Model-independent criterion for predicting cutoff (the “holy grail”)

Develop an easily verifiable, model-independent criterion that guarantees total-variation cutoff for sequences of finite irreducible Markov chains without requiring 1+o(1)-precise asymptotics of the mixing time.

Background

After surveying model-specific proofs of cutoff that rely on determining mixing times within a 1+o(1) factor, the notes argue this brute-force approach lacks conceptual explanation and is fragile. The author frames the central challenge as finding general, checkable conditions that trigger cutoff across models, analogous to universal criteria in concentration of measure or sharp thresholds. The immediately following Problem [Holy grail] asks for such a criterion.