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"conceptual edifice" is correct and is usable in written English.
You can use it to describe an abstract idea or an abstract structure of something. For example: "She built a conceptual edifice of her idea, laying out its foundation and structuring its components."
Exact(2)
One motivation for axiomatizing a theory, not the one for the case now under discussion, is to express the theory in a completely rigorous form in order to standardize the expression of the theory as a mature conceptual edifice.
To erect such a conceptual edifice is to explain the development of the field by assuming a major presupposition, namely that there is a definable self that might be defended.
Similar(58)
Scruton is brilliant at the patient demolition, in sorrowful yet witty tones, of wobbly conceptual edifices.
Might Woodger's and Williams' respective axiomatic systems simply lack the power and conceptual resources to axiomatically reconstruct a mathematical edifice actually cast in terms of probability theory?
The edifice is cracking.
Conceptual art?
Today Corcoran's edifice is the Renwick Gallery.
But the whole edifice now looks rickety.
The edifice is a kind of greenhouse.
Temple, edifice constructed for religious worship.
It's too conceptual.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com