The bootstrap paradox is a paradox that plays an important role throughout the Zero Escape series. Each game contains some elements that are a direct result of the paradox, despite the series never referring to the paradox directly by name. An example of the paradox is as follows:
Suppose a man discovers a note on a bookshelf instructing him on how to create a time machine. The man creates the machine, and after using it to travel back to the past, places the note back on the bookshelf. If this is the case, then where did the note originally come from?
Nine Hours, Nine Persons, Nine Doors
Akane Kurashiki's survival was a matter of the bootstrap paradox. When Akane was trapped in the incinerator at the end of the First Nonary Game by Gentarou Hongou (Ace), she needed to solve a Sudoku puzzle in order to escape. However, during this time, she foresaw that Junpei, 9 years in the future, during the climax of the true ending to the Second Nonary Game (which is the main plotline for 999), would solve the Sudoku puzzle -- Akane would take Junpei's solution to save herself.
So as a result, Akane survived because Junpei helped her, and then needed to create the Second Nonary Game (in conjunction with her brother Aoi Kurashiki and the rest of Crash Keys) to allow Junpei to find the solution.
Though if this is the case, it leaves the question of how Akane saw the solution in the first place in the air. It can be interpreted that information in the Morphogenetic field is timeless.
Virtue's Last Reward
The entirety of the Nonary Game: Ambidex Edition is an instance of the paradox. Sigma Klim, in his older age as Zero Sr., would create the game -- but he would only create it after his 22-year-old consciousness observed it in the first place. Therefore, where did the original envisioning of the game come from?
(For another paradox introduced in the game, see: Schrödinger's Cat)
Zero Time Dilemma
Also see: Bootstrap paradox in Zero Time Dilemma
Phi and Delta are further instances of the paradox. During D-END: 2, Sigma and Diana, trapped with no hope for escape in the Mars Mission Test Site, bond and create Phi and Delta, sending them back to the past with the Transporter. However, in this instance, they name Phi after their memories of her. But if this is the case, then Phi would be named after herself. It is also implied that the original Phi was Phi's own mother.
Likewise, if Delta was not born yet in the D-END: 2 ending, then it is somewhat confusing that the test site (built by Delta) could exist at all in this ending.