The true transition guns will have the large convex ribs on the bottom of the receiver, squared lug,finer checkering, wider for-end (compared to Fulton guns) with the duck bill and vase shaped ebony tip. They would have the rounded breech balls compared to the slanted type of the Fulton guns. The barrels will be either Good Damascus to Finest Damascus and will not have a makers name on the barrels.
There are some guns in my records in the 23000 range (hammerless) that do not have a makers name on barrels and I also have guns in the 30000-37000 range without a makers name but some have the Fulton type rounded lug. Some have no engraving and others have engraving like the No. 2 with the Nautilus style engraving and others had line engraving and some yet at no engraving.

It all depended on what stage the guns from Syracuse were in when shipped to Fulton in 1888-89 for assembly. Some could have been in many parts and some were not engraved yet.
None in my records show Chain Damascus on Syracuse guns.