SCP-XXXX - The Diagonal Argument
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Item #: SCP-XXXX

Object Class: Keter Neutralized (?)

Special Containment Procedures:

Research Task Force INFINITY (∞) is established and funded with the remit to investigate the presence of other
and prevent any reemergence of SCP-XXXX which appears to be currently lacking anomalous properties.

All existing copies1 of Galeni (2002) Inconsistencies in Cantor's Diagonal Argument , whether in digital or paper form are to be secured and destroyed.

Academic conferences and publications are to be scanned for papers with related titles and similarly disposed of.

scpxxxx1.jpeg
A snapshot of the first published instance of SCP-XXXX.
0.jpeg

██████.

Mathematicians working on similar topics are to be vetted for recruitment within RTF-∞. Should they decline they will be required to undergo deep amnestic treatment and kept under surveillance to verify they pursue a different field of research.

Definition
SCP-XXXX is a computable transcendental number, referred to using the hebrew character ℶ (beth).

The number has an infinite decimal expansion in all bases and is defined as the limit2 as k goes to infinity of the recursion:

(1)
\begin{align} \beth_{k+1} = \max\left\{ \int_D █(\xi) d\xi, \beth_k \right\},\ \beth_0 = \gamma, \end{align}

where $D$ is the set of all definable real-numbers and $\gamma$ is the Euler-Mascheroni constant, and $█$ is a suitably normalized ███-███████████ Green's function.

Another, much simpler recursion, known as Greg's Trick3 allows to practically compute the number to arbitrary precision:

(2)
\begin{align} \beth_{k+1} = \frac{\beth_k^█ -1}{███}. \end{align}

Anomalous properties

The number $\beth$ posessed extraordinary anomalous qualities.

The first type of anomalous behavior displayed by $\beth$ , eventually leading to its discovery, is that when used within the context of Cantor's diagonal argument4 it invalidates the proof, hinting at the presence of deeper inconsistencies within the mathematical language.

As for the second anomalous property if mass is carefully weighted according to (2) this resulted in a net loss of $O(k)$ milligrams (mg) violating the first law of thermodynamics.

Thirdly it was later discovered that by weaving $\beth$ in mathematical pen and pencil computation it was actually possible to apply changes of arbitrary amounts to any measurable quantity at a possibly unboundend distance. This effect could be used to not only effectivly alter any aspect of reality, but to interfer with physical laws themselves by altering physical constants.

Activation and deactivation of $\beth$

$\beth$ is thought to have been discovered by Emeritus Professor F.S. Galeni in 2001 and publicly disclosed in a presentation at 2002 Math ConF.

In 2015 videos of disappearing mass went viral on youtube and publicized Eq. (2). The anomalous properties of this number were soon evident to a multiplicity of ill-poised actors who sought to appropriate the technique to use it, leading within five months to the CK Class "Fine-Tuning Race Condition" reality restructuring scenario.

On the 15th of August 1999 all anomalous effect suddenly ceased5. Any and all sideffects caused by direct alterations through the usage of $\beth$ were retconned.

** Paradoxical cliometric analysis**

The deletion of all effects which presumably were directly imputable to SCP-XXXX has left many memories and recording (inderect effects) available, often leading to paradoxical events and inconsistencies in recordings between 1999 and 2015-16. A detailed analysis of many of this, as well as a "counterfactual" historical account of the period is attached, see DOCUMENT.

Footnotes