Serial number/id/reference/label as noun postmodifier?
There are so many novel usages of references, IDs, keys, codes:
If we substitute variable a in the equation (3) with string "ABC" at the address 0x801234 as pointed by Smith [SM2005] we might crash our database Prometheus located in the zone us-west-2.
We might fail test 3 in the trial AA5.
Please open book 2 paragraph 14 section 3.
I could not find grammar describing the topic, particular:
- what part of speech is it? Aren't they determiners?
- why does it come after the noun (street addresses usually use numbers as premodifiers, though we say November 7, 2021)?
- as reference/label/code identify an entity I see no reason for use of definite article...
Why does it come after the noun?
This English construction is called apposition
In particular, see "restrictive apposition". Two examples of this from the link are:
My friend Alice Smith likes jelly beans. – I have many friends, but I am restricting my statement to the one named Alice Smith.
He likes the television show The Simpsons. – There are many television shows, and he likes that particular one
All of your examples (except possibly "Smith [SM2005]") fit this construction.
equation (3) - There are many equations, this is a particular one.
our database Prometheus - There are many databases, this is a particular one.
I agree with Peter Shor: the definite article is not needed.
If we substitute variable 'a' ((i) “'a'” is in apposition – or a post positional attributive proper noun - to “variable” and creates a proper noun phrase) in the equation (3) (ditto, with suitable changes = (adverbial phrase modifying “substitute")) with string "ABC" (ditto (i), with suitable changes - (adverbial phrase modifying “substitute")) at the address 0x801234 (ditto (i), with suitable changes) as pointed out by Smith [in] SM2005] (in SM2005 is an adverbial phrase) we might crash our database.
Prometheus located in the zone us-west-2. (Meaningless for insufficient context)
We might fail test 3 (ditto (i), with suitable changes) in the trial AA5 (ditto (i), with suitable changes).
Please open book 2 (ditto (i), with suitable changes) [at] page 14 (adverbial phrase modifying “open") [and refer to] section 3 [proper noun as object].