Help me understand this. In 1969 everything hinges on getting the Arc Net in place, to repel the Boglodotian invasion. Griffin makes the point that if they are stopped here, at earth, they will starve before they can reach the next planet. In the original history, K activates the shield, and by 2012 all records say that the Boglodites are extinct, and thus Griffin apparently was right. So far, so good.
Now we hit the second history, in which Boris kills K but flees from Earth back to Boglodotia. Because it is twenty light years away, it takes about twenty years for him to get there; it then takes another twenty years for the Boglodotian fleet to reach earth, so we're looking at roughly forty years round trip. Since there is no Arc Net defense, the Boglodotian attack is not impeded.
Wait--why were the Boglodotians extinct? The answer seems to be that they could not survive long enough to reach any planet other than Earth; but it took forty years for them to reach Earth, so they obviously could survive those forty years without conquering Earth. So perhaps they were destroyed by the Arc Net--but the Arc Net defends the planet, and they would have to have made the trip across twenty light years after being notified that Earth was ripe for destruction. Thus there seems no simple way for the Boglodites to be extinct at this point.
We might suppose, in search of a solution, that Boris has some means of contacting Boglodotia via a faster-than-light communicator to let them know to launch the attack, but that in the second history, although K is killed by Old Boris, the communications system is destroyed and Young Boris must make the trip back to Boglodotia. Following this line, in the original history Boris must have sent the call for the Boglodotian fleet to begin, and twenty years later, around 1990, it encountered the Arc Net and was destroyed, causing the extinction of the race; they would have lived another twenty or thirty years apart from that, so had plenty of time to make the trip still when Boris carried the message to them in the second history. They would not live long enough to make it to the next nearest suitable victims.
The problem with this supposition is that Boris knows, in the original history, that K has activated the Arc Net, so he knows the fleet will be destroyed. The only solution is that he must be arrogant enough to have ordered the attack before he obtained or destroyed the Arc Net, and then could not recall the attackers. This then hits the snag that if he was so arrogant in the first history, why was he not so arrogant in subsequent histories? The only obvious answer is that the arrival of Old Boris persuades Young Boris that he had better not call for the fleet until he knows he has succeeded; that means he did not call for the fleet in the original history until early on the morning of the 16th, because it has to have been after Old Boris arrived in subsequent histories.
So we have an original history in which Boris, on the morning of the 16th, summons the fleet, and then attempts to get the Arc Net, failing and being jailed; the fleet arrives twenty years later and is destroyed by the activated Arc Net. In our second history, Old Boris arrives before Young Boris sends the signal, but together they succeed in killing K and preventing the activation of the Arc Net; however, the communication device is destroyed, so Young Boris must travel to Boglodotia to bring the fleet, and it takes forty years for the invasion fleet to arrive, at which point there is no defense. In the third history, it does not much matter, but we conclude that Young Boris does not send the signal and does not make the trip, and therefore the fleet never comes, and the Boglodotians become extinct by starvation when they have no signal calling them to attack. When they become extinct is more problematic, but we aren't there yet.