2287 — The Compiled D(S3) Source Lie Algebra Has Dimension Thirty-Four
Result
Composing the exact microscopic compilers for B^t, B^c, and
with the endpoint Lie certificate gives
The 28-dimensional derived algebra is the complete direct sum of the within-block special-unitary algebras. The separator raises accessible central rank from five to six and distinguishes all eight sectors. Two independent central phases remain absent, so full 36-dimensional block-unitary control is still false.
The 34-dimensional algebra is sufficient for the algebraic ingredients of within-block twirling and eight-sector dephasing. Channel sufficiency does not imply arbitrary coherent block control.
Scope
This is an exact finite composition theorem relative to the compiler gate contracts. It does not establish hardware availability, calibrated pulse execution, random-branch access, leakage bounds, or fault tolerance.
Durable verification
- Packet:
research/kitaev/s3-source-generated-lie-closure.md - Checker:
python research/kitaev/checkers/check_s3_source_generated_lie_closure.py - Result:
research/kitaev/results/s3-source-generated-lie-closure.json - Input result SHA-256 digests are frozen in the result packet
- Eight aggregate gates pass
- Epistemic graph:
ev-000000003155-af3f2420-45cc-463e-8240-058e000290a2 - Ledger allocation:
seqclaim-74f76a81935a355049fe5a17