= Dressed stabilizer under a weak local perturbation
Suppose a <quasi-adiabatic continuation> maps a <stabilizer code> projector $P_0$ to a perturbed low-energy projector $P=UP_0U^\dagger$. Each original <stabilizer generator> $S_i$ has a dressed operator $\widetilde S_i=US_iU^\dagger$. Conjugation preserves mutual commutation and $\widetilde S_iP=P$, so the dressed checks characterize the transported subspace.
They generally have spatial tails rather than finite <Pauli operator> support. They need not commute with the entire perturbed <Hamiltonian operator>; preserving its selected spectral subspace does not make them global conserved quantities. Likewise, a non-Pauli component alone does not destroy <quantum error correction>, since correctable error sets have a linear span. For bare local errors, accuracy instead depends on the spread of the corresponding conjugated errors, the original <quantum code distance> and the <Knill--Laflamme condition>. Bounds on spatial tails can control approximate local correction under the stated gap and locality assumptions.
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