Reproduction kit for the K-tensor cascade hierarchy and K*(t) L→H transition diagnostic (JHTDB DNS, MAST tokamak, WIND solar wind)
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Version 1.2 adds the K*(t) rolling time-series pipeline and results accompanying: R. A. Satnoianu, "Real-time cascade-complexity diagnostic for the L→H confinement transition," PPCF (submitted May 2026). See README_v1.2.txt for details. <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 ζ<sub>K</sub>(p) = Σ<sub>k</sub>(log(k+1)/log B<sub>K</sub>)·ζ<sub>(k+1)</sub>(p), built from the tensor product of n-modal golden-ratio cascades on a composite base B<sub>K</sub>=(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–Stokes</b> (n=64 velocity profiles): K* = 3, mean |Δζ| = 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 |Δζ| = 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* = 4–5, mean |Δζ| = 0.072 [0.071, 0.074], statistically tied with KO62 (one fitted constant, 0.072) and She–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
v1.2版本新增了K*(t)滚动时间序列流水线及配套研究成果，对应论文为R. A. Satnoianu所著"针对L→H约束转变的实时级联复杂度诊断"，发表于PPCF（《等离子体物理与受控核聚变》，2026年5月投稿）。详细信息请参阅`README_v1.2.txt`。 本Zenodo存档配套两篇介绍完全发展湍流结构函数指数ζ(p)的无参数乘性级联闭合形式层级的论文： 1. R. A. Satnoianu，"等离子体湍流结构函数指数的无参数闭合形式预测：基于MAST托卡马克（tokamak）数据的跨装置验证"，《核聚变》（2026年，审稿中）。 2. R. A. Satnoianu，"作为无参数湍流可观测量的最优级联复杂度"，《物理评论快报》（2026年，审稿中）。 K张量层级ζ_K(p) = Σₖ[log(k+1)/log B_K]·ζ_{k+1}(p)，基于复合基底B_K=(K+1)!上的n模态黄金比例级联的张量积构建，任意阶均无拟合参数。本存档论文与可复现脚本中证明的饱和定理保证，可由数据选出有限的最优复杂度K*，排除了无限优化的曲线拟合可能。 **跨域验证**在三种独立湍流流态上选出了三种不同的最优复杂度，全部来自同一无参数层级，并附带聚类自助法（cluster-bootstrap）置信区间： - **JHTDB DNS各向同性三维纳维-斯托克斯（Navier–Stokes）流**（n=64条速度剖面）：K*=3，平均|Δζ|=0.023 [0.019, 0.027]，相较KO62（1个拟合常数）性能提升30%。 - **MAST托卡马克逐发磁涨落数据**（从Neale 2021中精选的113发级联波段实验发次）：K*=1，平均|Δζ|=0.042 [0.034, 0.051]，相较KO62性能提升47%。 - **WIND-MFI 11Hz太阳风磁场数据**（50天宁静太阳集合，n_rec=4800条记录）：K*=4~5，平均|Δζ|=0.072 [0.071, 0.074]，在无参数框架下与KO62（1个拟合常数，0.072）及She-Lévêque模型（2个拟合常数，0.073）统计性能相当。 K*值随底层级联物理复杂度单调递增，提供了可量化的级联复杂度可观测量，可用于区分不同湍流流态。 **数据集内容**：涵盖三个领域的预处理JSON集合数据；无参数K张量闭合形式的Python实现；原始数据获取流水线（FAIR-MAST S3客户端、NASA HAPI客户端）；用于并行重跑的Modal云执行脚本；最终论文PDF。核心结果可通过`code/tensor_cascade_test.py`，从存档的JSON文件中在一分钟内复现。 所有原始数据均为公开数据：JHTDB（Li等，2008）、FAIR-MAST存档（英国原子能管理局UKAEA）、通过HAPI获取的NASA WIND-MFI数据。复现工具包采用MIT许可证授权。本作品为单作者成果，无外部资助，仅使用公开数据。专利优先权：本存档中公开的方法已提交美国临时专利申请，编号64/058,298（确认号9119；发明人案卷号FW-PROV-14），提交日期为2026年5月6日。在遵守适用专利权利要求的前提下，本算法源代码以MIT许可证发布。
