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'shows that even though' is correct and usable in written English.
You can use it when you want to introduce a contrasting idea or idea of contrary/opposite opinion. For example: "The data shows that even though the majority of people supported the new law, it remains unpopular in some parts of the country."
Exact(60)
This study also shows, that even though the empirical potentials developed by Vijaykumar et al.
Also, the historical evidence shows that, even though insurgents were successful in assuring that foreign troops leave Afghanistan, they were not capable of ousting existing governments.
Courchamp said the research shows that even though charismatic large carnivores receive much more conservation funding than other animals, it's still not enough.
Thus the world's biodiversity struggles because of this discrepancy, and this shows that even though mining is economically very efficient, it is a major proponent of the downward spiral in the specter of global biodiversity.
We know that research from the RAND Corporation shows that even though military members are more likely to be married at every age than their matched civilian counterparts, we are no more likely to be divorced.
In an engaging biography, Miller shows that even though the flag story is riddled with improbabilities, the life of the woman who came to be known as Betsy Ross is worth recovering.
"This shows that even though lawmakers now have to disclose their pet projects, we're not getting a full accounting of earmarks," said Ryan Alexander, director of Taxpayers for Common Sense, a group in Washington that tracks earmarks.
The modeling shows that even though the heat extraction levels from the entire furnace, flue gas pass, and EHE increase with increases in the inlet O2 concentration, the heat extraction from the EHE dominates the heat extraction for high inlet O2 concentrations and, consequently, requires an increase in the circulating solids flow, which transfers heat from the furnace to the seal.
The analysis shows that even though low-carbon power requires a larger amount of metals than conventional fossil power, renewable and nuclear power leads to a reduction of a wide range of environmental impacts, while CO2 capture and storage leads to increased non-GHG impacts.
This Article shows that even though aspirational norms and arbiter norms serve different objectives, they share a common characteristic overbreadth.
This study shows that, even though its regolith is young, micrometeoroid impacts have altered the regolith of asteroid Itokawa.
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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