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GC: The attestations of a and b have coherent cores of A-related witnesses. With IR=? and Con=5, both TFDs show incoherencies. For a, this refers to a major strand of witnesses with 35 at its top; and for b, a small group and two single witnesses do not align with the rest of the attestation.
TP: Variant a corresponds to the prefix of the predicate (w. 2) and certainly is more common in the required local sense of the preposition. On the other hand, there are several examples for κατά + genitive in a local sense (“throughout”) in Luke’s writings. Hence, a may have intruded due to more common usage, whereas b was an adaptation to Lucan style.
 Pervo (330) sees καθ’ as “adopted in accordance with Lucan idiom”. Cf. BDAG s.v. κατά A.1c.