An n/s Scaling-Spectrum Framework for Generalized Moment Scaling: Curvature, Signed-Moment Asymmetry, and Prospective Moment-Order Validation

This preprint introduces an n/s scaling-spectrum framework for generalized moment scaling. The proposed model parameterizes the generalized Hurst spectrum as H(q,t) = |q|^(n−1) / [s₀(t) exp(kq)], separating power-curvature (n), baseline scaling state (s₀), and signed-moment asymmetry (k). Building on established power-law generalized-Hurst representations and multifractal formalisms, the framework adds prospective sequential moment-order validation as an applicability and falsification criterion before parameter interpretation or extrapolation. Exploratory computational experiments include monofractal reference signals, IAAFT surrogate testing, binomial p-model and lognormal multiplicative-cascade sweeps, blind classification, parameter-recovery simulations, competing-model benchmarks, and held-out moment-order prediction. The results support n as an identifiable curvature coordinate within compatible scaling-spectrum families while also identifying important limits of applicability, including inferior high-order extrapolation for some p-model spectra. This record contains the preprint, frozen reproduction pipeline, supporting results, and appropriately attributed reference data. The framework is presented as a testable, family-conditional research hypothesis rather than an established universal physical law.