The paper by Grigory Belousov and Konstantin Loginov proves that all general smooth Fano threefolds with Picard rank 3 and degree 14 are K-stable. The authors explicitly state the generality condition under which this result holds. They show that if a Fano threefold \(X\) satisfies this condition, then it is K-stable. The generality condition involves the behavior of the conic bundle structure on \(X\) over \(\mathbb{P}^1 \times \mathbb{P}^1\), specifically that multiple fibers of the conic bundle have only \(A_1\) singularities along the fibers. The paper also includes corollaries stating that if the discriminant curve of the conic bundle is smooth or if the singular fibers have specific types of singularities, then the Fano threefold is K-stable. The authors use techniques from K-stability theory and properties of del Pezzo surfaces to prove their main theorem.The paper by Grigory Belousov and Konstantin Loginov proves that all general smooth Fano threefolds with Picard rank 3 and degree 14 are K-stable. The authors explicitly state the generality condition under which this result holds. They show that if a Fano threefold \(X\) satisfies this condition, then it is K-stable. The generality condition involves the behavior of the conic bundle structure on \(X\) over \(\mathbb{P}^1 \times \mathbb{P}^1\), specifically that multiple fibers of the conic bundle have only \(A_1\) singularities along the fibers. The paper also includes corollaries stating that if the discriminant curve of the conic bundle is smooth or if the singular fibers have specific types of singularities, then the Fano threefold is K-stable. The authors use techniques from K-stability theory and properties of del Pezzo surfaces to prove their main theorem.