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"remain on the level" is correct and can be used in written English.
It is used to mean staying focused and/or maintaining a certain level or standard. For example, "We must remain on the level if we want to complete the project on time."
Exact(2)
Much of these connections remain on the level of conjecture, but they may illuminate some of the lost secrets about how the Auburn System spread across the Northeast in the first part of the 19th Century.
Several challenges exist despite the potential benefits, and questions remain on the level of evidence needed to support product approval or labeling.
Similar(58)
Finally, I felt the students developed a more personal approach to literature by answering questions about the production of art rather than remaining on the level of reception.
But the interpretations put forward, even when they were founded partly on accurate observation, most often remained on the level of myth.
After 300 cycles at charge/discharge rates of 0.2 C the cell showed a very good cycling stability with its capacity remaining on the level of 87%.
On the other hand, transport costs from Finland to country 2 have varied annually, yet in the end remained on the level of 2001.
In the case of Perception, the emergent new shape of consciousness, the Understanding, explored in Chapter 3, is a shape identified with the type of scientific cognition that, rather than remaining on the level of the perceived object, posits underlying forces involved in the production of the perceptual episode.
Interestingly, when using the attenuation map derived from 300-s emission data for AC and SC, no such increase in halo artefacts with reduction of acquisition duration was observed, and halo scores remained on the level of 300-s emission data (Fig. 2).
Subsequently, the number of pathways down regulated remained on the level of the experimental error.
HSP70a1 and gluthatione-reductase mRNA expression in the DiabCin group remained on the level of healthy controls (Fig. 2c).
However, in most cases the intention to carry out the index threat was low and remained on the level of passive thinking.
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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