A computerized, bandwidth-reduced system that will reconcile two ordered sets of values such that a series of changes made to the one are reflected in the other by creating defined REMOVE SERIES, SWAP SERIES, INSERT SERIES and CHANGE SERIES for one set of ordered values, transferring the REMOVE SERIES, SWAP SERIES, INSERT SERIES and CHANGE SERIES and using the REMOVE SERIES, SWAP SERIES, INSERT SERIES and CHANGE SERIES to reconcile another ordered set of values.