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We use semi-analytic models of structure formation to interpret gravitationallensing measurements of substructure in galaxy cluster cores (R<=250kpc/h) atz=0.2. The dynamic range of the lensing-based substructure fractionmeasurements is well matched to the theoretical predictions, both spanningf_sub~0.05-0.65. The structure formation model predicts that f_sub iscorrelated with cluster assembly history. We use simple fitting formulae toparameterize the predicted correlations: Delta_90 = tau_90 + alpha_90 *log(f_sub) and Delta_50 = tau_50 + alpha_50 * log(f_sub), where Delta_90 andDelta_50 are the predicted lookback times from z=0.2 to when each theoreticalcluster had acquired 90% and 50% respectively of the mass it had at z=0.2. Thebest-fit parameter values are: alpha_90 = (-1.34+/-0.79)Gyr, tau_90 =(0.31+/-0.56)Gyr and alpha_50 = (-2.77+/-1.66)Gyr, tau_50 = (0.99+/-1.18)Gyr.Therefore (i) observed clusters with f_sub<~0.1 (e.g. A383, A1835) areinterpreted, on average, to have formed at z>~0.8 and to have suffered <=10%mass growth since z~0.4, (ii) observed clusters with f_sub>~0.4 (e.g. A68,A773) are interpreted as, on average, forming since z~0.4 and suffering >10%mass growth in the ~500Myr preceding z=0.2, i.e. since z=0.25. In summary,observational measurements of f_sub can be combined with structure formationmodels to estimate the age and assembly history of observed clusters. Theability to ``age-date'' approximately clusters in this way has numerousapplications to the large clusters samples that are becoming available.

Connecting Cluster Substructure in Galaxy Cluster Cores at z=0.2 With Cluster Assembly Histories