In an interesting exchange between Come-From-Beyond (CFB) and a Nxt developer, the question is asked:
DEV. So when can a transaction be considered irreversable?
CFB. Never, look at formula #14 in http://126.96.36.199/tangle.pdf. Just like in Bitcoin there is always a chance of double-spending.
This is further clarified:
DEV. Not even when the weight cap is reached ? (The paper mentions the cap but I'm not sure it ever states if the cap will actually be applied)
CFB. No. The cap is related to another issue.
... and more here: https://bitcointalk.org/index.php?topic=1216479.msg12759162#msg12759162
DEV. So for a transaction to be considered confirmed, the number of approving transactions multiplied by the minimal PoW must exceed the maximal possible adversary's PoW?
CFB. No, it's not that easy, if transaction flow drops then an adversary can catch up and double-spend. It's a never ending race.
The leads me to ask
Is this true, that a double spend attack can happen at any time in the future?
If so, is it the case that the POW of the honest majority of the network must ALWAYS FOREVER outweigh the POW of an attacker?