When Markov Models Fail: A Practical Diagnostic Framework for Single-Molecule Switching Data

Finite-state Markov (telegraph) models are the standard framework for analysing switching dynamics in single-molecule systems, implicitly assuming memoryless transitions and exponential dwell-time distributions. In practice, many datasets exhibit systematic deviations from these assumptions — including non-exponential dwell-time distributions, elevated or condition-dependent coefficients of variation (CV), and inconsistencies in rate scaling across experimental conditions. These effects are frequently addressed through increased model complexity (multi-state or hidden Markov models), but often persist despite additional parameterisation. This paper formalises a set of recurring empirical mismatch patterns between data behaviour and Markov assumptions, and introduces a practical four-step diagnostic framework that allows researchers to identify when model escalation is unlikely to resolve the discrepancy. The four steps are: (1) test dwell-time distribution shape against an exponential null; (2) check CV magnitude against the analytic ceiling for the assumed state count; (3) test CV for systematic condition dependence; (4) check rate scaling under viscosity perturbation. The paper then presents a decisive experimental discriminator based on viscosity perturbation (glycerol titration), exploiting a mathematical invariance of the Markov class: under Kramers scaling, all transition rates scale uniformly with viscosity, leaving the CV of dwell times exactly invariant. A measurable decrease in CV under viscosity perturbation therefore falsifies the entire Markov class without model fitting or parameter estimation. Three outcomes are distinguishable and mutually exclusive: Markov consistent, non-Markovian (classical memory), and non-Markovian (coherent). All classification thresholds were pre-committed on 17 February 2026 — six weeks before any experimental data were examined — and are publicly archived (DOI: 10.5281/zenodo.19324689). The required experiment uses standard single-molecule setups with approximately 2.5 hours of acquisition time. A pre-committed analysis script is provided in the companion protocol paper (Paper C, DOI: 10.5281/zenodo.19228700). This paper forms part of a pre-committed series. The empirical evidence base is in Paper B (DOI: 10.5281/zenodo.19228687). The theoretical foundation is in R1 (DOI: 10.5281/zenodo.17959914). Paper D is the adoption bridge: it speaks in the reader's language first — naming the problem they already experience — before directing them to the diagnostic framework and the decisive test.