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The phrase "acknowledged existence" is correct and usable in written English.
It can be used in contexts where you want to refer to something that has been recognized or accepted as being real or present.
Example: "The scientist's research provided evidence for the acknowledged existence of dark matter in the universe."
Alternatives: "recognized presence" or "accepted reality".
Exact(3)
Millions are bereft of what identity scheme chief Nandan Nilekani calls "any form of acknowledged existence", which essentially ends up depriving them of their rights and pushes them into a faceless existence.
Regarding the bird resource (Table 1), the enrichment in δ13C of spring migrants returning from their African winterquarters relative to autumn migrants was consistent with the acknowledged existence of a latitudinal gradient in δ13C [28].
However, apart from the acknowledged existence of two allogamous Dasypyrum species, Dasypyrum villosum (diploid, haplome V) and D. breviaristatum (Lindb. f).
Similar(57)
Multi-Agent System (MAS) models, on the other hand, acknowledge existence of different types of agents, but their poor empirical embedding remains a serious handicap.
The newspapers scarcely acknowledged the existence of New York, let alone the rest of the world.
Last year, Mr. Kelly acknowledged the existence of the database.
Once, even in television debates, she barely acknowledged his existence.
The victory speech by Mr. Romney barely acknowledged their existence.
Or even acknowledged his existence and given him his name...
Some pentiti acknowledged the existence of a hidden level; others did not.
Justice Breyer acknowledged the existence of such categories, using a colorful example.
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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