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The phrase "a first hypothesis" is correct and usable in written English.
It can be used when introducing an initial assumption or theory that will be tested or explored further in a discussion or research context.
Example: "In this study, we will present a first hypothesis regarding the relationship between sleep patterns and cognitive performance."
Alternatives: "an initial hypothesis" or "a preliminary hypothesis".
Exact(26)
Here's a first hypothesis.
A first hypothesis is that they reduce information asymmetries between management and investors.
A first hypothesis is that LRRK2's specificity is largely mediated by its N-terminal domain that is shown here to be located on the fringe of the LRRK2 dimer core (Figs 6 and 7 and ref. 28).
A first hypothesis is that the turbulence decays in the preheat layer (as the temperature rises and viscous forces increase), so that the reaction layer sees only a small fraction of the initial turbulence.
A first hypothesis involves a direct negative effect of Wolbachia on haemocytes survival via toxins.
A first hypothesis explaining these results is that they are due to a social affordance implicitly demanding greater visual control of sequence execution.
Similar(34)
Because no previous study has addressed the same issue using our methodology, we consider the present analyses as a first, hypothesis-generating study.
A second hypothesis is also about a clash of cultures.
A second hypothesis posits that turtles were more closely related to lizards and tuataras.
There was a third hypothesis, on a different level from the first two, which took the painting's supernatural origins into account.
A corollary of Vera's theory about large grazers is a second hypothesis, which he has pushed even more vigorously than the first, if that's possible.
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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