Harmonic Signature in Volcanic Recurrence: Observational Evidence for Unified Substrate Theory

Volcanic eruptions exhibit highly irregular recurrence patterns, yet their long-term statistical structure remains poorly constrained. An analysis of global recurrence in
tervals reveals that, when expressed in logarithmic time, these intervals display statistically significant phase organization aligned with the discrete harmonic exponents
β =16 and β =27.57. These values originate from a scale-invariant harmonic framework proposed for stress–release systems and were specified a priori. Using the NOAA
Significant Volcanic Eruptions Catalogue and a volcano-aware Poisson null model that preserves individual volcano lifetimes and eruption counts, recurrence intervals from 51 volcanoes (144 intervals, VEI ≥ 3, Year ≥ 1600) yield Rayleigh powers corresponding to 3.3σ for β = 16 and 3.9σ for β = 27.57, with a joint significance of 4.26σ. Ro
bustness tests confirm stability across VEI thresholds and temporal subsets. A leave one-out predictive experiment shows that harmonic phase geometry alone identifies
the high-likelihood recurrence half-space in 69.4% of cases (p = 2 × 10−6, Z = 4.64σ).

These findings indicate that volcanic recurrence intervals encode a discrete log-periodic structure inconsistent with renewal or Poisson models, and instead consistent with hierarchical stress-loading processes and discrete scale invariance. Harmonic phase offers a promising additional indicator for long-term eruption timing