Thanks for the share.
I'd also add that even though this is well written out theory, in practice we also know that there hasn't been any real PoS chain ever being 51% attacked and forked. Yet, we know that kind of thing definitely happens in PoW.
many POS coins have actually forked.
the reason there is no big news about them is that POS coins are for the pump&dump arena of "nobody cares"
even suggesting a POS coin cannot be forked is just wrong.
its like suggesting an eye can never suffer from sudden hearing loss... (logically because it never had the mechanism of hearing in the first place to lose),, to suggest that because of no 'sudden hearing loss' there is no chance of an eye suffering "sensory" deprevation
yes POS cant be 51% forked... but it can be forked in a number of different ways
as for the OP suggesting that the pdf document is a proof that POS is secure. its not. i can still see many attack vectors and ways to 'game' it and gain control.
POS has other issues too which make it technically less appealing as a secure code solution. and only appealing to users at the front end "getting free coin" for little work.