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The phrase "a core problem in" is correct and usable in written English.
It can be used to identify a fundamental issue within a specific context or subject matter.
Example: "The study revealed a core problem in the education system that needs to be addressed immediately."
Alternatives: "a fundamental issue in" or "a central challenge in".
Exact(21)
Decision making is a core problem in Supply Chains.
Orr's plan addresses a core problem in Detroit: systemic population drain.
The inability to interact socially is a core problem in autism.
A core problem in statistics and machine learning is to approximate difficult-to-compute probability distributions.
A core problem in such missions is the ability to visit distant places in rough terrain.
The service network design problem (SNDP) is a core problem in freight transportation.
Similar(39)
McWhorter also puts his finger on a core problem: "A difference in thought must be of a certain magnitude before it qualifies realistically as a distinct 'worldview.' " Even if it were true that the participle in English made us a mite more likely to think "actively," differences in ideology and belief overwhelm and obliterate those lexical tints.
J. Phillip Thompson, who was a housing official in the Dinkins administration (and is not related to William Thompson), says a core problem is "disarray and division in black leadership in New York," and the president finds himself tangled up in it.
Addressing a core problem of underrepresentation of women in STEM with early exposure to engineering concepts, Roominate aims to increase the less than 15% of women who enter college intending to major in STEM and close the STEM gender gap that starts with the low educational value in toys marketed to young girls.
For a decade, the core problem in relations between Afghanistan and the U.S. was Washington's lack of clarity towards Pakistan.
In my experience as a therapist, poor empathy is the core problem in most troubled couples or families; without it, nothing good is likely to happen; with it, even the toughest issues can be resolved.
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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