Blackle

Description: SCP-XXXX is a dihedral-like quasigroup that can be used as a polynomial-time universal translator between type-0 grammars. It was discovered independently in 1998 by three separate parties:

• Marius ██████, University of ██ █████ (March)
• Xin ███ ██, The ███-████ Institute of Science (April)
• William ███ and Vincent ██████, University of ███████ (October).

SCP-XXXX's anomalous properties were outlined in two of the three subsequent research papers. Foundation agents working under the journal ██████ ██ ██████████ initiated containment successfully, leading to the [REDACTED] of the above parties.

Throughout this description, SCP-XXXX is also referred to as simply $G$ for brevity in equations.

SCP-XXXX's algebraic structure is complex but easy to compute. Elements of SCP-XXXX are defined by a recursive formula, initialized by eight base elements: denoted $e_0$ to $e_7$. In spite of the simple definition, elementary properties of SCP-XXXX are disproportionately difficult to prove. For example, it is still unknown if SCP-XXXX has an identity element. Attempts have been made to prove left identity of $e_0$ and right identity of $e_7$ by computational exhaustion. As of ██/██/15 there exist no counterexamples in the first ██ million elements of SCP-XXXX.

The anomalous properties of SCP-XXXX manifest as follows: Two type-0 grammars $A$ and $B$ are encoded as elements of SCP-XXXX1, denoted $E_A, E_B$. Because the grammars are recursively enumerable there is a mapping $K_A : A \to G$ and $K_B : B \to G$ that is isomorphic to the recursive structure of $G$. Then the automorphism $F : G \to G$ defined by $F(E) = E_A / E_B * E * E_B \setminus E_A$ is such that $K_B^{-1} \circ F \circ K_A$ is a function that translates strings from $A$ to corresponding strings from $B$.

The existence of SCP-XXXX implies tractable solvability of several undecidable problems, including the halting problem, the morality problem and the entscheidungsproblem. However, when an attempt is made to use SCP-XXXX to solve these problems the result is invariably an identity function, understood to mean "no answer."

something something $e_0$ and $e_7$ define grammars understood by two sapient entities that can be made to talk to each other by repeated composition