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The phrase "the lookup" is correct and usable in written English
You can use "the lookup" to refer to a specific instance of searching for information. For example, "I performed the lookup in the library's archives and did not find the article I was looking for."
Dictionary
the lookup
noun
An attempt to retrieve data.
synonyms
Exact(60)
The lookup doesn't change.
Finally, the lookup performance declines.
These are the lookup table (LUT) and the switch box.
Figure 14 Implementation of the lookup table using binary search.
θ* is the coefficient saved in the lookup table.
Then it starts the lookup process in its intra-DHT.
The lookup process is carried out as follows.
The reuse affects both the lookup and update operations.
In general, the data structure of the lookup table is optimized in order to minimize the implementation cost and maximize the lookup performance.
In a situation like this, monotonicity is being represented as constraints on the lookup table parameters.
Instead, Twitter will act as a communications pipe, just like the Lookup app itself.
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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