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The phrase "accepted that the core" is correct and usable in written English.
It can be used in contexts where a conclusion or understanding about a fundamental aspect is being acknowledged or agreed upon.
Example: "In the meeting, it was accepted that the core principles of the project needed to be revised for better clarity."
Alternatives: "acknowledged that the essence" or "recognized that the foundation".
Exact(1)
While it is accepted that the core feature of frailty is increased vulnerability to stressors due to impairments in multiple, inter-related systems that lead to decline in homeostatic reserve and resilience [ 1], the pathophysiological pathways behind this condition are not well understood.
Similar(59)
The company's plan "seems to accept that the core European markets are not going to grow dramatically in the near future," Mr. Wells said.
Mr Netanyahu has been persuaded to change his mind by accepting that the "core issues"—the status of Jerusalem, the redrawing of borders and the rights of Palestinian refugees be put on the agenda right from the start.
"There is still a reluctance by clinicians and managers to accept that the care of this most vulnerable group of patients is a core function of acute hospitals.
One of the most contentious issues that will be raised is whether the US will accept that core human rights provisions apply outside its borders.
It's widely accepted that the thought of parents having sex is enough to chill their offspring to the core.
But if they are to accept the left's viewpoint, they must accept that the problem at core of their being is all in their heads.
We accept that retrospective recall of both core skill frequency and confidence rating is subject to the limitations of memory recall and potential bias of newly qualified doctors wishing to demonstrate experience, confidence or improvement during training.
However, while technically gene essentiality assignment always refers to a specific (genetic) background, as long as it is currently accepted that core physiology of all mammals is the same, consequently certain genes should be essential in mammals regardless of background.
When Democrats nixed letting Fox News moderate one of their presidential debates, this was grounded in a recognition that Democrats must forthrightly accept that Fox has become, at its core, a bad-faith purveyor of right-wing disinformation and propaganda, and act accordingly.
It is generally accepted that CD95 DISC core structures are composed of three molecules of CD95 and three molecules of CD95L [16].
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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