Okay so during Halo 4, the New Phoenix Incident occured on July 25th, 2557… and thus the ending of Halo 4.
In Halo: Escalation, ‘The Next 72 Hours’ segment explains John-117s journey post Halo 4, and how he re-unites with Spartan Blue Team. They are sent on a classified mission to investigate the silencing of the UNSC base on Installation 03, to which they discover the corpes of Spartan Black Team. They are then engaged by Prometheans, which John recognizes and follow the crawler tracks to the Composer’s Abyss. They move through the unknown active portal and are taken to the Composer’s Forge… to which John-117 and Blue Team discover the survival of the Didact. The battle ensues as the Didact attempts to use the Halo ring and composer in a plan against Earth… yet in the end he is thwarted by the quick thinking of John-117 and the Monitor, 859 Static Carillon. The Didact and the discarded section of Gamma Halo, crash into the 5 bystanding composers to which they disintegrate the Didact… During the last pages we discover that John-117 refuses his R&R and goes back to work with Blue Team… thus making it July 28th, 2557.
In Halo: Infinity, better known as Spartan Ops, the date is February, 2558… and so 6 months have past since the events of ‘The Next 72 Hours’. During the events of Halo: Infinity, Doctor Catherine Halsey is re-intiated onto the UNSC Infinity to assist with the problems that occured with the Forerunner engines and the Requiem artifact… she eventually is caught out, by Spartan Sarah Palmer, when she communicates with the Supreme Commander, of the Covenant Remnant. Now locked away, she maneuvers her way into the Infinitys database and learns of John-117’s survival… and attempts to escape, yet fails due to Smart-AI Rolands quick recovery. Having now lost contact with his source, Jul 'Mdama begins a raid on the UNSC Infinity to which he kidnaps Doctor Halsey, and takes her to the Librarian’s Rest. Having been marked as a conspirator, ONI Admiral Serin Osman, orders Sarah Palmer to assasinated Halsey… yet Halsey survives due to the help of Jul’s forces. Now learning of ONI betrayal, Halsey preludes to assist the Didact’s Hand in exchange for revenge…
The events, preceding Spartan Ops, in Halo: Escalation are ‘The Peace Summit’, ‘The Spirit Of Fire’, ‘The Re-Opening Of New Phoenix’ and ‘Exposure’ segments… which explain the journey of the UNSC Infinity and her crew. During the first segment a lone and insurgent Spartan-IV seems to imply knowledge of the Master Chief… that where is he, no one has heard from him in a while? Also during Exposure it suggests that the Covenant Remnant and the UNSC Infinity crew are about the re-engage each other over the Janus Key… what does this mean for Catherine Halsey, could she have been rescued by John and Blue Team, during the 2 months, post Spartan Ops? Have they all escape with the Janus Key half… or what?
Halo: Legends The Package is a short animated episode where John and Blue Team rescue Halsey… perhaps that was a foreshadowing of the events to come?
