@redweasel  
I’d suggest that the cutie marks are just a representation of “earth”, “pegasus” and “unicorn” magic. You’ll notice there’s one cutie mark per tribe on the board, that’s the most likely theory.
 
I’d suggest that what we see is the structure of Alicorn magic - all three tribes. Changelings would have something very similar, but would have only one group jutting out at a different position. Earth ponies would only have the group where Pinkie’s cutie mark is etc.
 
The main question is, what is the structure of these groups? We know there are some minerals in there from the fact that magic seems to turn stone into gemstones in Equestria, so that would give some idea - just look at what minerals are in those gemstones. Simultaneously, checking the distance at which Tempest’s horn can spark would be a way to determine the ‘charge-density’ behind her horn compared to open air. Then you could find out the mass in some roundabout way from the Ailicorn short’s display of accidental magic discharge.
 
Now that I write this out, another concept comes to mind… If an object were thrown a distance by a raw magic beam in Equestria, that distance would be dictated by the momentum of the magic particles being fired at them. p=mv … And if p and v are known, then p/v=m
 
Gatling Gun Twi from S2E26, anyone? The only difficulty would be figuring out how many moles in a single glob, I doubt it follows the ideal gas law. Though if it’s launched magnetically, it would be a high concentration gas or plasma…

@ThePonyTheorist
 
alright, so there are degenerate cases for each terminating branch, but if it’s like normal chemistry, chemicals with similar but very importantly different properties will have similar underlying structures, with different chemical groups on the ends, like amphetamine and pseudoephedrine. so you can substitute in other chemical groups for each plain old ch4 terminating branch, to get different but similar chemical properties.
 
so aside from whatever chemical groups those three… things represent, what other ones are there, and what are they associated with symbolically, if not unicorns, earth ponies and pegasi? or are those chemical groups related to cutie marks, not tribe, so there could be a butterfly, a candy, a heart, a gem, an apple, etc.? are cutie marks a phenomenon that emerges from molecular chemistry itself in equestria?

@redweasel  
If this is like normal chemistry, that’s hydrogen, if not single carbons…
 
Magic seems to be a form of bicyclohexyl with the addition of chemical groups in specific locations. As this chemical is usually a liquid, and the addition of new groups doesn’t help with that, the new chemical groups must be charged, creating a repulsive effect which allows the magic to take the form of a gas.
 
I’d guess that unicorns only have the unicorn group, earth ponies only have the earth group etc - alicorns have all three. This would make their magic more happy to stay a gas, and may explain why the time-travel potion is poison if you’re not an alicorn - less energy is stored in one molecule, the potion overproduces and.. Well, too much gas is created in the eyes at one moment, causing a serious and very squick-inducing injury.

what I want to know is what are on the other seven branches that aren’t unicorn, pegasus or earth pony?

I think the questions we should be asking are which chemical elements provide pigment to the Elements of Laughter, Loyalty, and Generosity.

Earth ponies have nukes?

Most likely minerals during reaction with stone are Mg, Fe, Mn and maybe oxygen?
 
Yes, i’m overthinking it. But it’s entertaining to do so, damnit!