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Discover Ludwig"filtered down" is a correct and usable phrase in written English.
You can use it to describe how information, ideas, or trends are slowly spread from their origin to those further away. For example, "The newest fashion trends filtered down to the small town after a few months."
Dictionary
filtered down
verb
Past of filter down
Exact(60)
Their work filtered down into the classroom.
It filtered down into pop eventually, too.
Some, though, has filtered down to miners, middlemen and commerçants.
"Now they have filtered down to the Home Depot market".
I guess the bidding wars have filtered down to us".
Looks like that message has filtered down to the candidates.
The messaging has filtered down to local races as well.
"It hasn't filtered down to the serious recreational athlete".
I guess our priorities have been changed, and it's filtered down to our daily routines".
Little of that money has filtered down to the local residents, however.
What's filtered down to us is a certain fiery yet ethereal spirit.
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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