I have beaten the main storyline, and now I'm looking to complete all the paradox endings. In order to do so, I need to activate my paradox scope at Serendipity. But, I can't seem to figure out how to get there. How do I navigate the Historia Crux to get there?
There are two nodes for Serendipity on the Historia Crux: one for the main storyline and another for the Sazh: Heads or Tails? DLC.
Using New Bodhum -003 AF- as the starting point:
Expanded Historia Crux
Sazh: Heads or Tails? DLC:
Compact Historia Crux
Go right seven times. For the Sazh: Heads or Tails? DLC, go up from there.
You can also check out snesmaster1's map on GameFAQs.
Just as an aside, though: there is no paradox ending associated with Serendipity. Only the following locations have paradox endings associated with them:
Serendipity is node 10 on this map.
There are two ways to get there, this is the way most people will access serendipity when you complete the chapter 3 in sequential order (part 1 then part 2) you get there by opening the gate to the very south in node 12 Yaschas Massif AF01X.
From there you are in an alternate Historia crux. Enter the void beyond, there are a few items hidden around here. Then open the gate in the middle of the map to return to the regular Historia Crux and unlock Serendipity in the process.
Now you just enter it like a normal node.
The second way is if you completed chapter 3 out of sequence (part 2 then part 1.) then only difference is that you have to open a gate in node 13 Sunleth Waterscape AF300 but as I didn't do it this way I am not sure which gate it is.
Node 35 is also serendipity but only accessible if you purchase the Sazh: Heads or Tails DLC.