I think there is a mistake in description for this skill.
It says: "+20 sience per anomalies on colonized planet on system, +20 sience on system" 
So, if you place the hero with this skill on system with 4 planets and 6 anomalies (set: 2+2+1+1 ), it has to be +140 sience (6*20+20), but it gives you only 100 sience points. 

Well, if you change description to "+20 sience per colonized planet with anomalies on system, +20 on system", it will match the calculation: 4*20+20=100. 

"Words wrong order" and "One word missing" issues are quite common in ES2 descriptions.
For exampe: Extreme Anti-Gluon beam, Antimatter Lock-on, Annihilator beam...

I'm not sure which way it is supposed to work. I'll try to verify with a Game Designer and get back to you.

In the meantime, I would be grateful if you have a save where you have already unlocked said skill, so we can test it more quickly.

I guess it's +20 for any planet within that system having anomalies (what I guess is given this case) and +20 for system. Perhaps the description is missleading or - if intended to get +20 for any anomaly within system - the calculation has to be changed.

Edit: @Evgenopolis aka Evgenich I see now, you had same explanantion and some additional reported stuff here: Odd ES2 descriptions: RiftBorn Skill - Arcane Knowledge

Thank you for the save. I've forwarded it to the team.

EDIT: After inspecting the save, we were not able to reproduce the issue. The skill worked as described on Galtur.

The-Cat-o-Nine-Tales wrote:

Thank you for the save. I've forwarded it to the team.

EDIT: After inspecting the save, we were not able to reproduce the issue. The skill worked as described on Galtur.

Sorry! My bad - the skill works as intended on this planet indeed. It is another planet where I`ve found this issue, just mistaken the names. Please check the planet Rasam. There is the same hero - e (II). And there is 6 anomalies - as was given in my example. Arcane knowledge gives 100 sience exactly there . 

So I am confused now. It seems that sometimes skill does not work properly and sometimes it does? Or not all anomalies counts as "anomalies" for this skill? 

The anomalies on Rasam :  Dust nebula, Meteor  Strikes, Long Season, Permament Moonson, Psychoactive air, Hadopelagic life. 

There is 5 colonized planets with anomalies set: 0+2+2+1+1.  

So, it has to be +140 sience , right? Why there is only +100 from Arcane Knoledge? Please, enlight me!

I`ve found another oddity with the same nature - Riftborn skill "Tech Hubs". 

The same heroes (e and e-II) and the same planets in my save:

On Galtur with 5 anomalies set 1+1+0+2+1 it gives +250 industry (50 per anomaly)

On Rasam with 6 anomalies set 0+2+2+1+1 it gives +200 industry (50 per planet with anomalies?)

/or, again, not all anomalies counts as "anomalies" for this skill?  

"It`s... It`s hard to know who to trust, isn`t it, Jack?" (Cocoon, 1985)