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BACKSTORY
• Freddy Fazbear Diner opens in '83.
• Purple Guy + Co. are hired, business as usual.
• Purple Guy's son/daughter has a run-in with bullies at Fazbear Diner; child is bitten by Golden Freddy (Bite of '87)
• Child dies, Purple Guy goes crazy and kills security guard. Later kills bullies disguised as Golden Freddy.
• Spirits of children chase Purple Guy into Springtrap; Purple Guy is killed.

FNAF 1
• Purple Guy is "always there" as Springtrap locked away in extra room.
• Child possessed Golden Freddy. 1-9-8-7 on custom night triggers Golden Freddy kill-screen due to vengeful child.

FNAF 2
• Security guard from '87 possesses Puppet to aid the bullies in killing "threat" (Purple Guy is still "present"; PC hides in Fazbear head, mistaken for threat)
• Pieces of FNAF 1 animatronics still visible in Freddy Fazbear's Pizza.

FNAF 3
• Springtrap is released. Puppet is still about and eventually burns down Freddy Fazbear's Fright to end the reign of Purple Guy.
• Pieces of FNAF 1+2 animatronics still visible in Freddy Fazbear's Fright.

FNAF 4
• The "nightmares" have been released into the world (classic "you never know where they're going to be; they could be ANYWHERE *bum bum BUUUUM*")
• Child must fend off nightmares.

Foxy is thrown into the loop strictly because he was Purple Guy's "favorite"

Fnaf 4: Story origin
Animatronics Status:
• Fazbear and "Mangle" Foxy Completed/Functioning
• Bonnie as a prototype for future inclusion with restaurant's growing popularity
Events:
• Purple Guy is hired
• Purple Guy is attacked by Foxy (Bite of '87. Also where Purple Guy starts developing his future bias towards Foxy as revealed in the recordings (a form of stockholm syndrome)
• Purple Guy goes to hospital where they piece his brain back together (he's never the same after this)
• Purple Guy comes back and starts killing kids as Golden Freddy
• Spirits of kids chase after Purple Guy who hides inside Golden Bonnie and is crushed to death (A phone call informs the player of Purple Guy biding his time in a room while the animatronics bang on the door. This could be him tampering with the Golden Bonnie suit to allow him to fit in it and hide, though it all goes wrong and the suit constricts around him due to the missing mechanisms keeping it in place)
• Room is boarded off and restaurant eventually closes

Fnaf 3:
• Springtrap (Golden Bonnie) is found in abandoned Fazbear Diner along with prototypes and misc supplies. These are found strewn around Fazbear's Fright during the game.
• As evidenced by a previous theory, Springtrap approaches the player in order for them to "free/save him". Springtrap's demeanor during the death sequence would appear that he's less prone to immediate violence than the vengeance-drive animatronics that follow.
• Purple Guy's brain has deteriorated during his time spent locked away as Springtrap, resulting in the zombie-like level of reasoning that I believe this theory aludes to.
• During the game's bad ending, the player didn't put an end to Springtrap and the childrens spirits haven't been avenged, leading to Fnaf 1. In the good ending, Springtrap has been destroyed along with the building during a fire and the childrens spirits are at rest.

Fnaf 1:
• First rendition of the official Freddy Fazbear's Pizza opens. Prototypes have been finished by restaurant chain producers and are released as Freddy, Bonnie, Chica and Foxy, though Foxy falls into disrepair.
• Purple Guy's spirit now inhabits Golden Freddy which would explain his ability to teleport into the room while the doors are closed (paranormal activity). This is a callback to his murderous origins. This also fills in the Purple Guy's need to come back as he "always does".
• 1/9/8/7 resulting in a Golden Freddy death screen is a double reference both to the Purple Guy himself and him being the victim of the Bite of '87 which angers him resulting in the player's death. The handprints on Freddy's face are also symbolism for his ties to the Purple Guy and his fate.
• Through the game, the animatronics are trying to stop the security guard from doing his duty out of their quest for vengeance against the last security guard who killed them (Purple Guy). Holding them off results in their eventual "tampering" and the security guard's being fired.
• Obviously the protagonist doesn't actually tamper with the animatronics as he's always kept himself away from them until 6 AM each day. Instead, the spirit of Purple Guy used his knowledge of the inner workings of the animatronics to tamper with them and dismantle them (perhaps to use the wreckage to piece back together his favorite animatronic, Foxy).

Fnaf 2:
• Second rendition of Freddy Fazbear's Pizza (the grand re-opening).
• Technologically advanced animatronics are built to be able to reference from a criminal background database and identify people accordingly (implied present-day setting). Animatronics are also redesigned to be more sleak and appealing to a modern audience (Toy Chica also gaining a very feminine figure compared to her earlier version which may be the result of a societal movement towards sexual openness).
• Purple Guy now inhabits the body of "The Puppet"; its appearance a physical manifestation of the tortured/crying children that he murdered (he now carries the same face).
• His ties to the puppet are furthered solidified with him being the sole animatronic (besides Foxy*) to react to the security guard regardless (or perhaps, especially) of the Fazbear mask the player can hide behind, which - like Golden Freddy's 1/9/8/7 death screen in Fnaf 1 - is a sign of anger or an act in retaliation to perceived mockery.
• Once again the security guard does the Purple Guy's bidding in holding off the animatronics, resulting in the store being closed for good.

*Foxy and the Purple Guy are closely linked following the events of the Bite of '87. This plays a role throughout the entire series.