While the main male character explains how time is looping he draws several circles on a virtual white board. He mentions that time loops every 3 hours 14 minutes and 15 seconds. The ratio of a circle's circumference to its diameter, is commonly approximated as 3.1415, commonly known as Pi.
The character, Sonny, gives his code name as Ouroboros, which is an ancient symbol of a snake eating its tail. This traditionally represents the infinite cycle of nature's destruction and recreation; life and death.
Automatic Repeat reQuest (ARQ), also known as Automatic Repeat Query, is an error-control method for data transmission that uses acknowledgements (messages sent by the receiver indicating that it has correctly received a data frame or packet) and timeouts (specified periods of time allowed to elapse before an acknowledgment is to be received) to achieve reliable data transmission over an unreliable service. If the sender does not receive an acknowledgment before the timeout, it usually re-transmits the frame/packet until the sender receives an acknowledgment or exceeds a predefined number of re-transmissions .
When Sonny is speaking to Mobius Command around the 39:00 minute mark, he mentions "Operation Riverrun." This is a reference to James Joyce's "Finnegan's Wake," (1939). The last sentence of the novel is a fragment, and completes the first line of the novel, forming a closed loop.
In an early scene (-1:19:43) when Hannah and Renton are attempting to escape while Father, Brother and Sonny are in the kitchen, you can clearly hear a broadcast in the background. In a section introduced by the phrase "Listen to the wise words of a madman," the speaker begins to cite one of Nietzsche's most famous summaries of his notion of the Eternal Recurrence. The citation is from a translation of Nietzsche's Die fröhliche Wissenschaft ("The Gay Science") #341 (Das grösste Schwergewicht = "The Greatest Weight").. This is the beginning of that passage from one translation: "What, if some day or night a demon were to steal after you into your loneliest loneliness and say to you: 'This life as you now live it and have lived it, you have to live once more and innumerable times...'"