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The phrase "critically depends on" is correct and usable in written English.
It can be used to emphasize the importance of a particular factor or condition that is essential for something to function or succeed.
Example: "The success of the project critically depends on the timely delivery of materials."
Alternatives: "is heavily reliant on" or "is fundamentally based on".
Exact(60)
The validity of these statements critically depends on one sentence: "In the absence of intracellular interactions".
The use of scintigraphic diagnostic agents critically depends on their targeting properties.
The success of partial breast irradiation critically depends on proper target localization.
The performance of nanoelectronics devices critically depends on the distribution of active dopants inside these structures.
The performance of nanoelectronic devices critically depends on the distribution of charge carriers inside such structures.
Such overflow critically depends on the amount of storage space allotted to the transmission channels.
The biological activity of nanoparticle-directed therapies critically depends on cellular targeting.
This capacity critically depends on the development of the prefrontal cortex (PFC).
The conservation of biodiversity critically depends on the value that humans attach to it.
The transmission through waveguide bends critically depends on the photonic crystal architecture in the bend region.
The THE critically depends on carrier concentration and diverges at low doping, near the metal insulator transition.
More suggestions(16)
strictly depends on
decisively depends on
acutely depends on
heavily depends on
enormously depends on
essentially depends on
particularly depends on
importantly depends on
absolutely depends on
immensely depends on
fundamentally depends on
utterly depends on
significantly depends on
overwhelmingly depends on
deeply depends on
extremely depends on
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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