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The phrase "ascertain the continuity of" is correct and usable in written English.
It can be used in contexts where you need to determine whether something is continuous or consistent over time or space.
Example: "The researchers aimed to ascertain the continuity of the data trends over the past decade."
Alternatives: "determine the consistency of" or "verify the ongoing nature of".
Exact(1)
To ascertain the continuity of the LfHha locus, partial exon1-exon2-partial exon3 was amplified from Lampetra cDNA obtained previously [23] with primers His_hha_for3 (GTCGCTACGAGGGGAAGAT) and His_hha_rev2 (TTCACGCACGAACACAAAGT), followed by cloning into pGEM®-T Vector and sequencing.
Similar(59)
In stage III, we used this measure in a cohort of patients with cancer to ascertain whether continuity of care was associated with their health needs, psychological status, quality of life, and satisfaction with care.
Therefore, the continuity of f, g, S, and T and (n rightarrowinfty ) ascertain that (fu=gu=Tu=Su).
This highlights the continuity of the politics of control.
The continuity of folk music is similar, because it is also our continuity".
The continuity of the sculpted object is governed by the continuity of the trivariates.
"The concept was to restore the continuity of the narrative.
The most important difference is the continuity of the leadership.
"It sort of reinforces the continuity of life," he said.
"That cut the momentum, the continuity of the campaign".
The continuity of follows from the continuity of f.
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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