Wilson Effects Do Not Determine Instruments, and Non-Abelian Braiding Is Matrix-Valued
Sector: Kitaev (measurement instruments / perturbations / quantum doubles)
Artifacts: research/kitaev/toric-source-instrument-and-capability-fiber.md,
research/kitaev/wilson-constructor-single-fault-audit.md,
research/kitaev/local-perturbation-logical-order-threshold.md,
research/kitaev/s3-quantum-double-ribbon-typing.md
Instrument theorem at finite cutoff
A controlled logical-Wilson pointer dilation on the four-dimensional toric
ground space derives Kraus maps K_+=Pi_+ and K_-=Pi_-; the QND repeat
probability is one. The alternative maps X_1 Pi_b have the same effects
but flip the logical successor, giving repeat-plus probability zero. Thus
an effect-valued readout does not determine a physical instrument.
Fine edge measurement followed by parity coarsening also has the same parity
effect but kills exactly L star expectations on protected inputs, whereas
global Wilson measurement preserves all of them. Classical coarsening does
not undo quantum backaction. Across the group sectors, this yields a type
census rather than a morphism: toric and bounded double-slit constructions
are source-derived QND instruments, one-mode UDW is source-derived and
absorptive, scattering/flavor Lueder maps are formal completions, radiative
memory lacks an apparatus dilation, and cosmology lacks an outcome algebra.
Fault and perturbation boundaries
For a mobile CNOT string, a pointer Z fault after gate k propagates to a
suffix of weight L-k. Every nonzero suffix has two endpoints and weight at
most L-1, hence is detectable and nonlogical; pointer X flips only the
record and Y combines the two effects. This does not include pointer
preparation, verification, two-qubit gate faults, or repeated rounds.
For arbitrary sums of weight-one edge Paulis, every perturbative monomial of
order r<L projects to zero or scalar stabilizer action on the code. Logical
paths first become combinatorially possible at order L, with 2L minimum
representatives in each CSS channel. A bare marked Wilson loop nevertheless
anticommutes with L terms of a uniform conjugate field, so the bare port is
not conserved. Formal order is not a convergence or spectral-flow theorem.
Non-Abelian frontier
The exact D(S_3) census has conjugacy-class sizes 1,3,2, centralizer
orders 6,2,3, eight anyon dimensions 1,1,2,3,3,2,2,2, and squared total
quantum dimension 36. Conjugation by (01) sends flux (12) to (02)
and permutes the transposition basis as [0,2,1]. Non-Abelian braiding is
therefore a matrix action, not a scalar mod-two intersection phase.
Carrier support must refine from unoriented chains to oriented ribbons with endpoint/base framing. The quantum coefficient lens must supply the Drinfeld-double representation, fusion, and braid data. A braided fusion category is not yet claimed: locally clockwise/counterclockwise ribbon operators, ribbon multiplication, fusion coefficients, associators, and pentagon/hexagon coherence remain the theorem-changing typing boundary.
Verification
Fresh exact runs exit zero: toric instrument 6/6, constructor faults
6/6, perturbation threshold 5/5, and D(S_3) ribbon typing 6/6.
Results are saved under research/kitaev/results/. The consolidated report
was admitted to Nima through the epistemic graph. No thermodynamic,
hardware-threshold, perturbative-convergence, or cross-sector naturality
claim is made.