Markov Models Fail in DNA Torsional Dynamics: Three Independent Signatures and a Decisive Test

Single-molecule magnetic tweezers studies of DNA torsional hopping universally treat the process as a finite-state Markov (telegraph) chain. We show that this assumption is violated in the Walker, Vanderlinden & Lipfert (2018) benchmark dataset via three within-condition statistical signatures: (i) dwell-time distributions are non-exponential at every motor position in both torsional states (Kolmogorov–Smirnov test with Lilliefors correction, p < 0.05 at all 11 conditions in both HIGH and LOW states); (ii) the coefficient of variation (CV) of dwell times exceeds the pre-committed discriminator threshold of 1.50 (pooled CV_HIGH = 1.681, CV_LOW = 1.726), with individual positions 29.0 and 29.2 exceeding the analytic 2-state Markov ceiling of √3 ≈ 1.732; and (iii) CV varies systematically with supercoiling density (Spearman ρ = +0.718, p = 0.013, LOW state, 11 conditions, computed per-condition). All three signatures are within-condition or per-condition results, independent of pooling effects. The Walker benchmark was acquired near the buckling transition midpoint under near-equilibrium conditions — the setting least favourable for detecting non-Markovian memory. Its failure of the Markovian assumption establishes a conservative lower bound: driven biological systems operating far from equilibrium are expected to show these deviations more strongly. We propose a decisive experimental discriminator: glycerol titration under Kramers viscosity scaling. By theorem, CV is exactly invariant under viscosity change for any telegraph model regardless of state number or parameterisation. A measurable CV decrease under glycerol therefore rules out the entire Markov class. Pre-committed classification thresholds (ΔCV < −0.30, Spearman ρ < −0.90, both required simultaneously) make the verdict automatic and non-adjustable. The practical protocol is in the companion paper (Paper C, DOI: 10.5281/zenodo.19228700). All thresholds were pre-committed on 17 February 2026 before the Walker dataset was examined.