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The phrase "since the existence" is correct and usable in written English.
You can use it when expressing the idea that something has been true or present since the beginning of a particular time period, or since something has existed. For example: "Since the existence of the internet, our lives have changed immensely."
Exact(60)
However, the versions of cocyclic block-wise inverse Jacket matrix (CBIJM) are still absent since the existence of the CEIJM has attracted minor attention in the existing literature[8, 21].
According to Evans, zoos have been giving animals pumpkins "since the existence of zoos".
The moment, called Implementation Day, marked a turning point in the nearly 14 years since the existence of Iran's uranium enrichment and heavy water programme was first revealed.
Since the existence of the nuclear weapons program became known, the United States and its regional allies have struggled to come up with measures to force North Korea to abandon the project.
Like riverboat gamblers casting loaded dice, Iran's leaders have played a double game of deceit, duplicity and Persian blind man's bluff in on-off talks with western countries since the existence of suspect nuclear facilities was first exposed.
That is a pretty bold claim, given the wealth of reporting about the site over the years, since the existence of the Arak heavy water project was first reported in 2002.
"The more we know, the more dangerous this situation becomes," he said, adding that people believed to be intent on doing harm to Americans were already altering their activities since the existence of the programs became public.
Since the existence of fraudulent credits became common knowledge late last year, many refiners have been bypassing the scores of small producers in favor of larger, household-name suppliers.
The step was a major modification of a White House stance that has limited briefings on the highly classified program to no more than a small group of Congressional leaders, even since the existence of the program was disclosed late last year.
Since the existence of the program was first revealed by the Guardian and the Washington Post on June 6, the companies have repeatedly denied all knowledge of it and insisted they only hand over user data in response to specific legal requests from the authorities.
Since the existence of the first settlements, a close relationship between RM, urbanization and technological development has been present.
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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