I -Extremization with Baryonic Charges

We propose an entropy function for AdS4 BPS black holes in M theory with general magnetic charges, resolving in particular a long-standing puzzle about baryonic charges. The entropy function is constructed from a gravitational block defined solely in terms of topological data of the internal manifold. We show that the entropy of twisted black holes can always be reformulated as an I-extremization problem - even in cases where existing large-N field theory computations fail to provide an answer. Furthermore, we correctly reproduce the entropy for a class of known black holes with purely baryonic magnetic charges. Our results offer both a conjecture for the general gravitational block for AdS4 black holes in M theory and a prediction for the large-N limit of several partition functions whose saddle points have yet to be found.