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The phrase "any specification of the" is correct and usable in written English.
It can be used when referring to any detailed description or requirement related to a particular subject or item.
Example: "Please provide any specification of the product that you think is relevant for our review."
Alternatives: "any detail of the" or "any description of the".
Exact(12)
This philosophy has its origins in the earlier work of the Dutch mathematician-logician L.E.J. Brouwer, who criticized "mainstream" mathematical logicians for accepting proofs that mathematical objects exist without there being any specific construction of them (for example, a proof that some series converges without any specification of the limit which it converges to).
The presented method uses a simple, robust, and efficient algorithm: least-squares projection (LSP), which projects points onto the point cloud in a least-squares sense without any specification of the projection vector.
Any specification of the middle class as being people with incomes between two numbers is an arbitrary definition made by whoever is providing the statistics.
O'Neill's argument does not rely on any specification of the content of the obligations that might be owed by adults to children.
Also assumed is the absence in the relevant myth of any specification of the genetic structure, evolutionary history, or other potentially defining essential features of the unicorn.
The formal definitions of EH do not make explicit appeal to randomness and the usual ways of presenting EH do not involve any specification of the notion of randomness that is supposed to underlie EH.
Similar(48)
But Mr Brown vetoed any specification of where the cuts might fall.
None of them contains any specification of conditions for securing the board's written permission.
DA embraces the assumptions that any assessment must include a specification of the degree to which the testee's performance is modifiable and that assessment must include an active teaching process aimed at modifying cognitive functioning.
"The request for comments is a bit vacuous, since there is not yet any specification of what [the] input is needed for," reads one public comment posted on DBI's blog item announcing the hiatus.
A fruitful discussion of "terrorism" requires a specification of the exercise's purpose.
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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