Remark: Family 024. An asymptotic formula for the number of totients

Gives an asymptotic equivalent for the number $V(x)$ of distinct totient values up to $x$, with a positive bounded phase-dependent factor determined by convergent arithmetic approximations. In particular, $V(cx)/V(x)\to c$ for every fixed $c>0$, answering Erdős and Hall’s scaling question.

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.