I've seen speculation here that the king Kvothe kills is Ambrose, which seems like the logical choice. However, it almost seems too logical. I think that Kvothe kills someone (perhaps Baron Jakis) and Ambrose ends up as king because of it. Thus, Ambrose is the king in the time the story is being told. That would help to explain the huge reward for Kvothe's life. It would also explain why Kvothe is trying to keep his friends from joining the King's army.
What of Princess Arielle? This name was mentioned when trying to convince Aaron (i think) from taking the king's coin (joining the army). Perhaps there is a chance that Ambrose betroths the princess and moves up his chances of being the king?
Most speculate that Kvothe is a bastard Lackless, which puts him in the line of succession above Ambrose. The king who is killed is possibly Maer, and once Meluan Lackless accepts Kvothe as her nephew HHe becomes legitimized. That would also explain his possession of the Lackless box (a family heirloom) I believe it’s possible that before this information becomes common knowledge, Ambrose uses malfeasance to off the king, frame Kvothe, and claim the throne. The nobles that knew Kvothe, back his story and refuse to support Ambrose in his claim to the throne hence, the rebel faction that is mentioned in the gossip around the inn. Even though Kvothe fakes his death it still delegitimized Ambrose. I only mention this because I've only read theories on Ambrose being killed and that is why Kvothe gets the title King Killer. Ambrose has shown to always have the upper hand via circumstance so I think that fits in with the dynamic of their relationship. Also it is hinted at that the kingdom is being taxed heavily and I believe that Ambrose's poor opinion of those of lower station would also fit into his character.
Turntuptiger wrote: The shoulders are wearing alverons colors it's almost been confirmed that Alveron is the king, the penitent king could Ambrose father but that seems unlikely since he's 13th in line to the throne.
When Kvothe is testing the poison on the Calanthis (which is also the name of the royal family of Vintas) Stapes eventually confesses that 4 or 5 have been dieing each day. Its not explict but this could easily add up to 13 or 14 over the course of 3 days and hints that Ambrose or his Father will eventually be king.
I think Ari is Princess Arielle. Thats why Elodin was surprised that Kvothe picked the name Ari. Thats why Kvothe was invited to Elodins naming class. Her father will be the King (imo) that Kvothe kills.. maybe for mistreating her or trying to force her to marry Ambrose?? Ambrose becomes king and thats why Kvothe has a bounty on his head and tries talking Aaron out of taking the kings coin