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The Skasis Paradigm (also known as the God Maker or the Universal Theory) was the mathematical equation behind the way the universe worked. Anyone who cracked the paradigm would be able to control the very building blocks of the universe, granting them the power of a god (TV: School Reunion) over space and time. (COMIC: Fugitive) For this reason, the Tenth Doctor believed that the Paradigm was never meant to be solved due to the immense power it had; he himself was briefly tempted to use it before being talked down. (TV: School Reunion)
History
The Krillitanes took over Deffry Vale High School to crack the paradigm. The Krillitane, Lassar, posing as headmaster Mr Finch, believed that if he could crack the paradigm he would be able to redo all of reality and improve it.
Unfortunately for him, the Skasis Paradigm did not just require computational power to crack it. It also needed imagination. That was why the Krillitanes were using the Krillitane oil to enhance the children of the school, since they had the imagination needed to crack the Paradigm. However, their integration of other species' biology from conquering their planets made the oil lethal to the Krillitanes. The Tenth Doctor, Rose Tyler, Mickey Smith, Sarah Jane Smith, and K9 Mark III all fought against the Krillitanes to keep them from cracking the Skasis Paradigm. Though Lassar tempted the Doctor with a way to reverse the horrors of the Last Great Time War and undo aging and death by use of the Paradigm, Sarah Jane reminded the Doctor that these experiences were necessary to make life meaningful.
With the Doctor destroying their computers, the Krillitanes responded by preying on every human life at the school. Mickey then stopped the calculations by unplugging the network and evacuating the students. K9 Mark III would give up his life to slay the entire horde with the same oil they had grown vulnerable to, destroying the school in the process. (TV: School Reunion)