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The phrase "are equally consistent with" is correct and usable in written English.
It can be used when discussing multiple theories, ideas, or pieces of evidence that support the same conclusion or interpretation.
Example: "Both studies are equally consistent with the hypothesis that climate change is accelerating."
Alternatives: "are similarly aligned with" or "are equally supportive of".
Exact(15)
Without more information it is impossible to calculate which crimes deserve which punishments; an infinite number of different penalty schedules are equally consistent with the retributivist's proportionality principle.
Statistically speaking, he notes, with an expected background of one event, the probability of seeing zero events is almost the same as the probability of seeing two, so both are equally consistent with no WIMPS at all, he says.
While Kegl et al. endorse the language bioprogram hypothesis that ISN emerged 'in one leap,' in the minds of children exposed to degraded Mimica or LSN inputs, their data are equally consistent with the idea that ISN developed more gradually by means of successive elaborations and innovations among a community of highly-motivated (because language-starved) young users.
However, the various specificity results are equally consistent with task-specific reweighting of the "read-out" connections from early visual areas, with no changes in the areas [29], [30].
However, these results are equally consistent with the hierarchical account.
Our results are equally consistent with either of two possibilities.
Similar(45)
However, a liquidity crisis is equally consistent with an inflow of foreign capital in the form of mergers and acquisitions (M&A).
In Cotton v. Wood (11 C.B. N.S. 568) it was held that a Judge is not justified in leaving the case to the jury where the plaintiff's evidence is equally consistent with the absence as with the existence of negligence in the defendant.
It is, of course, true that credibility judgments have to be made about the experts who testify in patent cases, and in theory there could be a case in which a simple credibility judgment would suffice to choose between experts whose testimony was equally consistent with a patent's internal logic.
For if we think of such separation as a state of being estranged or alienated from God, or if we think of it as simply the absence of a loving union with him, then (3) is equally consistent with many different conceptions of hell, some arguably milder than others.
An inquest determined his death a suicide, but it has since been noted that the known evidence is equally consistent with accidental poisoning.
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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