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The phrase "critically dependent" is correct and can be used in written English.
It is typically used to describe a situation where something is heavily reliant on another factor or element. Example: The success of the project was critically dependent on the timely delivery of the materials.
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"We're critically dependent on mass," said Dr. Brownlee.
"Our economic system is critically dependent on the free flow of credit".
Both are critically dependent on revving up the institute's research role.
We at Google are critically dependent on this infrastructure building out".
America's defence is already critically dependent on space technology in the form of satellites.
"My friends, whom we are critically dependent on, are having problems," he said.
"So Bangalore is very critically dependent on lakes for drinking water and ecosystem services".
"Posco by pulling out of Australia doesn't mean the whole deal's dead but it makes it so much harder because it's so critically dependent on Korea," he said.
The strains on America are manifest: wars in Iraq, Afghanistan and Pakistan, and an economic stimulus package critically dependent upon a continued Chinese appetite for American debt.
"Our economic system is critically dependent on the free flow of credit, and the consequences for the broader economy of financial instability are thus powerful and quickly felt".
"We have enormous segments of agriculture that are critically dependent on hired farm labor," said Keith Collins, the chief economist at the Agriculture Department.
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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