Here we actually disagree. Jughead didn't factually do anything in terms of the 'flash sideways narrative'. Jack was wrong, and even admitted it. The term "flash sideways" is itself the final red herring, they weren't flashing to anything... this was a reality created after death by those whose journey we saw in life. This was their journey after death.
As Locke said after he awakened: Jack had no son. None of these people were real. I know some people will be disappointed with this, but this was the ending for those "men of faith." LOST was a journey from birth to death and after for these characters, and all we saw this season was the culmination of that. There was no part of the sideways that even existed that wasn't part of these LOST characters lives. The island was sunk because they needed to move on from it - it even needed to EXIST because some of them were born on it (Charlotte, Miles, etc). Even Ben visited the Island, but we learned in the flash sideways they moved off it young.
The island needed to go away for everyone to continue to exist and reunite, so in this purgatory, it was removed. In that sense, the 'bomb worked' - but again, it was all a spiritual illusion. Until each person "awakened" - i.e., came to the realization and acceptance of their own mortal death, they are born, died, and renewed within this karma cycle. Some people are ready (Jack, Locke, everyone we saw in Church) some are not (Ben, Ana Lucia as told by Desmond, Hawkings, etc) and some never will (Michael, Whispers, etc). After these people in the Church go to their deserved afterlife, all that will not touch the remaining people still in this purgatory lives... ceases to be.
