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The phrase "a first explanation" is correct and usable in written English
It can be used when introducing an initial or preliminary explanation of a topic or concept. Example: "In this report, I will provide a first explanation of the underlying principles of quantum mechanics."
Exact(42)
The aim of this paper is to propose a first explanation of this particular wear with the help of finite element simulations and experimental observations.
A first explanation is the typical very high CNR values of DSL copper wires.
A first explanation for the lack of impact is that the various tests we employed did not reveal any new information about the employability of graduates.
A first explanation is that richer people may already be taking precautions against air pollution and, therefore, be less willing to contribute to a public good.
A first explanation for this is that as the number of users in the local market increases, the number of SIS would consequently have to increase.
A first explanation refers to the assumption that, to begin with, entry-level workers might have jobs for which they are overeducated and later on move to jobs that better match their educational attainment.
Similar(18)
A third explanation is arrogance.
A second explanation is the old political-bureaucratic imperative.
Still a third explanation offered is Mrs. Kumaratunga's character.
A second explanation is more relevant to the work onstage.
A second explanation is that Islam bans usury.
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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