Just call him Schrödinger's Baratheon.
In a comment on his website, Song of Ice and Fire author George R. R. Martin confirmed to readers that while Game of Thrones' Stannis Baratheon may be dead, his book-Stannis is indeed alive.
"In my books? Alive, beyond a doubt," writes Martin, about the last-standing legitimate Baratheon.
This information proves that the letter Ramsay Bolton sends to Jon Snow in A Dance With Dragons is at least partly false, confirming Tormund Giantsbane's suspicions. In the letter, Ramsay wrote, "Your false king is dead, bastard. He and all his host were smashed in seven days of battle. I have his magic sword."
Of course, this information doesn't give much hope for show-only fans, as the episode's director David Nutter has confirmed the death of the show-Stannis.
So, Stannis is both alive and dead, depending on who you ask. Okay then.