Warning: spoilers ahead for the A Song of Ice and Fire book series.
When Game of Thrones debuted back in 2011, the show had four books of source material to draw upon, with a fifth due out later that year. It was practically inconceivable that the show would catch up with the novels before George R.R. Martin would publish the sixth installment in the A Song of Ice and Fire saga. Unfortunately for book fans, Winds of Winter still has yet to be released, but the delay has allowed the show to go in some exciting directions that nobody could have predicted. That said, there is one huge plot point from the books that made it into the show and has not yet been resolved on screen: the assassination attempt on Bran back in the second episode.
Book readers know what happened, thanks to the inner monologues of both Tyrion and Jaime. In A Storm of Swords, Tyrion has a moment of clarity when he sees Joffrey receive his Valyrian steel sword at his wedding. He realizes that Joffrey stole the Valyrian steel dagger with the dragonbone hilt from his King Robert, who had won it from Littlefinger but didn't care about just another blade. It was Jaime, later in the same book, who figured out why Joffrey would have done such a thing. After hearing Robert opine at Winterfell that Bran would have been better off dead than crippled, Joffrey took it upon himself to try and have Bran killed in the hopes of pleasing the man he believed to be his father. In the book saga, the famous dagger was originally Littlefinger's, won by Robert in a bet, stolen by Joffrey, and given to an assassin to kill Bran.
Joffrey technically never came out and admitted to sending the assassin, but both of his uncles were convinced, and Cersei didn't argue much in her son's defense when Jaime shared his theory. George R.R. Martin pretty definitively answered the question of who tried to have Bran killed, and it was Joffrey.
Now that we're in Season 7 of Game of Thrones, the plot has long advanced beyond the plot of A Storm of Swords that would have allowed Tyrion and Jaime to easily jump to the conclusion that Joffrey sent the catspaw with the dagger. If the show means to have either of them realize that Joff was to blame, it will have to go in a different direction from the book. Joffrey's cruelty is a thing of the past and has been surpassed by the likes of Ramsay Bolton (and arguably Euron Greyjoy). The time may have passed for it to really matter if Joffrey is the one responsible for the whole mess with the dagger.
The dagger is finally back in play in Season 7, brought to Winterfell by Littlefinger and given to Bran, who then gave it to Arya. When she asked who would arm a common assassin with a Valyrian steel blade, Bran suggested that somebody very wealthy wanted him dead at the time. That could have been Bran connecting the dots between the valuable blade and the nobody who tried to kill him, or it could be a sign that he used his abilities as the Three-Eyed Raven to learn the truth about who made the attempt on his life, but simply doesn't care anymore.
If Bran used his Three-Eyed Raven abilities, the show could simply have him reveal that it was Joffrey and have that be the end of it. We'd have an answer to one of the longest-standing mysteries of the series, and that would be that. Alternately, Game of Thrones could go in a brand new direction and reveal that some other wealthy person wanted him to die. If not Joffrey, Jaime or Cersei could have been the culprit. Jaime's not one to get somebody else to do his killing, but it would undoubtedly win him a spot on Arya's list if he was the one to have ordered Bran's death, and that could be entertaining. Cersei likely wouldn't be held back from ordering the death of a child, given how little she seemed to care about Joffrey's purge of Robert's bastards (other than Gendry) in Season 2.
Then again, the Lannisters aren't the only wealthy people of Westeros. Besides, if Bran didn't delve into the past to figure out the mystery of who tried to kill him, then his statement that a wealthy person sent the assassin is just a guess. The person who had the Valyrian steel dagger between when Littlefinger lost it and the assassin tried to use it is the key. In fact, Littlefinger himself isn't out of the question. He loves Sansa because she reminds him of Catelyn; he might not be so sentimental about any kids that Catelyn had with another man. Who knows? Maybe it was Robert himself in a huge lapse of love for Ned. Stranger things have happened on Game of Thrones.
At the end of the day, we still don't know who ordered the assassination of Bran in the show. If we do ultimately discover that it was Joffrey after his trip to Winterfell just as it was in the book, Game of Thrones will almost certainly have to change the reveal. Tyrion has no reason to suddenly realize why Joffrey might have been familiar with Valyrian steel, and Jaime probably won't spare any thoughts for the Stark kids now that he's facing dragons (or is dead). We'll have to wait and see. The return of the dagger means we'll likely find out the person who sent the man to kill Bran. The blade surely means something, especially given that Valyrian steel will be a valuable tool in the Great War.
You can catch the next new episode of Game of Thrones this Sunday at 9 p.m. ET on HBO. For your viewing options once Season 7 comes to an end, our fall TV premiere schedule can help you out. In case you're not up on what has been renewed and what has been cancelled on the small screen, check out our breakdowns for cable/streaming and network TV. Lastly, don't forget to take a look at our picks for 9 wild Game of Thrones theories that just might be true.