After Season 7, Episode 6, a lot of people spotted something funny about the eye on Longclaw, Jon's sword, when Jon emerges from the water after the wight battle.
Yep, many thought Longclaw's eye "opens".
Which spawned theories that the sword might be alive, and connected to Jon.
Sorry if you're a fan of this theory, but the director of Episode 6, Alan Taylor, has officially called bullshit on it.
So there you have it. Whether it's water or frost or some kind of reflection – Longclaw is most definitely not alive.