Benchmark dataset and reproducibility artefacts for: A symbolic-regression instrument for spectral-exponent estimation in turbulent and critical scale-invariant systems

Companion dataset to the manuscript "A symbolic-regression instrument for spectral-exponent estimation in turbulent and critical scale-invariant systems: design, characterisation, and uncertainty budget" submitted to SciPost Physics Core (April 2026, single-author: Igor Merlini, ActarusLab). This deposit contains the complete reproducibility package for the symbolic-regression spectral-exponent instrument described in the companion manuscript. It includes all primary and derived numerical results referenced in the paper, plus high-resolution figure files. The dataset comprises five distinct experimental campaigns: (1) Synthetic Rogallo benchmark (Section 3.1): n = 735 configurations spanning p ∈ [0.30, 3.00] at three grid resolutions (N ∈ {64, 96, 128}) and five seeds. Aggregate metrics: MAE = 0.0144, mean bias = +0.0066, R² = 0.9993. (2) Additive-noise stress test (Section 3.2): n = 110 cases across 11 SNR levels from −3 dB to +30 dB plus the noise-free limit, with two reference target exponents (p = 5/3 and p = 0.91). (3) Three-class asymmetry verification (Section 3.3): n = 90 cases verifying the falsifiable physical prediction that recovery error scales monotonically with spectral steepness; confirmed at 4 out of 5 SNR levels. (4) Bootstrap uncertainty quantification (Section 3.4): B = 2000 resamples on the per-seed estimates of the class-separation observable Δ. Clean-limit estimate: Δ = 0.7547, 95% CI = [0.7445, 0.7652]. (5) Direct numerical simulation validation (Section 3.5): in-house pseudo-spectral DNS at N = 96^3, Re_box ≈ 2000, with feedback-controlled stochastic forcing. Recovered exponent on the early steady-state subset: p_DNS = 1.6163 ± 0.0436, consistent with Kolmogorov 1941 (5/3) within the synthetic-benchmark systematic bias. All results are reproducible bit-exactly from the included data tables on dual NVIDIA T4 GPUs in approximately 50 minutes total runtime. Software environment: Python 3.12, JAX 0.4 (CUDA 12), PySR with SymbolicRegression.jl 1.11, Julia 1.11.5. The package is structured in two subdirectories: data/ (CSV + JSON tables) and figures/ (PNG, 200 DPI). Complete schema documentation for every column of every data table is provided in README.md. Released under CC BY 4.0.