Remark: Family 063. The generalized Mukai conjecture

Proves the generalized Mukai conjecture: every positive-dimensional smooth complex projective Fano manifold of dimension $n$, Picard number $\rho$ and pseudoindex $\iota$ satisfies $\rho (\iota -1)\le n$, with equality exactly for $({\mathbb{P}}^{\iota -1}{)}^{\rho }$. Here the pseudoindex is the least anticanonical degree of a rational curve.

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.