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The phrase "are however based on" is correct and usable in written English.
It can be used to indicate that something is founded or grounded on certain principles or information, often following a contrasting statement.
Example: "The results of the study are however based on a limited sample size, which may affect their generalizability."
Alternatives: "are nonetheless grounded in" or "are still founded on".
Exact(28)
Their data are, however, based on one particular BRCA2 mutation - 999del5 - and hence it is not possible to rule out that this phenotype represents a peculiarity of this particular mutation.
These hypotheses are, however, based on a limited number of characters; two for Apoditrysia, two for Obtectomera, and one for Macrolepidoptera.
A number of these reports are, however, based on erroneous mathematical modeling and thus resulting incorrect results.
Most of the available modal combination rules are however based on the assumption that nonstationarity affects the structural response alike at the modal and overall response levels.
These methods are, however, based on heuristics and greedy approaches to generate rule sets that are either too general or too overfitting for a given dataset.
Our results are, however, based on a relatively small-scale case study, and we have identified further challenges associated with Stream reasoning that will need to be overcome for the approach to become adopted in practice.
Similar(32)
This conclusion was, however, based on only one original study [37].
The diagnosis of HF was, however, based on information derived from medical records only in all but one study included.
Generally, this technique is, however, based on the study of the invariance property of the differential equations under one-parameter Lie group of point transformations [13, 14].
The expert consensus is however based on the scientific evidence.
This hypothesis was, however, based on in silico prediction but never demonstrated at the molecular level.
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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