zebrespace
·I do not have photos or documentation of ref. 5981.
Another reference that comes to mind is 5971, which is a gold-plated 30CH reference. The case design of ref. 5971 differs from your watch as its bezel is sloped not stepped. Additionally, the case-backs of ref. 5971 are not gold-plated. This is consistent with gold-plated 13ZN reference 5523. Further, both ref. 5971 and 5523 have case-backs that are marked "Fond Acier Inoxydable". Though odd, I suspect that the case of your watch was plated after it left the factory.
Beyond the case, I notice a few other things. Looking at a photo of the movement (seen here: https://orologi.forumfree.it/?t=80104160), the column wheel screw is from a later 30CH movement. Also, the very worn condition of the movement (e.g., exposed brass on main bridge, missing reset hammer) does not appear to be consistent with the relatively clean condition of the dial. I have long been curious about this exact dial design, as I have seen many examples in almost perfect condition. I wonder if they could be service dials. Finally, neither of the sub-dial hands are the correct style.
" I suspect that the case of your watch was plated after it left the factory. "
The answer is in the Longines extrait of archives:
" the column wheel screw is from a later 30CH movement ":
Later movements had the writing 30CH engraced on the bridge. Mine isn't, so maybe a replacement screw?