Well, after seeing the 0th episode of the 4th season, it is at most probable to assume that Moriarty is dead. It is even certain. After Moriarty's death someone will inheret the idea and take the role upon him/herself.
Agaist the main consensus, Moriartys motives are not as primitiv as they seem to be. Considering the moral behind the 0th episode the idea behind being Moriarty is of an revolutionary nature. In other words, to change world, to wake up the doomed and dumb people, living in their own stupidity-bubbles without seeing the porky-pie the governments throw at them. But not to go too deep inside the interpritation on it's motive. More important is the name redbeard. You people think it was Sherlocks and Mycrafts pet dog in their childhood? -nonsense. Why would Mycraft name a whole secret project after a dog? Maybe something happend, which touched the two brothers so deep, sherlocked was shocked when Magnus and Mycraft mentioned the name "Redbeard". One possible theory to come up with, is the existence of the eldest brother Sherrinford. How can those be connencted? Elementary. Sherinnford was intellegent, even more than both Mycraft and Sherlock together. What could that mean? As seen at Sherlock and Mycraft, high intellect implies less sentiments and an other unterstanding of moral action. So what would the eldest brother look like? No feelings, no sentiments, sole reason. The elder is likely very similiar to sherlock( i will explain this later in the text). So he was bored by the monotonious dump people sorrrounding him, even hIs younger brothers. So at one point at time he killed the dog. It doesnt matter why , however what happend from thar point on is. The eldest brother left home. He acknowledged that stying there would impede his enoumours intelligence. From then on every thing is clwar. Mycraft and Sherlock knew about Moriartys web before Moriarty appeared in the series. Thats because sherinnnford made Moriarty. They knew about it as some thig similar must have happend in the past, which involved Mycraft dealing hus older brother. So why I supposed Sherinnford is to be similar to Sherlock. Well we all know that ACD chooses the charaters names with reasond. The best example Dr. Watson. Why Watson? Because he continiusly keep asking what, so he named him Watson. A little sarcasmus. So what dies Sherinnford mean? Ford has also the meaning of a deep hole, falling into would mean never coming out of there. So apparently ACD wanted to make Sherlock an evil Charakter at the End. As it would become too Boeing for him just solving easy cases. But that would be just too easy. So he left the character name Sherinnford for another person , who follow the path of being criminal.