A Space-Time Dual-Domain Test of the Source-Superposition Law in Volcanic Systems: Temporal Recharge Repulsion, Spatial Supply-Shadow Repulsion, and the Spectral Superposition Theorem Across Four Natural Targets

The capstone of a Random Matrix Theory (RMT) program applied to Earth-system rhythms, probing a single volcanic class in both the time and space domains across four independent natural targets using the parameter-free spacing-ratio statistic mean-r and the coefficient of variation CV, with no tunable preprocessing. Target A (time, single source): 86 Mount Etna flank eruptions (1169-2021 CE) give mean-r = 0.518 and CV = 1.16, lifted toward GOE by magma-chamber recharge memory. Target B (time, many sources): per-source-unfolded intervals from six independent volcanoes (Mauna Loa, Piton de la Fournaise, Hekla, Vesuvius, Klyuchevskoy, Colima), randomly interleaved, collapse mean-r from a per-source mean of 0.574 to 0.470, confirming the spectral superposition theorem. Target C (space, single arc): 17 Cascade stratovolcanoes (Baker to Lassen) give mean-r = 0.594 and CV = 0.56, with a GOE Kolmogorov-Smirnov fit that cannot be rejected (p = 0.79), reflecting magma-supply-shadow repulsion with quasi-regular 54 km spacing. Target D (space, complex multi-rift): 67 Icelandic vents from seven rift systems, projected unfiltered onto one transect, give CV = 1.59, the signature of structural-inheritance clustering. The four targets confirm one law across both domains: a single long-memory source repels in both time and space, a mixture of independent sources relaxes to Poisson, and inherited spatial localization clusters. Targets A and D reproduce, in volcanic form, the time-space asymmetry first reported for orogenic gold systems.