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The phrase "distilling the core" is correct and usable in written English.
You can use it when you want to indicate that the essentials of something are being identified or clarified. For example, "Our team worked together carefully, distilling the core values of our organization into one concise mission statement."
Exact(1)
The aim of this paper was to review and synthesize the relevant literature with the objective of identifying and distilling the core enabling technologies of big data analytics and context-aware computing as ecosystems in relevance to smart sustainable cities, as well as to illustrate the key computational and analytical techniques and processes associated with the functioning of such ecosystems.
Similar(59)
In the following section, we distil the core features that can be used to show similarities and differences among diverse conceptualizations of competing demands.
Distilling the ingredients is not easy.
BEST: Great job distilling the news.
Distilling the important from the not so important.
Therefore, this paper endeavors to systematize the very complex and dense scientific area of smart sustainable cities in terms of identifying, distilling, and structuring the core dimensions of a foundational framework for smart sustainable city development as a set of future practices.
"It's hard for these guys to distil down to the core use case".
But it has also distilled the group down to a committed core of members willing to be martyrs.
While it successfully distilled the complexity of biology down to only five core concepts, the recommendations set forth in Vision and Change were intentionally broad.
In relation to Lacan, the 1970s could be characterized as the decade of the "matheme," Lacan's neologism for a unit of formalization (qua a mathematical-style symbolization) distilling and fixing the core significance of a specific Lacanian analytic concept-term.
Exhausting stuff, distilling team sport to the core pleasures of throwing, receiving, defending.
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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