Which Gem works on Freya?

Both the Gems, the Gem of Isolation and the Gem of Binding, slow your target by 25%. The Gem of Isolation doing so when they are hit by a damaging ability. The Gem of Binding slows when they are hit with a basic attack. Freya's skills are about changing and making her basic attacks stronger and her 2 counts as basic attacks, does that mean both gems would work the same way regardless?

Gem of Binding will make her sword-hits and pulse hits slow.
Gem of Isolation will make her pulse hits and ultimate hits slow.

What if you use her 1 and 2? Does it still count as a pulse hit?

Yes. Let me rephrase it because I can see how it was a bit unclear.

Gem of Binding can be applied from her regular sword hits, her irradiated sword hits, pulsed hits, and irradiated + pulsed hits.

Gem of Isolation can be applied from her irradiated sword hits, pulsed hits, irradiated + pulsed hits, and Valkyrie's Discretion hits.

I'm not 100% sure about irradiated hits by themselves on either Gem, but due to the spell effect stating that her basic attacks deal magical damage, it leads me to believe they count as both basic attacks and abilities. Everything else I'm positive about.

I'm no genius but I have to say your incorrect on this one. Damaging abilities are like Valkyrie's Discretion and say Gungnir's Might. Her 1 and 2 both augment her basic attacks. So I have to say that Gem of Bnding works for her 1 and 2. While Gem of Isolation only works on Freya's ultimate.

No, Gem of Isolation applies the slow effect for any ability as long as it does damage any kind of damage (Do note that it works for both magical and physical damage). It affects all of her abilities except for her Banish since it does not do any damage upon hit.

Yes I know that, but those aren't her abilities, they are her basic attacks. That's what gem of binding is for.

The thing is, her basic attacks with those buffs up count as both basic attacks and ability hits.

The only difference between the Gems for Freya is that Isolation doesn't slow on regular basic attacks (non-irradiated sword hits) and Binding doesn't slow on her ultimate hits.

WHERE ARE THE SMITE MYTHBUSTERS I DEMAND THEY SOLVE THIS!!!!!!!

This would be the correct assessment to my understanding as well.