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Discover Ludwig"breakthrough on" is a correct and usable phrase in written English.
It can be used to indicate a significant improvement or advancement in a particular situation or problem. Example: The scientists announced a breakthrough on finding a cure for cancer, bringing hope to millions of patients and their families.
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The breakthrough on hydraulic fracturing came in the late 1990s.
A breakthrough on borders is still the big hope.
The Paris agreement marked a breakthrough on climate change.
Sony's technical breakthrough on the A300, therefore, was this: "Duh!
Finally, a breakthrough on the international championship stage.
Pac-Man has a breakthrough on his wedding night.
The Dardanelles expedition failed, and there was no sign of a breakthrough on the Western Front.
That is a direct result of the breakthrough on shale gas.
A potential breakthrough on long-term deficit reduction poses a tougher test.
Shulman engineered a breakthrough on the queenside and won a pawn.
But there was still no sign of breakthrough on the treaty issue.
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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