ETH and Many-Body Localization Through an Operational Basin Diagnostic A Model-Dependent Bridge with Exact Coarse-Dynamics Identities

Thermalization described by the eigenstate thermalization hypothesis (ETH) and its failure in many–body localization (MBL) are usually treated as distinct phenomena. We show that both arise as regime limits of a single structural mechanism. Within Modal Triplet Theory, effective many-body dynamics is governed by projection onto an admissible coherent sector, inducing stable basins with finite margins in a coarse-grained state space. ETH corresponds to a high-mixing regime with a dominant thermal basin, while MBL corresponds to fragmentation into many long-lived basins with suppressed escape. The ETH–MBL crossover is governed by collapse of basin margins and admits a sharp but smooth knee regime under standard barrier assumptions. Noise, baths, and monitored measurements probe the same margins, explaining why monitored-circuit entanglement transitions mirror ETH–MBL behavior. The framework yields falsifiable predictions for memory retention, echo protocols, entanglement scaling, and noise sensitivity, and unifies three previously separate research programs within a single reduced-dynamical description.