What the chronicle strongly implies but never states outright, and what the author has said beyond the page — set apart from the established record, and never sworn to by the maesters.
Theorized
Five direwolf pups found in the summer snows for five trueborn Stark children — and, set apart from the litter, a white runt with red eyes for the boy called bastard. The old gods rarely speak so plainly; the odd wolf out reads as an omen that Jon Snow was ever a thing apart from his father's house.
SourceA Game of Thrones, Bran I
Theorized
The realm speaks of a single savior of the Long Night, yet the sources hold two figures who need not be one man. The fire-priests of the east name Azor Ahai, who forged the sword Lightbringer against the dark — a hero the eastern tales also call Eldric Shadowchaser. Westeros remembers instead the Last Hero, who sought the children of the forest through the killing winter with a failing blade and a dwindling band. The legends rhyme but do not match, and the Last Hero's deeds — the mustering against the Others, the founding of a line of winter kings — read as the work of the first Stark, Brandon the Builder, though no maester can bind the two tales into one.
SourceThe World of Ice & Fire, "The Long Night" & "The Age of Heroes"
Theorized
Legend heaps every wonder of the North upon Brandon the Builder — the Wall, the raising of Storm's End, Winterfell itself — yet the tales never quite say he built Winterfell so much as raised it, and a careful reading suspects a smaller, stranger truth: that his hand set the enceinte round the godswood and delved the Crypts beneath, whose deepest vaults, some whisper, may keep more than the bones of dead kings. No maester can attest to a man who lived, if he lived at all, eight thousand years gone; this is a reading of the chronicle, and is set down plainly as such.
SourceThe World of Ice & Fire, "The Kings of Winter" — a reading the maesters cannot confirm