Reference Partial Trace Makes D(S3) Monodromy Independent of the Target State
Sector: Kitaev (universal R / non-Abelian instruments) Artifacts: research/kitaev/s3-universal-R-target-state-independence.md, its checker, and results/s3-universal-R-partial-trace.json.
Claim
Construct all eight induced irreducible representations of D(S3), then evaluate the universal-R monodromy M_ab = R_21 R for every ordered pair of simple sectors. All 64 monodromy matrices are exactly unitary.
For every pair,
Tr_b(M_ab)/d_b = [6 S_ab/(d_a d_b)] I_a.
Consequently, for every target density matrix rho_a,
Tr[(rho_a tensor I_b/d_b) M_ab] = 6 S_ab/(d_a d_b).
The normalized-monodromy readout does not require maximally mixing or otherwise calibrating the unknown target internal state. Mixing only the prepared reference suffices. This is verified microscopically, not inferred only from the modular table.
The checker builds the conjugacy-class transporters and centralizer representations, verifies the S3 gauge group law, tests unitarity of all 64 monodromies, and compares all 64 reference partial traces with the independent modular matrix. Seven aggregate gates pass and fresh stdout matches the saved JSON.
Boundary
The target must lie in one simple superselection sector. Coherent sector superpositions, leakage, and unresolved multi-anyon fusion spaces need a larger instrument. Reference mixing, controlled monodromy, ancilla readout, and local fault-tolerant synthesis remain apparatus requirements.