.md - Checker:
uv run --with sympy python research/kitaev/checkers/check_s3_within_block_twirl_protocol.py - Result:
research/kitaev/results/s3-within-block-twirl-protocol.json - Exact saved-result reproduction: true; eight aggregate gates
- Epistemic graph:
ev-000000003158-63b6c83a-fc71-4ddc-963a-d25b6799c4c5 - Ledger allocation:
seqclaim-be8373651c61c0452b75933c