Remark: Family 009. Bogomolov–Pop and Milnor K -theoretic reconstruction

Reconstructs function fields of transcendence degree at least two over algebraically closed constants from ${K^{\mathrm{M}}}_1/\ell$, ${K^{\mathrm{M}}}_2/\ell$, and their product. These data recover the perfect closure and constants when $\ell$ differs from the characteristic, and the original field and its named base in equal characteristic. Also proves Bogomolov–Pop reconstruction from abelian-by-central pro-$\ell$ Galois data away from the characteristic.

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.