Abstract: BCOV theory predicts a rich structure for the higher-genus potentials $F_g$ of the quintic threefold. Two particularly important features are finite generation and the conifold gap, which play a central role in the higher-genus calculations of Huang, Klemm, and Quackenbush. In this talk, I will describe a general strategy for proving the conifold gap using master spaces. For the quintic, this strategy is realized by mixed spin $P$-field (MSP) theory, which relates the Gromov–Witten theory of the quintic to a cone-vertex theory. The key step is to establish the gap for the cone-vertex theory and then transfer it to the quintic through the master-space construction. This talk is based on joint work with Huai-Liang Chang, Lei You, and Huaigong Zhang.