Demon

Demons are a type of powerful being that exist within the Mindscape. They are able to be summoned with certain circles/symbols and incantations, and can make deals with those who summon them. They have a wide range of powers and abilities and can do nearly anything, given the right sacrifice and contract. The more powerful the summoned demon, the more powerful magic the contract will have.

Ranking

Demons are categorized into three (a fourth being theoretical) ranks - Legion, Spirit, Elite, (and Exalted). 

When getting more detailed however, there is a ranking scale that go from F to A to S and SS, least powerful to most powerful. F-class demons tend to be little more than smoke or tiny creatures, barely able to pop into the physical realm only when summoned or during a magical storm with natural portals opening. A-class demons are capable of destruction on a national level. S-Class demons could potentially endanger the entire world. SS-Class demons are more of a theoretical class that goes hand in hand with Exalted, and was actually proposed solely to accommodate Alcor, who can pop into the physical realm at will, and harbors a possibly unlimited potential that could eventually give him the power to alter reality itself.

Summoning

Demons, by default, exist in a non-physical state in which they cannot directly affect the material world or communicate with the majority of beings in that world. Humans or other physical beings wishing to make contact with a demon must summon the demon to the physical plane.

To summon a demon, a person must typically draw a specific circle (usually one with symbols specific to the demon and a binding circle element to protect the summoner), recite an incantation with the demon's name or title, and make a sacrifice or offering (typically blood or a dead animal, but everything from candy to human sacrifice can be used successfully with the right demon). Summoners typically draw circles in chalk or blood on a solid-surface floor and surround the circle with lit candles. Candle scent and chalk color may be changed according to the demon being summoned, as different demons have different preferences and may be more or less likely to show up based on these details.

In most cases, the intent and will of the summoner are more important than the physical details of the summoning. A person with a strong desire to summon a demon will likely be able to even with a pencil-and-paper circle, botched incantation, and small offering, as long as the demon is not exceptionally powerful or busy.

Cults

The Cult of Dipping Sauce

An official cult created by Casie.

The Gathering of the Seven Hands

A cult that hold's the demon Zadkiel as their savior and main focus of worship. After surviving a previous run-in with Dipper and Mabel, they would later try to offer her and Henry as sacrifices to their lord. Of course, Dipper didn't let them get away with it.

Types

Dream Demons

Masters of the mind. They also keep nightmares (and in Alcors case dreams) as their subordinates. The apearance of these nightmares (and dreams) changes to fit their current master. Ex: Alcor has sheep.

Barrier Demons

A type of demon potentially able to break through the very "barriers upholding reality".

Time Loop Demons

A looper demon will look for a likely victim; preferring mortals of the heroic, wilful, stubborn or highly tenacious variety. They study their victim for weeks or months on end and look for weaknesses.

Then they setup a way to lure them towards a semi-remote location with some form of physical limitation on the outside, generally along with various other people, loved ones, friends, maybe some enemies or acquaintances.

Then they cause a series of unfortunate events, manipulating thoughts, illusionary sights, arranging accidents, pushing others to kill each other- all throughout the span of a single night.

Making sure to leave their intended victim as the last survivor, then they appear, with an offer:

“You have met with a  terrible fate have you? But dear child I offer you a way out. To undo all that’s happened. But first I want to play a game. The clock shall turn back to when the moon rose and your fellows shall rise again, no memory, no injury. A clean start for all including you, but your mind shall remind unchanged. Here is my game; Save your fellows before Sunrise and you may avert your fate, but fail and it shall all begin again. Defeat me and you may go with your fellows. But if at Sunrise you have failed I shall stand before you and offer you the option of surrender or to try again. Surrender and you’re soul is mine, and your friends may pass over, refuse and you may continue until you find the answer.”

Of course such a highly specialised is good at short term Temporal manipulation and apt on a general level with most forms of manipulation.

When they are in the middle of a looping cycle they have an incredibly powerful source of power fuelled by the deaths, the emotion, the trapped souls and the stubbornness of the main victim and the subsequent emotions from the victim slowly going mad.

Of course this also means that these locations are their weak points. If someone can enter the temporal loop.  They can cause the entire thing to unbalance by introducing unknowns into the entire problem crafted by the looper demon

The other solution is that the main Victim is able to actually beat the demon, an almost impossible proposition since the Demon holds all the cards.

Looper demons react badly if they see with someone who isn't supposed to be in their loop.

Known Demons

Kushiel

A demon who poses as an angel in order to manipulate others. His summoning circle is that of hands clasped in prayer, usually paired with thoughts of divine retribution. The summoner will see him however they imagine an angel to be, but when he is sent out to do his work, his target will see him as he truly is. He often tricks people into thinking they will be going to heaven, and then devours their souls.

Morsus

A powerful barrier demon within Gravity Falls. During the Transcendence he was let loose for some time and caused havoc.

zk’Alfrubash

Soul Eater, Bringer of Darkness, Blood Fiend

This is a demon relatively powerful demon who eats the souls of those sacrificed to him in return for his power. Has been known to gift his cultists demonic powers. Once has a dispute with Alcor and has not been seen since.

Brian

A sentient amalgamation of organs in the shape of a duck. He's most notable for being elected president of the United States.

Dave

The demon of patience (class F). He takes the form of a golden slug.

Chole

She used to be a demon, but ascended to a goddess.

The Tailor

The Tailor is a humanoid, ram-headed demon (possibly formerly a member of Dipper's flock) who keeps a tailor shop in the mindscape.

Kellior

The main object of worship of Maka's cult.

Desmona

A demon who brought misfortune to Toby since she first recognized his soul as Bill Cipher's while he was a baby.

Miss Dellen Take

A fairly lenient yet powerful demon who specializes in helping school children with things such as proofreading.

Ebony

The personification of fandoms and their doings.

Xethis

Xethis is a demon that offered to provide Alcor with a demon child, for naught but the cost a single dram of his power and night in her bed. She claimed that, in this way, she could even make one of the souls he favored- say Mizar, perhaps- immortal, so that he'd never have to let them go again. Alcor refused.

Canella

Canella is the cinnamon scented demon of schadenfreude, passive-aggressiveness, and petty revenge, and the only demon it’s considered appropriate to summon with store bought candles.  The glass jar she rides around in is actually a lesser demon she’s roped into doing her bidding.

Zadkiel

A fairly powerful demon covered in more eyes than skin that posses several sets of bird's wings.

Milchiresa of Unknown Darkness

The demon whom, along with Alcor, was responsible for the California Apocalypse.

Kashnalia 

A demon Dipper caught wind was eyeing his territory. He crushed him with a (bedazzled, curtesy of Mabel) skeletal puppet army of his own creation.

Melancholia 

The Fourth Humor (as in the four tempermants) Demon, representing Black Bile and its general associations. He constantly emanates an aura of sorrow. It should be noted, however, that this does not reflect his actual emotional state. He's fanboy of mortals and what they create, and is being inexplicably fascinated with Alcor the dream bender.

Sanguina

Sanguina is another humor, this time representing blood. She's quite chipper for a demon, and her favorite sort of sacrifice is something that can keep her entertained (such as a video game counsel). She's also Meloncholia's mortal enemy/friend.

Phlegmus

Phlegm's is a humor, and a friend of Melancholia's mother.