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The phrase 'central idea of' is correct and usable in written English.
You use this phrase when you want to introduce the main concept or point of a statement or argument. For example: The central idea of this essay is to introduce the concept of sustainable energy.
Exact(59)
They believe in the central idea of Hinduism, which is internal cleansing.
The central idea of swans is where the production is dimmest.
Finishing the job of the MDGs should be the central idea of the report.
The various teachings of Judaism have often been regarded as specifications of the central idea of monotheism.
In trying to describe how Turing resolved the decision problem, Leavitt gets wrong the central idea of a "computable number".
Throughout the novel there persists a search for faith, for God the central idea of the work.
"Well-being is actually the central idea of economics," the Princeton economist Alan Krueger said last week.
The central idea of evolutionary game algorithm [14] includes "choice" operation and "mutation" operation.
The central idea of our framework for fragment composition can be captured from Fig. 7.
The central idea of this proof, or the proof strategy, is clear.
Hewlett-Packard's Failure To Communicate 02.14.02 The central idea of the HP Way was truth.
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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