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"systematically shown" is a correct and usable phrase in written English.
It means something has been displayed or revealed in a methodical or organized manner. Example: The study's results were systematically shown in the final report, with clear graphs and tables to support the findings.
Exact(14)
CA varied among different sites and season, but its levels were systematically shown to be minimal at site S1.
In recent studies we have systematically shown that the freezing properties of flexible, elastic polymers depend on the precise chain length.
On the basis of the combined insight gained from these, it is systematically shown that the allowable size needs to be slightly increased to give a practically useful design.
Evidence from cognitive sciences has systematically shown that time pressure influences decision-making processes.
ARID5B gene variants have been systematically shown to increase the risk of childhood ALL in various populations [ 14, 18- 23].
Meanwhile, the best available evidence from three consecutive large meta-analyses has systematically shown that people with metabolic syndrome are at increased risk of cardiovascular events.
Similar(46)
Opinion polls systematically show a substantial majority against Trident.
A team at the University of Maryland then published a paper in March, systematically showing 802.11b's collection of security features to be ineffective.
Widmanstätten laths systematically show misorientations of ∼65° around the axis ⟨1¯100⟩α2 with respect to the embedding lamellar structure.
In this article we systematically show that the observed discrepancies may also be caused by a different reason: the external classification itself.
This result is consistent with all the successive Molchan diagrams, which systematically show that two consecutive forecasts have no specific skills with respect to one another.
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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