1. A non-transitory computer-readable storage medium comprising instructions stored thereon for maintaining a current state of a document that is concurrently being edited by at least a first user associated with a first computing system and a second user associated with a second computing system, the instructions, when executed by at least one processor, being configured to cause the first computing system to at least: generate a collection of inverse transformations of an index of the document, the collection of inverse transformations being based on at least one asymmetric local edit to the document by the first computing system; determine a location within the document to perform a remote edit by the second computing system based on the collection of inverse transformations of the index of the document; perform the remote edit to the document at the determined location based on the remote edit by the second computing system; and perform at least one local edit to the document based on the at least one asymmetric local edit to the document by the first computing system.