Algebraic and complex geometry·OpenAI Math·Result 063
The generalized Mukai conjecture
One of the 372 results in OpenAI's public mathematics catalogue, filed under algebraic and complex geometry: 1 preprint, the latest dated 24 September 2026. This page quotes OpenAI's own summary of the claim, links the paper and abstract, and will embed the animation.
Latest paper
The generalized Mukai conjecture
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What OpenAI claims
Proves the generalized Mukai conjecture: every positive-dimensional smooth complex projective Fano manifold of dimension n, Picard number ρ and pseudoindex ι satisfies ρ(ι-1) ≤ n, with equality exactly for (ℙι-1)ρ. Here the pseudoindex is the least anticanonical degree of a rational curve.
Paper
The generalized Mukai conjecture
We prove the generalized Mukai conjecture: every positive-dimensional smooth complex Fano manifold of dimension n, Picard number ρ, and pseudoindex ι satisfies ρ(ι-1) ≤ n. Equality holds precisely for the product of ρ copies of ℙι-1.
Status
Preprint. The paper has not been independently reviewed. Treat the result as OpenAI's claim until other mathematicians have checked it. If a video exists, it illustrates the statement; it is not the proof.
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