Gravitational Blocks: Symplectic Covariance Unveiled

By working in a symplectically covariant real formulation of special Kähler geometry, we propose and give strong evidence for a canonical BPS partition function for AdS${}_2{\times }_w{M}_2$ near-horizon geometries with arbitrary rotation and generic magnetic and electric charges. Here, $M_2$ is either a two-sphere or a spindle. We also show that how the attractor equations and the Bekenstein-Hawking entropy can be obtained from an extremization principle.