I've developed this concept in numerous books and articles. A search for such a mandate proves fruitless. The Bible never even hints that this is to be the responsibility of the church between Christ's first and second comings. The Biblical Basis for Modern Science. Procreation, animal husbandry, and culture are in mind, for culture is one of the earth's potentialities.
Culture includes art, music, literature, technology, and the sciences.
We should not expect to find such a mandate in a pre-fall command. The case laws of Exodus, the wisdom literature of Proverbs, and the fuller revelation of the New Testament are God's instructions for dominion. In a word, dominion is the faithful and righteous application of God's Word to every area of life. There's certainly nothing to disagree with here. I don't think one will find a Reconstructionist who would advocate anything different.