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The phrase "widespread over time" is correct and usable in written English.
It can be used to describe something that has become common or prevalent throughout a certain period. Example: "The use of smartphones has become widespread over time, changing the way we communicate."
Exact(5)
One thing CEO's of e-tailers agree on: cohort pricing is going to become more widespread over time.
The pattern they set grew more widespread over time, so that many deities in local cult centers, like Ptah, Sekhmet, and their child Nefertum at Memphis and Amun, Mut, and Khonsu at Thebes, were assembled into family triads.
Is mechanical shaking becoming cheaper and more widespread over time?
As NFD and microglial dystrophy become more widespread over time they eventually reach critical levels and become symptomatic.
When the mutation was associated with a mitochondrial genome that had a strong drive towards replication, the mutation became more widespread over time, and in most cases, this eventually resulted in the mutation killing the flies.
Similar(55)
Models with sequential stages assume that an impact or output at one stage may, or may not, lead to increasingly concrete and widespread impacts over time.
5 12–15 Models with sequential stages assume that an impact or output at one stage may lead to increasingly concrete and widespread impacts over time.
However, as advanced stoves come into more widespread use over time, SFU by itself will become increasingly problematic as an indicator for impacts from household combustion in terms of health, climate, and environment.
However, in our experience, widespread use over time among patients of a portal offering secure email with clinicians is associated with an increase in secure email workload that must be taken into account.
Over time, widespread mobile payment will be a reality for the mass market.
Human suffering, though still widespread, is being reduced over time.
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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