We test whether the eruption timing of deep mantle plumes carries the level-repulsion signature of random matrix theory (RMT), motivated by a thermal-shadow hypothesis: a plume that depletes the local thermal boundary layer at the core-mantle boundary must re-accumulate heat before its next major eruption, imposing a minimum recurrence interval analogous to eigenvalue repulsion. Using absolute ages of 44 Large Igneous Provinces (17-1880 Ma) and four independent long-lived hotspot tracks (Hawaii-Emperor, Louisville, Tristan-Gough, Rurutu-Arago), we contrast mixed-source and single-source configurations. Mixed sources (global LIPs, or LIPs grouped by African/Pacific superplume domain) collapse onto Poisson statistics, as the spectral superposition theorem predicts. Single sources instead show GOE-class repulsion: the pooled four-track distribution gives r-bar = 0.630 with a bootstrap 95% CI of 0.422, 0.563 that excludes Poisson and contains GOE. The African superplume is significantly clustered (CV=1.39, p=0.017), while the Pacific is intermediate, indicating distinct superplume dynamics. Spectral superposition is both a warning and a surgical tool: one must descend to the single source to reveal the deep Earth's quantum-like rhythm. Third in a three-racetrack RMT program spanning Earth from crust to core.
Ruqing Chen (2026) studied this question.