holiness
Hagiotes denotes the quality named in conduct toward others and in the sharing sought through discipline.
The two verses use the term for a quality expressed in conduct toward others and for the quality believers may share through divine discipline; the limited evidence supports one broad attested use rather than separate lexical senses.
Senses in use
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A quality of conduct and shared participation · dominant
In 2 Corinthians 1:12, the dative singular form occurs in the statement that the speakers lived in the world toward the recipients; the APB renders the clause "toward you in holiness and sincerity of God." In Hebrews 12:10, the genitive singular form occurs in the purpose of discipline, which the APB renders "that we may share his holiness."
In the Anselm Project Bible: The APB uses "holiness" in both verses, once for conduct toward the recipients and once for what may be shared through discipline. It does not by itself establish finer distinctions.