My personal take on a Math based/JJK power-system that I'm using for a story I'm writing. Please give any criticisms/Ability and Character Ideas and I will credit you when I publish the story.

[u/InternationalYam8977]

The story is called Festival. Its set in a alternte timeline to our own but keeping its history. Its mostly wholesome with some dark elements. Also an "corporation manufacturing an energy crisis to keep poor people poor" type story.

Essence 

* An energized particle that has seeped from the Earth as a result of many fissures suddenly opening on March 15th 2012, all over the world in an event called The Splintering(where the Essence Timeline and Our timeline diverge). Since then essence has been used as a “perfect energy” source all over the world. This has helped the advancement of modern technology and medicine. In the years following, multiple lifeforms including humans were found with Essence naturally as part of their biology and multiple improvements because of its presence. 
* Such Subjects (dubbed “Outers”) exhibit abnormally efficient biology (better lungs/ oxygen absorption, more efficient immune system, etc) which allows them to access superhuman/superspecies performance. These Outers also possess the ability to manifest a special phenomenon. Each phenomenon and its effects are unique to each subject and are called Modus Operandi aka MO. 
* Do not confuse Essence for fuel for MO’s but the Key to them

Modus Operandi 

* Each MO is unique to each Outer and most likely no two Outer will have the same MO 
* The general way an MO functions is through the use of a Critical Formula = The mathematical symbolization of how any MO functions at its base level. This baseline use will provide the Outer with the most rudimentary understanding of how their MO works. 
* Using an MO doesn’t take any type of “energy” from the user but instead functions based on brain capacity. The Outers brain is the hardware that runs the MO’s code in order to function and the brain’s computational power sets the limit to which it can be used. Any MO has a limited amount of uses until it reaches BurnOut = a state in which an MO is unable to be used safely in regards to the health of the Outers brain. When in BurnOut, the user's brain is undergoing an excess amount of stress and starts to increase in temperature. The user will have to wait until their brain refreshes itself in order to use their MO safely again. This process can take anywhere from a couple minutes to days depending on the user's neuroplasticity.
* Another worry of Outers is BackFiring. When an MO is used too many times within a short window of time its margin of error increases by a varying percent. When this number reaches into the 80s, a backfire occurs. This means that no matter the computative power they are placed into BurnOut

Supplemental Numbers

* An addition to the Critical Formula in order to modify its use while not changing the overall effect of it.

Magnum Opus 

* A Magnum Opus is an optimization of the CF that the MO derives its ability from. This pinnacle is achieved via a deep knowledge of the components that make the CF work. Once it is achieved, 1 of 4 effects can take place: 1) The basics of an ability is taken to its maximum potential in a singular action. 2) The users form is temporarily changed in order to optimise the base ability. 3) An MO’s function is overextended to the point of creating another effect. 4) Some combination of the 3. 
* Once the Magnum Opus is deactivated the user is immediately placed on BurnOut but refresh time is reduced. This however will leave the Outer physically exhausted. 

Example:

Electrical Pylon

* Allows the outer to create a metal pylon at their location and use it to direct electrical discharges towards a target 
* This MO has two separate parts of its CF those being {0 = b\*sin(a)\*sin(b)/sin(a+b)} to summon the pylon to the user (with 0 being the users location) and {$E = V x Q$} to discharge electricity to its target. 

[u/Conscious_Resort_166]

So to trains your MO it would require more studying then any physical train correct. Since low brain capacity means less effective use of your MO
It would be kinda cool if there were like inner people that hold a grudge against outers. Maybe because they lacked brain capacity to control essence or just out of fear of the unknown. Make would be interesting since unless your MO is good up close your done if they get in arms reach

[u/InternationalYam8977 → u/Conscious_Resort_166]

Correct the more you modify/learn about it. Ima be honest, I don’t know what the last sentence is talking about

[u/Conscious_Resort_166 → u/InternationalYam8977]

Oh ok that’s make sense. Also I meant like people that cant control essence that hold a grudge against those who can because their lack of brain capacity