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"is the first study" is a correct and usable phrase in written English.
It is commonly used when talking about a specific study or research that is the first of its kind. It can also be used to refer to the first study in a series of studies. Example: "This is the first study to examine the effects of social media on adolescent mental health."
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This is the first study to examine total phenol antioxidants in breakfast cereals and snacks".
"This is the first study that looks at paralysis in this kind of way," she said.
"This is the first study to show this happens in the field," van der Sluijs said.
This is the first study of this level of detail and scale in the world.
But this is the first study to look at the personality of such children in adulthood.
It is the first study to show that these publicly sourced photographs are suitable for use in conservation work.
But most have been based on relatively small samples; this is the first study to compare national programs.
But this is the first study to see how this varies across the 376 local authorities in England and Wales.
It is the first study to demonstrate clear and wide-ranging differences between organic and conventional fruits, vegetables and cereals.
The authors say this is the first study to report an association between infant sleep time and children's being overweight.
This is the first study that contradicts Darwin's invasive species hypothesis using animals.
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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