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The phrase "are known with" is not correct in standard written English.
It is not typically used in any context, as the preposition "with" does not fit well with "are known."
Example: "The results of the study are known with certainty." (This should be rephrased for clarity.)
Alternatives: "are known for" or "are recognized for".
Exact(60)
Some elements of the future are known with reasonable accuracy.
Its leading electronics firms are known, with good reason, as the "big five".
Only central Texas populations are known with respect to integrated features of life history, behavior, and ecology.
The heart of phase two would include digitized Dickinson letters; 1,049 are known, with 99 correspondents.
Mr. Yoshimura ranks the Columbia springers, as they are known, with the Yukon kings for taste and oil content.
More than 120 species of the family are known with the largest numbers in North America and Australia.
More than 30 radioactive isotopes of barium are known, with mass numbers ranging from 114 to 153.
Nearly 200 OB associations are known, with distances up to 80,000 light-years from the nucleus.
A number of oxides with the K2NiF4 crystal structure are known, with La2NiO4 being a prototypical example.
Traditional NDP models are often posed as a deterministic bilevel program assuming that all relevant inputs are known with certainty.
However, most DEA models applied to airports assume that inputs and outputs are known with absolute precision.
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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