I figured that the two were equivalent. If we find something that magic does not consider information (but we do), we can use it to receive information from an arbitrarily far future.

For example, suppose that magic does not consider merely "Does a timeturned person show up at time T at this location or not" to be information, and we want to know if the world ends in the next 10 years.

Four people with time-turners agree to the following scheme (using Unbreakable Vows if necessary):

• If, at 12:01 AM on March 14th, 2025, the world has not ended, Alice goes back 6 hours using a Time-Turner.
• If, at 6:01 PM on March 13th, 2025, Bob sees Alice appear out of nowhere, he goes back 6 hours using a Time-Turner.
• If, at 12:01 PM on March 13th, 2025, Carol sees Bob appear out of nowhere, he goes back 6 hours using a Time-Turner.
• If, at 6:01 AM on March 13th, 2025, Dan sees Carol appear out of nowhere, he goes back 6 hours using a Time-Turner.
• If, at 12:01 AM on March 13th, 2025, Alice sees Dan appear out of nowhere, he goes back 6 hours using a Time-Turner.
• ...

Also, they make sure that in case of anything not world-ending, they will have a substitute available so that the chain will not break.

After agreeing to this, if Alice sees Dan appear out of nowhere at 12:01 AM tomorrow, then they know that the world has not ended. If not, then something sufficiently bad to cause the chain to break must have happened in the next 10 years. (Either way, they must continue to implement the plan for as long as possible.)

Using further chains of Time-Turners, we can use our favorite unbounded binary search scheme to narrow down a more precise date for the world ending.

(Edit: actually, we can probably improve the resolution simply by using the Time-Turners at a different specified time depending on circumstances.)

This story will collapse after a very few prior incantums on Quirrelmort's wand by the investigators.

This is the real magic, when you see something impossible happening. I had no idea how you can realistically beat immortal and powerful dark wizard.One "Obliviate" and your perspective shifts and that's it. It now looks pretty simple despite being impossible 5 minutes ago.

I just noticed something:

Chapter 79:

When he was alone in the room, the old wizard looked down at the map, which had now written upon itself a fine line drawing of the Gryffindor dorms in which they stood, the small handwritten Albus P.W.B. Dumbledore the only name left therein.

The old wizard smoothed the map, bent over it, and whispered, "Find Tom Riddle."

Chapter 108:

"Yes," Harry said in an even voice. "What did you do to the Weasley twins? Dumbledore thought - I mean, the school saw the Headmaster go to the Weasley twins after Hermione was arrested. Dumbledore thought you, as Voldemort, had wondered why Dumbledore had done so, and that you'd checked on the Weasley twins, found and took their map, and Obliviated them afterward?"

"Dumbledore was quite correct," Professor Quirrell said, shaking his head as though in wonderment. "He was also an utter fool to leave the Hogwarts Map in the possession of those two idiots. I had an unpleasant shock after I recovered the Map; it showed my name and yours correctly! The Weasley idiots had thought it a mere malfunction, especially after you received your Cloak and your Time-Turner. If Dumbledore had kept the Map himself - if the Weasleys had ever spoken of it to Dumbledore - but they did not, thankfully."

It seems like Dumbledore knows quite a bit more than Voldemort thought. Did he know Q=V and HJPEV=TMR?

And finally, Chapter 110:

"I am there," Albus Dumbledore said, "and also inside the Mirror, unfortunately for you. I have always been here, all along."

Always? That's an odd turn of phrase. Who was elsewhere?

Not in HPMOR.

Chapter 16:

Yes, I was in Slytherin and I am offering to formulate a cunning plot on your behalf, if that is what it takes to accomplish your desire.

We don’t know enough details about how the Horcrux Network and the Special Connection between V and H work, but …

"OBLIVIATE!"

And it all poured out of Harry into the spell.

Harry fell over on his side, dropping his wand, gritted screams coming from his throat, his hands going helplessly to his scar, even as the sudden blast of pain in his head began to fade. Only dimly did his eyes see that the air was filled with glowing snowflakes, drifting motes of silver light like tiny specks of Patronus Charm.

… this is highly unusual for an obliviation, so I think it is very likely that V has not left his body.

I don't believe leveraging Voldemort's bargain will work the way you suggest, because Parseltongue does not enforce promises, only honesty. When Harry demands that he himself be saved, Voldemort can simply say "No."

Harry's assets:

• Glasses - probably a distraction, but could be just about any nonhuman object, transfigured.
• Cedric - probably in the mokeskin pouch, not easily accessible, probably only useful as a human shield, which is not Harry's style
• Invisibility cloak - might be able to block the Killing Curse, useful in general, Harry is the Master of this Deathly Hallow, it's plausible but unlikely that he'd be able to Call it without words or gestures.
• Voldemort's bargain - Voldemort has promised in Parseltongue to protect one person for each power Voldemort knows not that Harry names.
• Partial transfiguration - both a Power Voldemort Knows Not and a tactical tool
• Wand
• Harry's own flesh (which he can use for partial transfiguration)
• The air
• The death eaters (including their robes, their bones, etc.)
• Sirius ("Mr Grim")
• Stuporfy

Foreshadowing / prior hints of resources:

• Thick/heavy enough physical objects can block curses aside from the Killing Curse
• Resonance between Harry's and Voldemort's magic more likely to harm/incapacitate Voldemort than Harry
• Harry was instructed by Voldemort to cast Mahasu on any student in the classroom, chose himself. Foreshadows choosing to use promise of protection on himself?
• Antimatter was mentioned earlier, Voldemort may not know enough about it yet.
• Hermione transfigures a Buckytube
• Use of Muggle devices
• Harry's prior weakness is that he doesn't ask others for help
• Harry decided to accept the idea that the air can't be transfigured before he figured out the insight necessary to do partial transfiguration, this could be wrong, the air as well as his flesh could be transfigurable
• Prophecy about tearing apart the very stars (meaning Sirius and Bellatrix and Draco?)

Harry had to remove his left shoe, and take off the toe-ring that was his emergency portkey if someone kidnapped him and took him outside the wards of Hogwarts (and didn't put up anti-Apparition, anti-portkey, anti-phoenix, and anti-time-looping wards, which Severus had warned Harry that any inner-circle Death Eater would certainly do).

That seems to rule out apparition, portkeys, phoenixes, and time looping, so transfiguring a time turner into his hands is out, as is trying to get into a Phoenix frame of mind to summon Fawkes or another phoenix to send a message, or using his portkey.

"There are desks which are heavy enough to be fatal if dropped from a great height. There are chairs with metal legs that could impale someone if driven hard enough. The air in this classroom would be deadly by its absence, since people die in vacuum, and it can serve as a carrier for poison gases."

Harry had to stop briefly for breath, and into that pause Professor Quirrell said:

"That's three. You need ten. The rest of the class thinks that you've already used up the whole contents of the classroom."

"Ha! The floor can be removed to create a spike pit to fall into, the ceiling can be collapsed on someone, the walls can serve as raw material for Transfiguration into any number of deadly things - knives, say."

"That's six. But surely you're scraping the bottom of the barrel now?"

"I haven't even started! Just look at all the people! Having a Gryffindor attack the enemy is an ordinary use, of course -"

"I will not count that one."

"- but their blood can also be used to drown someone. Ravenclaws are known for their brains, but their internal organs could be sold on the black market for enough money to hire an assassin. Slytherins aren't just useful as assassins, they can also be thrown at sufficient velocity to crush an enemy. And Hufflepuffs, in addition to being hard workers, also contain bones that can be removed, sharpened, and used to stab someone."

By now the rest of the class was staring at Harry in some horror. Even the Slytherins looked shocked.

"That's ten, though I'm being generous in counting the Ravenclaw one. Now, for extra credit, one Quirrell point for each use of objects in this room which you have not yet named." Professor Quirrell favored Harry with a companionable smile. "The rest of your class thinks you are in trouble now, since you've named everything except the targets and you have no idea what may be done with those."

"Bah! I've named all the people, but not my robes, which can be used to suffocate an enemy if wrapped around their head enough times, or Hermione Granger's robes, which can be torn into strips and tied into a rope and used to hang someone, or Draco Malfoy's robes, which can be used to start a fire -"

"Three points," said Professor Quirrell, "no more clothing now."

"My wand can be pushed into an enemy's brain through their eye socket" and someone made a horrified, strangling sound.

"Four points, no more wands."

"My wristwatch could suffocate someone if jammed down their throat -"

"Five points, and enough."

"Hmph," Harry said. "Ten Quirrell points to one House point, right? You should have let me keep going until I'd won the House Cup, I haven't even started yet on the unaccustomed uses of everything I've got in my pockets" or the mokeskin pouch itself and he couldn't talk about the Time-Turner or the invisibility cloak but there had to be something he could say about those red spheres...

This vaguely suggests a few options:

• Harry could improvise a dark ritual to sacrifice some of his internal organs to "hire an assassin" (counting on some sort of magical healing afterwards).
• Susan Bones might also be in the pouch ("Hufflepuff [...] Bones"). Note that the real Susan Bones was not with the other students who encountered Snape in the corridor.
• Harry likely knows of some efficient poisonous gases, if he can hold his breath for long enough he can simply transfigure part of himself into one of these and wait for the Death Eaters to drop.
• Harry could somehow try to cast a spell on Voldemort to invoke the resonance, push him in a direction that disrupts the semicircle of Death Eaters.
• Harry could transfigure the air around him into a thick physical barrier that blocks everything except the Killing Curse.

Ignoring the gasps rising from behind him, Harry crossed the radius of the Patronuses, strode to a single pace from Death. Its unhindered fear burst around him like a whirlpool, like stepping next to the sucking drain of some huge bathtub emptying out its water; but with the false Patronuses no longer obscuring the level on which they interacted, Harry could reach the Dementor even as it could reach him. Harry looked straight into the pulling vacuum and -

the Earth among the stars

all his triumph at saving Hermione

someday the reality of which you are a shadow will cease to exist

Harry took all the silver emotion that fueled his Patronus Charm and shoved it at the Dementor; and expected Death's shadow to flee from him -

• and as Harry did that, he flung his hands up and shouted "BOO!"

The void retreated sharply away from Harry until it came up against the dark stone behind.

Harry can sort of wandlessly wordlessly cast something like a Patronus, he could try to do something like this to Voldemort.

Beneath the moonlight glints a tiny fragment of silver, a fraction of a line... (black robes, falling) ...blood spills out in litres, and someone screams a word.

This strongly suggests a Buckytube monofilament whipped around to decapitate all the Death Eaters. This is the most plausible solution, and it's somewhat compatible with the other Partial Transfiguration option, which is to tell Voldemort about it in exchange for protecting Harry's life (and to buy time). This is also compatible with Harry's glasses being a transfigured shield (or transfigured charmed magical shield, in either case there's no reason someone couldn't have just magically LASIK-ed his vision), which would give him a defense against any non-Killing Curse spells that go his way from anyone he doesn't immediately kill. Then he lunges for (or accios) the pouch and cloak, retrieving Hufflepuff (Susan) Bones and Cedric, to help him fight the remaining Death Eaters (or go for help). Then he casts a Patronus to get McGonagall (and insists she not disrupt the game).

Ah, better yet - the glasses should be his broomstick. Or his broomstick AND a shield. AND a gas mask. Fit together (since glasses are composite objects anyway).

OK, so here's the attack plan, to tear apart Voldemort's plan at every possible point of intervention:

1) While transfiguring a long buckytube monofilament out of his own flesh, tell Voldemort about partial transfiguration, demand that Harry himself be saved in return.

2) Wordlessly cast the Patronus at Voldemort to try to throw him off balance - as a bonus, if he manages a worldess wandless corporeal Patronus it can do step 5 early, OR possibly block a Killing Curse (not sure).

3) Whip the buckytube around to slice through a bunch of Death Eaters. Simultaneously, wordlessly wandlessly finite incantatem the glasses to detransfigure his broomstick.

4) Fly to (or accio while dodging curses) the pouch, extract Susan and Cedric, put on the cloak. They know from battle class that they should lift the sleep spell on their ally Hermione. (Harry shouldn't since it would be an interaction with Voldemort's magic that would be more likely to harm Harry than Voldemort.)

5) Cast a Patronus to get help from McGonagall (who can use her time turner so as not to disrupt the game), telling her to bring every competent battle mage she can get.

6) Cast Stuporfy at Voldemort to try and trigger the magical resonance, then fly straight at him to give him a hug.

A couple of problems:

Dumbledore just cast himself from time in order to fulfill the prophecy about Harry Potter.

Everything we've seen of Dumbledore shows him to be a man who thinks in stories. I can't see him fulfilling a prophecy by cheating, especially given that he's already lost a friend due to a failed attempt to mess with time. (plus it would raise the question of why he's spent the whole story telling everyone that Voldemort is Harry's fated foe)

For that matter, that is a hard prophecy to make apply to Harry and some new dark lord. What other candidates do we have for the "him" of "born to those who have thrice defied him"?

I don't know what the "stone of resurrection" actually is, but I think Voldy will not like what it does, not one tiny bit.

The only way Voldemort would know that the Stone of Resurrection grants him free-floating ghost powers is by testing it out, since no one has ever been able to use it in that fashion before. We must assume that he's tested it, and whatever else it does, it really does possess that devastatingly powerful function. How and why would Dumbledore and co. fake that?

I think that since this story is Harry Potter and the Methods of rationality, its going to be Harry who saves the day. But if this wasn't a story...

Harry is in a totally impossible position (baring some experimental transfiguration). The best hope lies with McGonagall. She's been seen going off scrip before and if she realises the magnitude of the threat Volde now poses (perhaps Harry could impress this upon her, and point out that Volde has recently resolved to stop wasting time and just take over the world) she might realise that the only way left to stop Volde is to go totally off-script, and seek help from the Muggles.

While a gun can't hurt a shielded wizard, the shielding only has so much strength. Bring in the Muggle army with overwhelming numbers, heavy weapons, helicopter gunships and so forth. Wizards have access to apperation, dissilusionment etc which might still allow them to win against a pure muggle army, but a combine force of Muggles and Wizards would also have access to anti-apperation jinxes and so forth.

Admittedly, this ends centuries of secrecy. Therefore, the second option she has is to go to the Wizard UN or whatever their equivalent is, and explain that without reinforcements she will be forced to go to the Muggles for help.