Karaethon Cycle

The Karaethon Cycle is a set of prophecies in Robert Jordan's The Wheel of Time series of novels.

The Karaethon Cycle says that the Dragon will be reborn on the slopes of Dragonmount, where he died during the Breaking of the World.

• Rand

"Blood of our blood mixed with the old blood, raised by an ancient blood not ours. On the slopes of Dragonmount shall he be born, born of a maiden wedded to no man."

This is a reference to Rand's heritage. His mother was Tigraine (Queen of Andor) who fled Caemlyn, on the advice of an Aes Sedai, to the Aiel Waste to become a Maiden of the Spear, of the old blood. His father was an Aiel chief who came the closest to uniting the Aiel for anyone coming before the Car'a'carn, of our blood. Taringail Damodroed of Cairhien was used to create an alliance between Andor and Cairhein when Tigraine left for the Aiel Waste the Cairheinin King, thinking the alliance abandoned, made a throne out of the Avensora or Tree of Life which cause four Aiel Clans to come over the Dragon Wall in the Aiel War. It is speculated that Rand was conceived during the Aiel invasion of Cairhien and then born under Dragonmount during the Aiel attack on Tar Valon. He was then adopted by Tam who was of The Ancient bloodline from Manetheren, who resettled in the Two River's region of Andor. its from the aiel point of view our blood rands father mixed with the the old noble blood of tigraine and raised by the old blood from manetheren in emonds field where manetheren died.

"When the winds of Tarmon Gai'don scour the earth, he will face the Shadow and bring forth Light again in the world."

"Twice and twice shall he be marked,
twice to live and twice to die.
Once the heron, to set his path.
Twice the heron, to name him true.
Once the Dragon, for remembrance lost.
Twice the Dragon, for the price he must pay."
"Twice dawns the day when his blood is shed.
Once for mourning, once for birth.
Red on black, the Dragon's blood stains the rock of Shayol Ghul.
In the Pit of Doom shall his blood free men from the Shadow."
The Great Hunt - Chapter 26, pg. 387

This is a reference, at first to the two herons branded into Rands hands. The first happened in The Great Hunt during one of the "dreams" from Ishamael, 'setting' his path towards admitting to him self that he is the Dragon Reborn. The second occurred at the end of the second book The Great Hunt when, after the fight with Ishamael, the image of the heron on his sword is branded into his hand. The Dragons were marked together, while Rand was in the 'remembrance' ter'angreal in Rhuidean showing him the history of his parentage (Aiel history from the point of view from his direct ancestors), 'for remembrance lost'. the second for the price he must pay (the bleakness). It is Speculated thet the two times his blood was shed were when Baalzamon and when Padan Fain attacked him and left him with two evil scars that have not fully healed.

• Mat

"Fortune rides like the sun on high
with the fox that makes the ravens fly.
Luck his soul, the lightning his eye,
He snatches the moons from out of the sky."

The first line refers to Mat's luck, how sometimes it is better than others, and as Mat notes seems to occur in waves
The second line describes how Mat, who is often associated with the fox, flees Ebou Dar with Tuon, therefore setting the Seanchan Ever Victorious Army on his heels, the raven being a symbol of the Seanchan Empire
The third line describes Mat's character, with luck being something he relies on heavily, and lightning symbolizing his ability to find a way out of most problems, but often with violent consequences. It is also worth noting the significance of "eye" rather than "eyes" as many fans speculate that Mat will lose an eye in the last book of the series - a theory reinforced by numerous dreams and visions seen by the characters Perrin Aybara, Egwene al'Vere and Min Farshaw.
The last line is clearly describing when Mat "kidnaps" Tuon, the Daughter of the Nine Moons (literally meaning the daughter of the empire), next in line to be Empress.