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The phrase "obtained independently" is correct and usable in written English.
It can be used when referring to a source or information that was obtained without help from another. For example, "The research team obtained their results independently, without any interference from outside sources."
Exact(60)
Seven hormone-independent variants (HID) were obtained independently from PAC120.
This particular transcript was obtained independently by the Guardian.
But this article is based on information obtained independently.
(The records were compiled for Congressional and Pentagon investigators and obtained independently by The Times).
And the number called should be obtained independently, not from the statement itself.
The documents, which include affidavits, lists of equipment and technical specifications related to tapping fiber-optic network links, have been obtained independently by a number of news organizations.
The government strictly controls information about security in Xinjiang, and little information can be obtained independently about suspects rounded up in crackdowns or the evidence against them.
The same result was obtained independently by Lande (1993).
Slightly weaker results were obtained independently in [30].
Such an ordinal was obtained independently about the same time by S. Feferman.
This approach also requires that the adsorption constants be obtained independently.
More suggestions(15)
collected independently
guaranteed independently
obtained regardless
generated independently
maintained independently
elicited independently
obtained irrespectively
gained independently
negotiated independently
obtained freely
acquired independently
obtained apart
obtained categories
obtained independence
gain independently
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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