What architectural problem do pendentives solve in Hagia Sophia?

In architecture, a pendentive is a spherical triangle that solves the structural challenge of supporting a circular dome over a square or polygonal room.12

At Hagia Sophia, the transition from a square ground plan to a circular dome base is complex. Pendentives address this by filling the upper corners of the square space, effectively bridging the gap between the angular base and the circular rim of the dome.12

Beyond merely facilitating this transition, pendentives serve a critical structural function: they brace and support the weight of the dome, transferring the load downward to the ground. By utilizing this system, Byzantine architects moved away from relying solely on massive walls to counteract stress, instead creating an organic structure where thrust is compensated by thrust and stability is achieved through balance.2