The Cappadocian Fathers established that any asymmetric causal dependence among the Three entails an inequality of essence, not merely relation, which is incompatible with homoousios.

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Asymmetric causal dependence(metaphysics/causality): A situation where one thing depends on another to exist or function, but that other thing doesn't depend back on the first one in the same way—like how a painting depends on a painter, but the painter doesn't depend on the painting.
Cappadocian Fathers(historical/religious reference): A group of three Christian theologians from the 4th century (Basil, Gregory of Nyssa, and Gregory of Nazianzus) who developed influential ideas about how God can be three persons (Father, Son, Holy Spirit) while still being one God.
Inequality of essence(metaphysics): A difference in the most basic nature or fundamental being of things, meaning they are different kinds of things at the deepest level.
essence(Medieval realist metaphysics): The defining nature of a species, held by some to be distinct from and capable of surviving the destruction of all individual members of that species

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