For Future Reference

Fancy, linear, timeline of events.

John (Future) appears in apartment building, furnishes it with a couch, tv, food, and a cat (Jeffery).
Presumably, he also leaves notes for himself.
John (regular John) is given the key to this apartment, and finds himself in possession of the aforementioned items.

Two weeks pass (possibly uneventful)

Feb. 11th - Regular John remembers to leave the door open.
Past Future John (still the future, but before he rented the apartment) appears in the apartment.
Crazy things (not being able to influence anything) stuff happens, he makes it back to George (whoever that is)

Two more weeks pass (possibly uneventful)

Past Future John (right after aforementioned craziness) talks to George about problems.
Readers get a sketchy idea of what these two hooligans are up to.
George creates the notes that Regular John reads when he first goes to the apartment.
The idea of sending someone back in time, but not accounting for the Earth moving through space, is addressed.
"...Sending you back one month..." -- obviously, this is about time travel!  Woah.

At some point soon,

John goes back in time, now able to control some things, and rents the apartment.
//see above

???

Reality might collapse.
Future? John is running.
Future? John reaches George before it's too late (vague suspense is vague)