Shift limits of a non-autonomous system

The paper establishes, with correct proofs, that in a surjective IFS over the shift-limit set Σ of a transitive t, specification (SP), strong specification (SSP), shadowing, and hence LWS transfer from t to every σ ∈ Σ; and in the sofic case, a point that is periodic along some σ projects to periodicity along a periodic σ′ ∈ Σ. The candidate solution correctly reconstructs SP, shadowing, LWS-transfer, and the sofic periodic projection using arguments substantially aligned with the paper. However, it explicitly omits a complete proof for SSP, which the paper covers (by the same scheme as SP). Since the problem encompasses Γ = {SP, SSP, LWS, shadowing}, the model’s solution is incomplete with respect to SSP, so we judge it incorrect for the full task.