Various spoilers ahead.
This will be resolved based on the future asoiaf books, sample/leaked chapters or author's notes if it becomes clear that the notes are all we're ever going to get. If the series is officially completed by an author other than George R. R. Martin, those books will also count. If the series is completed (or forever remains incomplete) but there's no definitive answer one way or another, will N/A or resolve to probability.
Clarification:
* R+L=J: Jon Snow is the son of Rhaegar and Lyanna.
* The notorious Pink Letter ostensibly by Ramsey Bolton is written by anybody other than him (presumably to manipulate Jon).
* Jojen-paste: Children of the forest have sacrificed Jojen Reed and the mysterious magical paste that Bran Stark eats is at least partially made of Jojen.
* Mad Queen Dany: by the end of the story Daenerys Targaryen becomes mad/evil/highly unsympathetic, a de-facto antogonist and ends up commiting greater atrocities than expected. Does not have to be literally insane. The way it went in the show would count as "Yes".
* King Bran: in the end, Bran Stark ends up ruling what remains of Westeros.
* Shireen burnination: Shireen Baratheon ends up sacrificed by Melisandre via burning to death, with or without approval of King Stannis.
* Aegon is a Blackfyre: Young Griff (supposedly Aegon Targaryen, son of Rhaegar) is secretly from the Blackfyre family, an offshoot of the Targaryen line and is therefore, an imposter.
* Nightlamp: Stannises battle plan is to lure the Bolton/Frey forces on the surface of the frozen lake and then make the ice break, drowning them.
* Lemongate: there's an inconsistency between Dany remembering seeing a lemon tree in Braavos and the repeated idea that lemon trees do not grow there. The theory is that this implies that she had spent her childhood elsewhere as a part of some secret plot.
* Bolt-On: Roose Bolton is an undying creature who stays alive by possessing his heirs, generation after generation.
* Somebody is Euron: some character from books 1-5 is secretly Euron Greyjoy in disguise/magical glamour or is posessed and controlled by Euron.
* Time-travelling fetus: Tyrion Lannister is a time-travelling son of Daenerys Targaryen and khal Drogo.
Related questions
If the series is completed (or forever remains incomplete) but there's no definitive answer one way or another, will N/A or resolve to probability.
Will you N/A or resolve to PROB? (I propose the latter. If you will N/A the questions, it introduces a strong bias: given theory will either be YES or N/A. They are unlikely to be directly refuted in the books.)
@Irigi Yes, that makes sense, I mostly intend to resolve unsettled stuff to probability. Maybe N/A will be appropriate in some cases, but stuff like the fetus theory is won't be it.
@Tasty_Y Thank you. Will you also use your judgement to prevent someone raising the probability on the last moment before close to gain profit?
@Tasty_Y Resolving to prob creates a different bias. It pushes prices toward 50%. I can explain this if needed.
I'm not sure about the argument in any case. Most of these theories are concrete enough that if untrue they will be expected to receive disconfirmatory evidence.
It's only the really weird ones (Bolt-On) that won't, and I think it's pretty fair to say that if you come up with an off-the-wall theory and no new evidence emerges to support it, we just resolve NO.
@MichaelWheatley Do explain using this example: imagine that in book one a character generates a random number from 1 to 10, we don't learn which. A theory is formed: "the number was 5". The true price should be 10%. Assume that I promise: "if later books don't reveal what number that was, I'll resolve it to the probability 10%". Does this incentivize traders to have the price closer to 50% (i. e. not at 10%)?
@MichaelWheatley in the case of this market: to whatever seems more fair to me when the moment comes, likely after discussing it with people. Probably some kind of compromise between the market price and the price that seems right to me.
Why do I want to resolve anything to probability anyway? We might end up in a situation where the story just stops and there will be no new information. If GRRM drops dead tomorrow after burning his manuscripts and the estate swears there will be no more asoiaf books by any other writers, what are we to do? I could just N/A the whole thing, but that doesn't seem fun. Seems more fair to reward the traders for moving the prices. In this scenario, I'd probably resolve everything to the current market prices. Not ideal, but it would probably be the least bad thing in that situation.
I can promise that if we somehow get all the books and they don't bother to specifically de-confirm some outlandish, specific and weird theory, I won't suddenly decide to resolve it to a high probability because I'm a big believer in fetus time-travel, it will be market price or lower.