The phrase "alleged existence" is correct and usable in written English.
It can be used when discussing something that is claimed to exist but has not been proven or confirmed.
Example: "The researchers are investigating the alleged existence of a previously unknown species in the rainforest."
Alternatives: "claimed existence" or "purported existence".
But cryptozoologists -- researchers who study the alleged existence of unknown animals -- say eyewitness accounts, photographs, films, videos, footprints, hair and even fecal material all suggest the possibility of an unknown species that doesn't seem to want to be discovered.
The old explanation for Euroscepticism was the alleged existence of a democratic deficit within the EU.
The alleged existence of these was the principal justification given for the invasion of Iraq.
The issue is not the alleged existence of terrible weapons but their actual use against helpless civilians.
The alleged existence of such evils throughout the United States led recently to an inquiry by the National Convention of Insurance Commissioners.
He has never addressed corruption accusations levelled against him, including the alleged existence of a lavish hidden palace on the Black Sea.
The Cicig's investigation, now in the Guatemalan courts, alleged the existence of a massive corruption ring that took bribes from importers in exchange from lower customs duties.
Notably, the court found that plaintiffs had sufficiently alleged the existence of a false statement because the company had disclosed only a security "vulnerability," when an actual breach had occurred.
Geneina, who led Egypt's anti-graft agency until he was fired by Sisi in 2016, previously gave an interview to Huffington Post's Arabic site, where he alleged the existence of video footage proving complicity by the country's top leadership in crimes committed during a period of military rule after the country's 2011 revolution.
It also alleged the existence of a "secret 19 June 2014 indictment" of unnamed executives involved in the case.
In 2012, Squidward became the center of a "creepypasta" (a term describing urban legends or scary stories that have become Internet phenomena) called "Squidward's Suicide", which alleged the existence of a lost episode of SpongeBob SquarePants in which Squidward commits suicide.
