It all rests on a hunch.

In TGS we learned that "LTT" knew things about that sword he wasn't telling Rand. Rand put it out of his mind. It has not returned since.

My hunch is that perhaps Jordan has made it rest on the same para-arthurian (it's from the same era in origin/not belonging to the cycle) legends of "hallows" Rowling also used in the finale of Harry Potter.

Death in WOT is of course the DO, so Hallows that would let you master death....

There's a whole lot in Rowling's treatment of the legend that's purely her own. She's kept the triad of hallows and that's about it.

If RJ had similar hallows, they'd be three. Linked, and predating the AOL when they were just legends. What could they be?

One would be totally different from "invisibility cloak", in fact it's the reverse at it marks you as the Champion of Life. That would be the Dragon's Banner.

The other one is akin to the resurrection stone, and it's the Horn of Valere.

What of the third? The third would be Justice. What does it do? I haven't the slightest idea. It would be like trying to puzzle out what the Horn does if we had no clue about the legends about it.

I think perhaps Justice is the Dragon's soul Sword. It may not have any power in the real world, it could be meant to be used in Tel'aran'rhiod.

Hawkwing had it because LTT was incarnated and he was his surrogate as the Heroes's leader back in Falme.

The full thing goes this way: the Horn calls the Heroes, the Heroes follow the Banner only, they are lead by the one with the Sword.

I believe that sword has been LTT's in the AOL. Hawkwing in the real world got it, so that it could be given to Rand down the line.

We know about the Horn of Valere that it existed in the AOL, it wasn't etched, it sat in a museum as an artifact of an earlier age surrounded by legends. RJ said no one believe those legends any more than scholars today would, so no one had the silly idea to try the Horn.

I suggest the sword and banner also stood in museums, and were also linked to old legends (the connection with those about the Horn lost in time) about the Dragon, a saviour, kind of avatar or child of the Great Serpent, its champion. Those legends belong with a pre-channelling era, and the Great Serpent/tree of life etc. conception of the world. Pre-AOL.

I think as the WOS began, some (the Da'shain Aiel...) believed in the old legends and gave LTT the sword and banner, named him The Dragon, started calling themselves "People of the Dragon"/Children of the Dragon. LTT wasn't a believer, thought the whole thing ridiculous, didn't embrace the name and couldn't care less, but he found himself in the same inner debate as Perrin with his banners. Some believed, and to them in was an important symbol of hope. So LTT eventually let it stand.

So LTT had two "hallows" he didn't believe in and never even tried to use as the old legends said they had to be used. He missed the third. RJ said the Horn got lost in the chaos of the WOS before Foretelling appeared about its importance.

Now Rand has the three Hallows, and he knows the purpose of two for sure. And I think he knows the legends surrounding "Justice", it's what in TGS he wasn't "telling" Rand about the sword. To LTT's memories, that's still silliness. Not to Rand. What we miss now is the trigger that will make Rand ponder on how the Horn might come into play in TG.

I think RJ (well, Brandon) will give us all the clues, all the elements, before the Strike itself. What he won't give us is how it all comes together.

I get the feeling the part we will know the most about in advance will be what Nynaeve (a woman needs to lead that circle, no? You will know this!) does to the residues of the sealing as this will come from Min when she comes across the "belief an order make strength" line in a book and reads what comes after... and ties it to what else Fel believed. We might not know all that much after what Rand means to do after. I have the nagging feeling he will hide from Nynaeve he intends to die, will have arranged all that secretely with Alivia.