Reproduction kit for the parameter-free K-tensor cascade hierarchy across three turbulence regimes (JHTDB DNS, MAST tokamak, WIND solar wind)

<p>This Zenodo deposit accompanies two manuscripts that introduce a parameter-free hierarchy of multiplicative-cascade closed forms for the structure-function exponents ζ(p) of fully developed turbulence:</p><ol><li>R. A. Satnoianu, <i>A parameter-free closed-form prediction for the structure-function exponents of plasma turbulence: cross-device validation on MAST tokamak data</i>, Nuclear Fusion (under review, 2026).</li><li>R. A. Satnoianu, <i>Optimal cascade complexity as a parameter-free turbulence observable</i>, Physical Review Letters (under review, 2026).</li></ol><p>The K-tensor hierarchy &zeta;_K(p) = &Sigma;_k(log(k+1)/log B_K)·&zeta;_(k+1)(p), built from the tensor product of n-modal golden-ratio cascades on a composite base B_K=(K+1)!, contains no fitted parameters at any order. A saturation theorem (proved in the deposit's manuscript and reproducibility scripts) guarantees a finite optimal complexity K* selected by the data, ruling out infinite-improvement curve-fitting.</p><p><b>Cross-domain validation</b> on three independent turbulence regimes selects three distinct optimal complexities, all from the same parameter-free hierarchy with cluster-bootstrap confidence intervals:</p><ul><li><b>JHTDB DNS isotropic 3D Navier&ndash;Stokes</b> (n=64 velocity profiles): K* = 3, mean |&Delta;&zeta;| = 0.023 [0.019, 0.027], beating KO62 (1 fitted constant) by 30%.</li><li><b>MAST tokamak per-shot magnetic fluctuations</b> (n=113 cascade-band shots curated from Neale 2021): K* = 1, mean |&Delta;&zeta;| = 0.042 [0.034, 0.051], beating KO62 by 47%.</li><li><b>WIND-MFI 11 Hz solar-wind magnetic-field</b> (50-day quiet-sun ensemble, n_rec = 4,800 records): K* = 4&ndash;5, mean |&Delta;&zeta;| = 0.072 [0.071, 0.074], statistically tied with KO62 (one fitted constant, 0.072) and She&ndash;Lévêque (two fitted constants, 0.073) at the parameter-free level.</li></ul><p>The K* values monotonically increase with the underlying cascade physics complexity, providing a measurable cascade-complexity observable that distinguishes turbulence regimes.</p><p><b>Contents</b>: processed JSON ensemble data for all three domains; parameter-free K-tensor closed-form Python implementation; raw-data fetch pipelines (FAIR-MAST S3 client, NASA HAPI client); Modal cloud-execution scripts for parallel re-runs; final manuscript PDFs. The headline result is reproducible from the deposited JSON in under one minute via <code>code/tensor_cascade_test.py</code>.</p><p>All source data are public: JHTDB (Li et al. 2008), FAIR-MAST archive (UKAEA), NASA WIND-MFI via HAPI. Reproduction kit licensed MIT. Single-author work, no external funding, public data only. Patent priority: the methods disclosed in this deposit are the subject of US Provisional Patent Application No. 64/058,298 (Confirmation No. 9119; Inventor Docket FW-PROV-14), filed 2026-05-06. Subject to applicable patent rights, the algorithm source code is released under the MIT licence