Given infinite time/tid/sid for gen 3 games, what exactly is possible?

[BLACKBERREST3]

I haven’t been able to figure this out and I would like someone with more knowledge on this topic to help me. Given infinite time, tid/sid combos, and seeds from a working battery, are all combinations of IV/Natures theoretically possible? how does pkhex detect the legality of this? I understand that all are possible when breeding as the rng calls for nature/ability/gender are determined at a different time than IVs, but what about method 1 legendaries?

[Kaphotics]

The generation 3 games use a repeating 32-bit LCRNG, meaning that there are only 2^32 possible states for the RNG to exist, and thus 2^32 possible result sequences (ignoring vblanks). Since a given IV spread is 2^30 odds, you're only left with ~4 results, thus every nature, gender, or even encounter is NOT possible.

PKHeX finds the state of the RNG and compares it to the Pokemon; if it can match it to a sequence on the RNG, then it is legal, otherwise, it is flagged. 

Breeding: not true -- PKHeX doesn't have any checks implemented for them. Since a PID in Emerald is 2 sequential 16-bit rand values, that pair should exist on the sequence (not guaranteed), and for the other games, one half of the PID and the resulting IV spread+inheritance should be possible on the sequence. Again, not checked by the program at this time.

Same for not-Emerald trainer IDs: two sequential rand calls must exist. Emerald determines TID and SID separately, thus all combinations are possible.