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This is a "Wild Mass Guess" entry, where we pull out all the sanity stops on theorizing. The regular entry on this topic is elsewhere. Please see this programme note.
Cube
The Cube series takes place in the Aperture Science Research Facility.
  • The first (purely mechanical) Cube was meant to stress-test potential research subjects. If you escaped with all your marbles, you were sent on to Portal Gun testing. The second Cube (featured in Hypercube) was a parallel experiment, refining the rather bendy physics used by Portal technology.
    • That is totally the kind of thing they would do!
      • But there was no Cake for the person who got out...
      • There wasn't any Cake in the Portal Gun experiment either.
      • There was. The Test Subject just didn't get any.

The two Cubes were developed or discovered by the SCP Foundation.
  • It just seems like something that would interest them.
    • Incidentally, nothing says the above two theories have to be mutually exclusive.
  • Hang on. It's stated that D-Class expendable personell can be taken directly from the public in times of shortage, if there aren't enough Death Row inmates to fill the quota. The characters are newly recruited D-Class, who haven't been formerly initiated since that would destroy the integrity of the test.
    • Hypercube keeps this rolling. The Foundation would definitely be interested in the Hypercube.
    • Still, Hypercube somewhat throws this into disarray because A. killing their own agents isn't their style even at the worst of times, B. it's implied that the hypercube was constructed by them and that definitely doesn't fit the SCP Foundation, and C. if Izon is a front company, the naming scheme doesn't match the SCP's usual way of doing it. However, all these things would fit Marshal, Carter and Dark. Theory: the original Cube is owned by the SCP Foundation, while the Hypercube is owned by MCD. Though, that leaves one question, why would the SCP Foundation interested in the original Cube? Well, it is wondered in the film if it's sapient and calculating...

The Hypercube is an experimental gateway to parallel universes.
  • The first cube was intended to test the reactions of humans when placed in unintuitive geometries. It proved that humans could, in principle, survive in a highly confusing space-time configuration. This was a precondition to the Hypercube, the actual purpose of the experiment. Assume there are three additional dimensions of time. Construct a singular cube room, place people in it, then rotate it from the spatial into these additional temporal dimensions - but your parallel-universe equivalents are doing the same thing, thus resulting in an infinite lattice of cubes in six now-spatial directions, joined at their entries/exits. But .. time isn't that neat. Maybe one of the parallel universes switched their cube on a microsecond later, maybe the atmosphere has a different composition, maybe some natural constant is subtly different - the rooms aren't traps, they're flaws in the lattice.

There is nothing outside the Cube.

The Cube is the only real thing. The memories of being in the real world are false. The prisoners were vat grown. When you go outside, you die almost immediately. Hypercube is another dimension.

The Cube is in space.

All survivors are shot out the airlock immediately. If they're particularly unlucky, they may have to listen to some poetry first.

The Hypercube is a failed attempt to recreate a TARDIS.
Just think about it. It's bigger on the inside, can manipulate space, time, gravity, etc. Some time ago, humans might have acquired a broken TARDIS and then built something that was supposed to resemble it. They failed.
  • Sounds like something The Forge or even the Silents would try.

Each room of the Hypercube has six interiors at a time.
The rooms rotate in three spacial dimensions; what's to say they don't rotate in four? This is how, before the collapse, some marked rooms seemed to contain variable contents. Whether the interiors each belong to one of six different internally consistent sets (forming the "parallel universes") or if each room has its own set of six interiors depends on how the cube was made. Simon has fewer than six of each kill trophy, so it could be either. If each room has more than 6^1 interiors, that really doesn't add any meaning to this guess other than narrowing down the possibilities of how the cube was unfolded/folded/formed/whatever. Obviously, this doesn't include the limited external room[s], since the external space in which the outside of the cube was kept seemed to be no larger than a single internal room.

Kazan knew that Quentin was going crazy.
In fact, he could tell a long time before anyone else did, but he couldn't communicate it to anyone else because of his severe autism (or brain damage, depending on your theory). That's why he yelped when Quentin was still in the sound activated spike cube.

The cube is a Lament Configuration.
A cube-shaped puzzle box with moving parts, which hides undescribable horrors and torrents of physical and psychological torture? Yup, I think we know what this is all about. Interestingly, note the opposition between people who solve the puzzle from the outside, hoping to reach the epitome of pain, and those solving it from the inside, trying to escape it.

Leaven was pretending that factoring prime numbers was harder than it was

She's obviously good at maths but spent ages on the first two numbers, which ended in "2" and "5". Given she was in a group of strange people, and was probably slowest and weakest, she pretended that her task was more difficult than it really was. She only seems to actually work hard (doing equations on the walls, etc) on problems that are more challenging. If she told the other people a few of the tricks for finding divisors of large numbers, or helped them tabulate all the powers of primes less than 1000, that would probably hurt her chances of survival.
Quentin was right it was a billionaire's sick joke.
Why else would the room they were looking for as a means to get out was in one of the rooms they should have stayed in the entire time.

The Hypercube is an attempt to simulate a multiverse.
It's ideal for simulating it. It has a starting point that can be traced easily (The activation of the Hypercube), allows easy surveillance (Since every "timeline/world" is a single room), and there is a limited amount of elements to keep everything simple and easily traceable. Of course, it was meant to be purely theoretical and at best involve no human subjects due to the natural ethical quandaries of the situation, but someone had the bright idea of putting human subjects in to allow for that free will aspect.

The cubes were made by the same people responsible for TheMazeRunner construct.
Again,seems like it might interest them.

The cube was created by Jigsaw.
He already knows how to design traps.

Kazan is imagining the cube.
He is just an autistic person playing with a Rubik's cube and imagining what it would be like if the cube was like this. The other characters are based on people he knows. Fridge Horror: Kazan is the only one to make it out because he wants the other characters' real-life counterparts to die.

The cube is Nintendo's Game Cube prototype.
Nintendo found a way to make players enter a virtual reality survival game. Unfortunately, the game erased their memories of the fact that it was a game. When they die, they are back in real life. Alternatively, when they die, they die in real life. In either case, Nintendo realizes that the game is too dangerous and decides to make a less advanced Game Cube.

Quentin was never really a police officer.
He lied. He was really a murdering rapist who was sent to prison. This explains his actions and how he knows about Rennes.
CSA The Confederate States Of AmericaWMG/FilmDamnatus

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