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The phrase "a direct correspondence between" is correct and usable in written English.
It can be used when discussing a clear and specific relationship or connection between two or more things.
Example: "There is a direct correspondence between the amount of time spent studying and the grades achieved by students."
Alternatives: "a clear relationship between" or "a direct link between".
Exact(29)
This fact suggests that assuming a direct correspondence between VRS and NRS scores (as for example: 0 corresponding to "None", 1-4 to "Mild pain", 5-6 to "Moderate pain", and 7-10 to severe pain1 [ 14, 27- 29]), should be interpreted cautiously in clinical practice due to relevant individual discrepancies.
In this theory, there is a direct correspondence between the matter-energy of the universe (expressed in the tensor) and the shape of space-time.
You can also see a direct correspondence between a series of 1983 lithographs of a young female dancer striking a pose with arms extended and some nearby preparatory graphite and charcoal sketches on brown paper.
Representationalist theories of perception, which posit a direct correspondence between appearance and reality, become untenable.
We identified 42 industries for which a direct correspondence between the two series could be established.
First, patches were classified into aspects, not classes, unless we assume as in [9] that there is a direct correspondence between aspects and semantic classes.
Similar(31)
First, law can be derived by a kind of immediate deduction from moral principles, such that there is a direct correspondence in content between a moral and a legal rule.
A direct correspondence was determined between ion current density during deposition and the sp3/sp2 ratio in the films.
The analysis reveals a possible direct correspondence between the sequence-dependent dynamical tendencies of DNA structure and the tendency to undergo transitions that "trap" them in nonstandard conformational substates.
Thus for the non-specific stabilization elicited by these compounds, there is a strikingly direct correspondence between thermal stability, as reported by the thermal denaturation assay, and polymerization kinetics.
The GTMA (Rao 2006) ranking shows a direct correspondence with the entropy-weighted MULTIMOORA method.
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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