Complex Resonance of Origami Wave–Nuclei CROWN

We present CROWN—a unified theoretical and computational framework for recon- structing multiscale spectral structures in origami wave–nuclei, where folded geometry and hierarchical stiffness generate proton-like resonances formed by superpositions of quark-like spectral modes. In this picture, each origami fold acts as a confined resonant cell, producing discrete peaks analogous to bound quarks inside a proton, while hierarchical twisting yields multifractal spectral tails—a continuum reminiscent of quark–gluon superposition. The spectral measure ν is constructed directly from origami parameters, and the inverse recovery of the nonnegative spectral density ρ(μ) from correlators G(p) is solved via a variational framework unifying classical finite-smoothing (FSP) and its fractional nonlocal extension(FROL). This allows stable reconstruction of both sharp proton-scale resonances and quark- like multiscale continua. The approach provides functional-analytic guarantees, matrix-free operators, a fractional Laplacian in log-mass space, ADMM/LSMR solvers, bootstrap pole statistics, and Kramers–Kronig validation. Numerical experiments recover effective spectral exponents seff ≈ 4, reveal clustered proton-analog resonances, and persistent multifractal behavior inherited from origami geometry. All theory, code, and reproducible results are contained in a single manuscript.