The Depletion Limit of Level Repulsion: Why Solar Flares Fail the GOE Test while Earth Systems Pass

A random matrix theory (RMT) program has shown that single-source, charge-and-release Earth systems (faults, mantle plumes, ore deposits, geysers, ice sheets, and the biosphere) exhibit GOE-class level repulsion in their event timing, while superposed multi-source systems collapse to Poisson. Here we test the most extreme single-source charge-and-release system in the Solar System: magnetic-stress accumulation and reconnection in an individual solar active region. Using the science-quality NOAA/NCEI GOES-R XRS flare report, we extract the M- and X-class flare sequences of the five strongest active regions of Solar Cycle 24 (AR 12673, 12192, 11515, 11429, 12297; 112 pooled waiting times). The result is a clean negative: single solar active regions do not show level repulsion. The pooled spacing ratio is r-bar = 0.453 (bootstrap 95 percent CI 0.37 to 0.49), excluding the GOE value 0.531 but including Poisson 0.386, with the KS test preferring Poisson. Individual regions scatter across the Poisson-GOE boundary (0.40 to 0.52), reflecting variable per-event depletion. The whole-disk 2014 solar-maximum sample collapses below Poisson into clustering (r-bar = 0.354, CV = 2.32), driven by sympathetic and homologous flaring. We interpret this through a reservoir-depletion mechanism: level repulsion requires that each release substantially empties the source reservoir, forcing a recharge wait. A geyser flushes about 100 percent of its thermal charge and shows super-GUE rigidity; faults, plumes, and ore systems flush 60 to 90 percent and show GOE; but a solar active region stores enormous magnetic free energy and releases under 10 percent per flare, so its reservoir is never meaningfully depleted and short waiting times are not forbidden, hence Poisson. The spacing ratio r-bar is therefore not merely a single-versus-multi-source discriminator but a quantitative probe of the reservoir depletion ratio, placing solar active regions at a pooled 46 percent (range 10 to 90 across regions), far below every Earth system studied. We further test, across 16 active regions, whether inter-region variation in r-bar is driven by single-event release strength (flare rate, X-class fraction, peak flux, integrated energy) and find no significant correlation (all p above 0.27): per-AR estimates are noise-dominated, so the depletion interpretation operates across systems, not within the solar active-region population. The single-AR Poisson behavior is invariant across the solar cycle (chi-square test p=0.81), while whole-disk clustering strengthens into the decline (CV rising 2.2 to 3.1). The failure of solar flares to repel is not a flaw in the unifying principle but a measurement of where its mechanism switches off. Seventh in a unified RMT program spanning ten Earth and stellar systems.