Remark: Family 006. Goldfeld's conjecture

Proves Goldfeld's conjecture for quadratic twists of every elliptic curve over $\mathbb{Q}$: analytic ranks zero and one each have density $1/2$, and the mean analytic rank tends to $1/2$. Both statements order signed squarefree twist parameters by absolute value.

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.