Cross-Domain Evidence for a Universal Scaling Law in Bounded Self-Driven Oscillatory Systems

We report a universal scaling law governing the rise dynamics of bounded self-driven oscillatory systems: T·√A = Γ, equivalently T_rise ∝ A⁻°·⁵, where T_rise is the rise time from oscillatory minimum to peak, A is the peak amplitude, and Γ is a system-characteristic constant. The scaling law is derived from the structural dynamics of bounded self-amplifying oscillations: when amplitude reflects driver strength rather than stored energy and the same mechanism produces each event, logistic self-amplification during the rise phase gives T_rise ∝ A⁻°·⁵ with exponent exactly −0.500. The Waldmeier Effect in solar physics — that stronger solar cycles have shorter rise times, empirically documented since 1935 and theoretically unexplained for 90 years — is confirmed as the primary expression of this law: slope −0.509 versus predicted −0.500, deviation 1.8%, R² = 0.587, 24 complete cycles, 270 years of data (SIDC/SILSO). Cross-domain testing reveals the same relationship in the QBO (R² = 0.848, 71 years), classical Cepheid variable stars (dimensionless Γ within 7.6% of solar), and a null result in financial market VIX spikes (slope wrong direction, explained by framework). The dimensionless Γ, normalised by each system’s characteristic scales, clusters within 10% across confirmed domains (CV = 3.7%). A three-criterion selection framework — same driver mechanism, amplitude reflecting driver strength not stored energy, separable rise phase — correctly predicts which systems show the relationship and which do not.