2322 — The Direct D(S3) Primitive Center Contains Only the Identity Direction
Verdict
The 15 declared Hermitian controls have matrix-span rank nine. Solving the
exact block-scalarity equations shows that their direct intersection with the
eight-sector center has signature rank one: only the common identity
direction. The optimal integer-lift generator Z is not a simultaneous
primitive Hamiltonian even though it belongs to the rank-six Lie-accessible
center.
Scope
This falsifies a one-pulse linear-combination shortcut. It does not deny the abstract existence of switched synthesis under a strong continuous-control contract, but Lie rank supplies no effective timed word.
Durable verification
- Packet:
research/kitaev/s3-direct-center-versus-switched-synthesis.md - Checker:
uv run --with sympy python research/kitaev/checkers/check_s3_direct_central_hamiltonian_span.py - Result:
research/kitaev/results/s3-direct-central-hamiltonian-span.json - Ledger allocation:
seqclaim-b919140f917b21e2eddb5283