Synchronizers can reduce the frame of a spread, but more importantly, make a spread that's normally impossible to reach with method J/K reachable. For example, the flawless spread with seed d2140289 is normally unreachable using method J, but a Timid synchronizer lets you reach it on frame 73.
The way the game works is like this:
When you encounter a wild Pokémon (including legendaries), the game rolls a random number between 0 and 24 - this becomes the wild Pokémon's nature. It then repeatedly generates Pokémon (technically just the PIDs) until it finds one with the correct nature (it doesn't actually modify the nature directly). This means that if there's another spread with the same nature as the one you're aiming at a few frames earlier, and no RNG value in between that tells the game to aim for your nature, the spread is unreachable.
A synchronizer simply gives you a 50% chance of having the random nature replaced by that of the synchronizer. That way, you can aim for a frame just before your spread (but after the one with the same nature), and have a 52% chance of the game selecting the correct nature (and hence hitting your spread).
It's a bit more complicated than this (for example, you specifically have to hit either an odd or even frame), but that's the basic gist.
Ah, I see. Thanks Wichu.
So, in your example.
PID: 7942ef72 (TIMID, ability 0) 31/31/31/31/31/31 (Seed: d2140289 Method 1: 114, J (synch): 71, J (no synch): None, K (synch): 71, K (no synch): 87) HP DARK 70
The "J (synch)" or "K (synch)" refers to the minimum frame (up to the method 1 frame) where if you have a the correct synchronizer and are on that seed, you can get that spread then, correct?
Whereas, for the "J (no synch)" and "K (no synch)," refers to the frame in which you can get that spread without a synchronizer.
(And I presume Method K is used for HG/SS over Method J, right?)
When I tried to look it up on the RNG Reporter with the same spread, but with synch nature Timid and Any for nature, I get the Modest perfect spread. So, can I presume that the RNG Reporter is not correct then for looking up potential synchronize frames?
Also, do you have a page explaining the nitty-gritty of using the synchronizer. I'm actually very interested in getting more in depth about what you mean regarding an even or odd frame (although if you mean journal flips and walking 128 steps, I already know).
EDIT: Also, I was wondering if you intentionally removed the very very high frames from you PokeRNGDP program in the current version. I used your old version and actually gutted out the frame below for Palkia:
351924326F 6463b3ad (HASTY, ability 1) 31/31/31/31/30/31 (Seed: bf17029e Frame: 3380) HP STEEL 70 (Method J)
So, I guess this seed below is the exact same thing except the delay is much higher.
PID: 6463b3ad (HASTY, ability 1) 31/31/31/31/30/31 (Seed: d51701b7 Method 1: 114, J (synch): 25, J (no synch): 41, K (synch): 19, K (no synch): None) HP STEEL 70
Thanks again Wichu!