Remark: Family 005. Irrationality of Catalan's constant

Proves that Catalan's constant $G={\sum }_{j\ge 0}(-1{)}^j/(2j+1{)}^2$ is irrational.

The authors are OpenAI. This companion does not verify the proof. The claim is not a theorem of the Enter series and not a premise of any registered sheet. It does not close O.1. O.1 stays NOT_CLOSED. It is not a de Sitter state and not the QdS external-leg scheme. No quantum coefficient is admitted. No compilation is asserted.