Proves the generalized Mukai conjecture: every positive-dimensional smooth complex projective Fano manifold of dimension n, Picard number ρ and pseudoindex ι 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.
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In The generalized Mukai conjecture, 24 September 2026
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Let X be a smooth connected complex projective Fano manifold of positive dimension n, Picard number \rho_X and pseudoindex \iota_X. Then
Equality holds if and only if
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Points to arXiv:2604.25023, which says OpenAI independently claimed the generalised Mukai conjecture by a different method.
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Theorem 1.1
In The generalized Mukai conjecture, 24 September 2026