Parameter Triad (α, βᵣel, 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, βᵣel, 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. βᵣel > 0 is the effective relaxation scale in fractional Mittag-Leffler dynamics  ^CDₜ^x (t) = -ₑ₄₋x (t), x (t) E_! (-ₑ₄₋t^),  explicitly distinguished from the spectral slope βₛpec. 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  D₊₋ (P|P^) =_P_ () () P^{ () }, = 1-! (-DKL).  A phenomenological scale-flow model  dd= - (-₀) + (-₀) ², >0, \ >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 βᵣel 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!, Nₘin=1500).