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We prove the convergence in distribution of the fluctuations of the freeenergy of the mixed $p$-spin Sherrington-Kirkpatrick model with non-vanishing$2$-spin component at high enough temperature. The limit is Gaussian, and thefluctuations are seen to arise from weighted cycle counts in the complete graphon the spin indices weighted by the $2$-spin interaction matrix.

Fluctuations of the free energy of the mixed $p$-spin mean field spin glass model