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The phrase "uniquely determined" is a correct and usable phrase in written English.
You can use this phrase to describe something that has no other option from which to choose and is limited to one particular outcome. For example, "The outcome of the case was uniquely determined by the jury's decision."
Exact(60)
The operator is, however, not uniquely determined by the measure.
The effective layer thickness t can also be uniquely determined from first-principles calculated bending energy49.
Asked why Mancunians seemed uniquely determined to wreck the bikes, he said: "We aren't sure.
Generally, a symmetric tensor decomposition can be uniquely determined by a generating matrix.
The structure of a star is uniquely determined by its mass and chemical composition.
Distributive shares are, in this view, uniquely determined by technical data.
Moreover, by the axiom of extensionality, this set X is uniquely determined by ϕ(x).
We come across as uniquely determined to hold on to our booty and not prepared to meet critics halfway.
The state of cells in such a landscape is susceptible to fluctuations and not uniquely determined.
The thickness of the initially formed microlayer was found to be uniquely determined.
Based on that, if the signal is timestamped, the controller's mode is uniquely determined.
More suggestions(15)
characteristically determined
uniquely calculated
uniquely ascertained
typically determined
ideally determined
exceptionally determined
only determined
distinctly determined
singularly determined
exclusively determined
particularly determined
uniquely established
solely determined
unusually determined
unique determined
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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