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The phrase "a steadfast core" is correct and usable in written English.
It can be used to describe a central, unwavering principle or belief that remains constant despite external changes or challenges.
Example: "In times of uncertainty, having a steadfast core helps individuals navigate through difficulties with resilience."
Alternatives: "an unyielding foundation" or "a solid center."
Exact(1)
But there was a steadfast core of us who believed that the tactics should be diplomacy and multilateralism, not the "go it alone" approach of the Bush doctrine.
Similar(59)
Any doubts about the party's steadfast core were dispelled in other pronouncements this week.
If anyone could be called the successor to Barbara Cook in interpretive insight and in conveying a steadfast resilience with a core of optimism, it is Ms. McBroom.
It has risen to that level by virtue of two core characteristics of the company: a stubborn adherence to customer service and a steadfast refusal to let excessive technological wizardry interfere with its shoppers' experience on the Web site.
With 12 billion transistors, the latest Pascal architecture, 12GB of GDDR5X memory and 3,584 cores at 1.53Ghz delivering an apparent 11 teraflops of performance, it's a steadfast attempt at being the best there is.
Nina Yoshida Nelsen, a mezzo-soprano, was a steadfast Suzuki.
Freddi was a steadfast patron of the arts.
And Karl Geary is a steadfast, affecting Horatio.
Phyllis Pancella, a mezzo-soprano, was a steadfast, deeply moving Delores.
"Denny" was a steadfast friend and supporter of this firm.
He was a steadfast, hardworking trade unionist, and unafraid.
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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