Do we actually have pictures of the case engravings? Is clean actually engraving one BLNR 116710 and the other 126710? The crown guards are the same on both right?
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When the 126710 Batman first came out with jubilee only, it's CGs were skinnier than the 116710 Batman with oyster. There were also some differences in the case shapes between the 126710 Pepsi with jubilee and the 116710 Batman with oyster.
ARF's 116710 Batman (and LN) with oyster has the markedly skinnier CGs, that are much more like the first release 126710 Batman with jubliee.
Here's an ARF 116710 Batman with oyster on top and a gen 116710 Batman with oyster on the bottom.
Here's a comparison of two gen Batmans
Some have said part of the reason for the case shape changes in the 126710s was due to how the jubilee bracelets attach to the case. The jubilee springbars are thinner in diameter with different size tips. The lugs on the 126710 are also slightly slimmer.
Since the release of the 126710 Batman with jubilee, I've seen many images of it with thicker CGs, like the 116710 Batman with oyster has. So Rolex may have started using more similar cases at some point.
The new 2021 126710 releases all have the same case shape in digital images on Rolex.com
This would make the most sense from a production standpoint but we'll see if it holds true in reality. In any event there are enough variations in existing gen CGs that you could get away with having just about anything reasonable. Even the CF CGs, lol.