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The phrase "a sufficiently high" is correct and usable in written English.
It can be used when discussing a level or degree that meets a certain requirement or standard.
Example: "In order to ensure safety, the structure must be built to a sufficiently high standard."
Alternatives: "an adequately high" or "a suitably high".
Exact(60)
Proper operation requires a sufficiently high coefficient of friction.
"There still isn't a sufficiently high premium put on education," Stanford says.
A sufficiently high tax on robots would prevent them from being produced.
With a sufficiently high density the "closed" universe has enough gravitational pull to overcome the expansion.
Hardening heat treatments invariably involve heating to a sufficiently high temperature to dissolve solute-rich precipitates.
"He had a sufficiently high opinion of himself," Dr. Botstein said.
Those implicated at a sufficiently high level are banned from holding public office.
A sufficiently high interest rate will make the burden of debt unbearable, and trigger default.
Only one interpreter has been deemed to be at a sufficiently high risk to get a visa.
Conceivably, an unscrupulous rating firm might award an AAA rating to any company that paid it a sufficiently high fee.
But, I will admit, they failed to pass the information up the chain to a sufficiently high level".
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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