The phrase "a unified conception of" is correct and usable in written English.
It can be used when discussing a cohesive or comprehensive understanding of a particular idea, concept, or phenomenon.
Example: "The researchers aimed to develop a unified conception of social behavior that incorporates various psychological theories."
Alternatives: "a coherent understanding of" or "a consolidated view of".
Molina in his Concordia aimed at a unified conception of divine justice and mercy, foreknowledge and divine guidance, predestination and condemnation, and grace and human freedom.
Such a unified conception of empathy is further supported by the above mentioned neuroscientific research on mirror neurons.
For the Mohists, then, the purpose of government is to achieve a stable social order by promulgating a unified conception of morality.
Whether he had a unified conception of what he was up to in all his intellectual efforts, and if so what this conception might be, has been a continuing source of controversy among Newton scholars.
He did not often spell out the precise chain of argument leading from evidence for survival to a unified conception of practical reason, but the general Theistic idea of a "friendly Universe" enjoying a utilitarian moral government was obviously behind his efforts.
Initially, the existence of these different pharmacological systems underlying hallucinations appears incompatible with a unified conception hallucination.
The usual way to approach the "Ring" is via the more or less unified conception of a single team of interpreters.
The strings could be melting, and the brass swoops were powerful, but not as thrilling as they might have been in a more unified conception.
A unified system-of-record (SOR) is the starting point for a unified system-of-engagement (SOE).
He builds on these views, clarifies and renders consistent the ideas of embodied, embedded, enacted, and extended mind, and develops a unified philosophical treatment of the novel conception of the mind that underlies the new science of the mind.
A third worry, to contemporary eyes probably the most serious, is that the Mohists' notion of a unified morality and their conception of social order (zhi) are disturbingly totalitarian.
