The following is based on Fallout 4 cut content and has not been confirmed by canon sources.
Vault 113 is one of the Vault-Tec CorporationVaults which was due to appear in Fallout 4. The Vault's original purpose in the Vault Experiment is unknown.
Appearances
Vault 113 was referenced in the game files of Fallout 4 in the form of an unused texture[1]. Also a piece of concept art found in The Art of Fallout 4 also depicts a male wearing a vault 113 jumpsuit.