1. A computer-implemented method, comprising: receiving, by a local computing device over a computer network, collection summaries for one or more data collections at a remote device, wherein a respective collection summary includes only a current additive hash value for each data collection, wherein a respective additive hash value represents a sum of hash values for two or more content items of a corresponding data collection; comparing, for a local data collection that also exists at the remote device, a current local additive hash value for a current version of the local data collection to a current remote additive hash value for a current version of the corresponding remote data collection at the remote device; in response to determining that the current remote additive hash value does not match the current local additive hash value, comparing the current remote additive hash value to one or more historical local additive hash values that were generated for a previous version of the local data collection; and in response to determining that the current remote additive hash value matches a historical local additive hash value for the local collection, sending, to the remote device over the computer network, structured names for content items that have been added to the local data collection after the matching historical local additive hash value was generated.