Parameter Triad (α, β_rel, γ): A Universal Calibration and Falsification Protocol for Detecting Regime Transitions in Complex Systems (v1.1.2)

This preprint defines a reproducible methodological standard for the triad (α, β_rel, γ) for observational time series of non-Markovian dissipative systems and regime-transition detection. α = H quantifies long-range dependence / self-similarity (monofractal approximation), estimated e.g. by DFA-2 or Whittle. β_rel > 0 is the effective relaxation scale in fractional Mittag-Leffler dynamics  {}CD_tαx(t) = -βᵣₑₗx(t), x(t)∝ Eα!(-βᵣₑₗtα),  explicitly distinguished from the spectral slope β_spec. γ ∈ [0,1) measures time-reversal asymmetry (irreversibility) via ordinal patterns (Bandt–Pompe): let � and � be the (add-ε smoothed) permutation distributions for forward and reversed series; define  DKL(P|P←)=∑πPε(π)log{Pε(π)}{P←{ε}(π)}, γ = 1-exp!(-D{KL}).  A phenomenological scale-flow model  dγ/d= -λ(γ-γ_0)+μ(γ-γ_0)^2, λ>0,\ μ>0,  yields two fixed points and a calibrated threshold � (not a universal constant). Falsification protocol G0–G4 is provided: stability (G0), irreversibility significance against ≥199 IAAFT surrogates (G1), artifact controls incl. α–γ dependence + cyclic-shift test (G2), regime-shift detection via Bai–Perron on local γ (G3), and identifiability of β_rel via CV ≤ 0.25 across segments (G4). The package includes bilingual PDF/LaTeX sources, figures, and reproducible pseudocode and defaults (m=3, τ=1, ε=1/m!, N_min=1500).