The best I've been able to untangle is that the NewYork address pistols started with ser# 10,000.
An arbitrary new ser# starting point aside from the old Hartford numbering system.
That seems to be agreed upon.

The first 400 (or so) of the NY address pistols carry over a couple of traits of the HArtford address pistols.
The most easily seen are the slide serrations.
The HArford guns used 12 serrations and they were a V cut in the slide.
The first 400 or so of the NY address guns had those same 12 V cut serrations.
Note that collectors generally feel that the first 400 of the NY address pistols were made in NewHaven Conn by the New Haven Arms Co. Perhaps they were only assembling parts already machined or in some partially mfg'd from the HArtford operation.

After NY address ser# (approx) 10,400,,those slide serrations turn over to a square cut style (no longer a sharp V cut) and the number is reduced. I think the number of square cut serrations is 10 but I might be off on the number.
These guns after ser#400 are said to have been made by the Page Lewis Firearms Co in Chicopee Falls, Mass.
(Page-Lewis was bought up by Savage Arms not long after this.
These square cut slide serrations on the late Reising look like those of the Savage 32 and 380 semiauto pistols)

Reports vary on the total number of NY address pistols made.
The 400 with the V cut serrations is generally accepted.
The total amt overall inclusive of the above is given anywhere from 1000 to around 2500.
I'd hazzard a guess,,and it's a guess only at the 2000+ mark.
That engraved one in the link is 11396.

2800 to 3000 pistols is the number given for production of the HArtford addressed guns. That's based on a 1921 patent that was roll marked on a few of the late Hartford guns.
Ser#'s of the pistols before that marking (1916 patent only) went just over #2800.
The changeover to the NewYork address came about in 1922.
The assumption is that only a few (200+ in this case) were made at Hartford before the slide address change to the NY address.
2800 pieces plus the 'assumed' extra 200+ with the added 1921 patent marking for a total of 3000+ Hartford marked Reisings.

Approx 5000 Reisings total

That's about all I got. I don't even have my Reising anymore.
It's a Bear..