On the Origins and Nature of the Dark Calculus

is a book. Its covers are black with a light blue stripe. Its contents describe "dark calculus" or "penumbra calculus", a mysterious formal system where theorems proven using it immediately become false upon proof. This is a contrapositive version of umbral calculus from the mid 1900s, where proofs that supposedly cannot be true for determining the identity for polynomial equations resulted in the correct identities anyway. "Penumbra" in this case means "Partial darkness".

Summary
A theorist from the seminary the Cupola formulated the basic concept of the dark calculus. It became a full fledged formal system, which defines the grammar, symbols, and set of rules to derive further concepts and theorems.

In mathematics, a theorem is a sort of statement about how the universe functions and must be proven with proofs. Proofs are essentially the step by step guide to how the theorem works. In this case, some theories proven using dark calculus will become false once the proofs are complete. With this discovery, systems based off of dark calculus were created and even more fragile, some making theorems false upon even the proposition (Assume ____ is true).

Because the proofs must be in some observable state in order to be made false, some theorists predicted that there is some level of self-awareness to the dark calculus. They created a complex computer system for use of dark calculus and launched it into space to prevent any outside observation. The results of their research are unknown, but caused the use of the dark calculus and all related formal systems to be strictly prohibited. The opinion was unanimous, including Ptoh, who agreed by imploding a research station. Most records surrounding the dark calculus have been or attempted to have been removed from written history.