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The phrase "are only based on" is correct and usable in written English.
It can be used to indicate that something is exclusively derived from or dependent on certain factors or information.
Example: "The conclusions of the study are only based on the data collected during the first phase of research."
Alternatives: "are solely derived from" or "are exclusively founded on".
Exact(60)
These results broadly confirm previous findings, but they are only based on one realistic population and one multivariate MAR missing data mechanism.
The 40 equations allowing the estimate of vapor pressure involve from 1 to 12 descriptors, and more than half of them are only based on one descriptor.
If one assumes that players' salaries are only based on their abilities, clubs that spend more should almost always finish higher in the league tables.
According to the SVM-based criteria, the top ranked features are only based on the subset of support vectors that are 'borderline' cases.
The media stories are only based on a hypothetical situation".
Claims of benign environmental performance in the research literature are only based on process centric suppositions.
Because the flow directions are only based on the topography, the other factors controlling the flow directions are overlooked.
That's because the topline numbers about Republican candidates are only based on 405 registered voters who are Republicans or Republican-leaning.
The Egyptian health ministry said that it had counted only 20 dead so far – though their figures are only based on bodies delivered to state institutions.
However, the traditional critiquing methods are limited in that they are only based on static attribute values (such as a digital camera's screen size, effectiveness pixels, optical zoom).
The proposed fault estimation/reconstruction signals are only based on the available plant input/ouput information and can be calculated on-line.
More suggestions(15)
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are exclusively based on
are just based on
are limited based on
are limits based on
are restricted based on
are techniques based on
are was based on
are only allowed on
are only discovered on
are only accepted on
are only shown on
are only stamped on
are only resolved on
are necessarily based on
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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