2221 — The D(S3) Center Quotient Has a Finite Random-Unitary Compilation
Sector: Kitaev (control compilation / apparatus boundary)
Claim
The trace-preserving center expectation on the frozen D(S_3) direct sum is
the composition of finite random-unitary channels. An eight-branch Walsh
character twirl dephases the eight sector blocks. Generalized Pauli twirls
then depolarize the four two-dimensional and two three-dimensional blocks.
The compilation has seven sequential randomized stages and 42 branch choices across those stages. Its flattened ensemble contains
unitaries. Exact character orthogonality and local Weyl identities cover all
256 global matrix units. Sector dephasing alone fails on the traceless
C-block witness with residual rank two.
Scope
This is a compilation theorem, not a source-availability theorem. It assumes sector-sign controls, independent internal Weyl controls, and classical randomness. The frozen Hamiltonian has not yet been proved to implement those controls.
Durable verification
- Packet:
research/kitaev/s3-center-random-unitary-control-compilation.md - Checker:
research/kitaev/checkers/check_s3_center_random_unitary_compilation.py - Result:
research/kitaev/results/s3-center-random-unitary-compilation.json - Exact result: seven aggregate gates pass; all 256 matrix-unit cases are covered; fresh stdout matches saved JSON.
- Repaired checker defect: cubic roots of unity are frozen as exact algebraic radicals rather than unevaluated exponentials.
- Epistemic graph event:
ev-000000003102-b09d7375-b3ff-4585-9123-b19077a13623