It was quite thick at the time and needed several improvements after the first versions were produced with the 12-600 AT, but was really nicely finished (in the 27-460 versions).
This M version has been released in1961 until it was replaced in 1985 by the flatter 240.
My guess is that, in that period of time, it has evolved and the source you've been reading mentions a number of jewels which was not the one implemented at the very beginning.
The 27-460M produced in the early period had a serial number between 1119000 and 1119140, concerning the 1961-1965 years.
And 1122500-1129999 for the 1965-1970 period.
Would it be possible that your version is an early version and that the second series may have know some changes?
Here is a picture I found on the net where we can see "37 jewels" stamped:
From the serial numbers I could give above, it seems indeed that there were changes in the 27-460 M movement during his lifetime.
So, it just seems to be an evolution of this very fine caliber. If you wish to go further, you can certainly contact your AD or Patek Philippe, they will certainly help you on this matter.
However, please keep us informed and do not hesitate to share some pictures of your 3445!
Cheers, Mark
This message has been edited by Mark in Paris on 2015-04-19 03:37:08