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Discover Ludwig"run across" is correct and usable in written English.
It can be used to mean coming into contact with something or someone unexpectedly. Example: I ran across an old friend while I was grocery shopping.
Dictionary
run across
verb
To cross by running.
Exact(60)
Critical pipelines run across it.
Deep cleavages run across the political landscape.
Or run across the road?
They've never run across anything like me.
So you may run across this model in the literature.
I've run across this a lot over the years.
I've only just run across this website today.
"Sometimes I run across and then back," he said.
Deep lines run across his forehead and under his eyes.
Three bands of wealth run across the state.
I run across the road and never make it.
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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