The evidence I have seen overwhelmingly supports that all Polarouters and Polerouters came with signed crowns.
Earlier produced UGs came with signed crowns, I've seen many Polarouters which look untampered and have signed crowns, and there are even signed crowns featured on all Polarouters in the vintage advertising material:
https://universalgenevepolerouter.com/vintage-advertising/#PBump
So i see no logical reason or evidence why only some of them would come with unsigned crowns. This doesnt make any sense from an economic or manufacturing perspective. It is much more likely they have either been worn or polished away, or replaced (lets not forget, this is one of the most commonly replaced components, and the watches are now 65 years old).
Which crown types exactly came with which references, is more up for debate, in my opinion.
The 18k 10234-x references however could have been unsigned, i see no evidence to support that one either way, and examples are pretty thin on the ground.
I wouldn't rely too heavily on the examples from the springbar page - it was written some time ago so you need to assess them with all the other evidence we have since documented for them. The are even a few examples on that page that are clear redials. The page was a great construction, but we are finding more and more about them almost daily at the moment.
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