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The phrase "the theory presented" is correct and usable in written English.
You can use it when referring to a specific theory or argument that has just been discussed or explained. For example, "After considering the evidence, I believe that the theory presented is the most likely explanation."
Dictionary
the theory presented
noun
Mental conception; reflection, consideration.
synonyms
Exact(60)
Those claims seemed to raise doubts among the jurors, because in the theory presented by prosecutors, the driver of the car did not fire at either of the officers.
Confirming the theory presented in Sect.
for which we apply the theory presented in Sect.
The agreement with the theory presented is good.
The theory presented is illustrated with a number of examples.
A numerical example is given to illustrate the theory presented.
When the resonant frequency changes, FOs are mitigated according to the theory presented in Section 2.
It is designed for testing the theory presented in the article against independent data.
Sufficient numerical examples are discussed to corroborate the theory presented herein.
The fact that these results satisfy Eq. (29) demonstrates that the theory presented is essentially correct.
The theory presented herein is built upon the classical plate theory.
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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