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The phrase "a next deeper" is not correct in standard written English.
It seems to be an attempt to convey a concept of a subsequent level of depth, but it is awkwardly phrased.
Example: "To understand the topic fully, we need to explore a deeper level of analysis."
Alternatives: "a deeper level" or "the next level of depth."
Exact(1)
However, we will now look at this level in terms of how, upon a decision at a next, deeper level, decisions are taken about the design of the infrastructure and how it will operate following the characteristics of Tables 1 and 2. (i.e., regulatory nature of the regime and complexity of the technical functionality).
Similar(59)
That next emotion may be nothing more than a hunger for the next, deeper shock.
At the next deeper, middle level collective choice situation decision-making takes place towards establishing a particular heat infrastructure (or changing or terminating its operations).
The next, deeper layer of the cornea is Bowman's membrane, which provides further protection for the eye and consists of collagen.
Forty years later, it is possible that we are entering the next, deeper phase of our initiation.
A tangible outcome of this study is disclosure of a next generation, deep-red fluorescent Zn-BDPA probe for enhanced molecular imaging of cell death.
Lana del Rey is making a good case for herself to be our next deep-voiced, soul darling.
Mark my words, they'll be charging the next deep-sea camera crew that conducts a video event in their, you know, park.
As doctors now try to uncover this phenomenon, the answer may lie in their next deep breath.
To the Russians crazy enough to live there, summer in the Siberian Arctic is merely a deep breath before the next winter, a few weeks of melted ice and midnight sun in which to gird for the next deep freeze.
This is dangerously shortsighted: the real concern ought to be how far it could cut rates in the next deep recession.
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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