Help identifying this movement

I recently acquired this Omega wrist watch with movement serial number 5310614.

The only other markings on this movement are under the bridges and the balance (marked 0614). I am assuming the 0614 was used to match parts to a specific main plate. I cannot find a reference to the caliber - even under the dial.

The dial has "27.5" with an "S" written on the backside. The diameter of the main plate is 29.52mm. I cannot find anything that seems close to this movement.

Does anyone have any ideas about what the caliber could be?

Unfortunately, I do not have a copy of AJTT, nor do I have access to a copy. I measured the mainspring and came to the following dimensions:

1.40 x 0.14 x 360 x 11.5

Assuming that is the correct mainspring for the movement, the only Omega calibers is could be would be either the 13" 003 NN, or the 13" NN (per the WatchGuy Mainsprings list).

I cannot find any information online about either of those movements (I am inclined to believe they are one and the same). I did find a pocket watch https://www.mywatchmart.com/listing...lock-from-1917-gorgeous-100-year-old-wwi-era/ that sold a while back that appears to have an identical movement.

I have posted a few more photos of the underside of the bridge and the balance.

If anyone has access to AJTT or have photos or information about the 13" 003 NN, or 13" NN, please let me know!