Dual-core comprising negative gradient center and positive gradient outer core layer

A golf ball comprising:

• an inner core having a geometric center and a first outer surface positioned about 0.8 to about 1.3 inches from the geometric center, the inner core being formed from a first substantially homogenous rubber composition comprising an antioxidant-to-initiator ratio of about 0.5 or greater;
• an outer core layer formed from a second substantially homogenous rubber composition different from the first, the outer core layer having a second outer surface positioned about 1.53 to about 1.58 inches from the geometric center;
• an inner cover layer disposed about the core, the inner cover comprising an ionomer having an acid content of about 16 wt % or greater and a maleic-anhydride grafted metallocene-catalyzed polyolefin;
• and
• an outer cover layer disposed about the inner cover layer, the outer cover comprising a castable polyurea or a castable polyurethane;
• wherein the first outer surface has a hardness less than a hardness at the geometric center to define a negative hardness gradient of about −1 to about −15 and the second outer surface has a hardness of up to 12 Shore C greater than a hardness at an inner surface of the outer core layer to define a positive hardness gradient outer core layer.