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: in response to receiving a remote edit from the second computing system that has not been performed by the first computing system, generate a collection of inverse transformations of an index of the document, the generating the collection of inverse transformations including: determining that at least one local edit remains to be added to a collection of local edits; determining that the at least one local edit is asymmetric; and adding an inverse transformation of the at least one asymmetric local edit to the collection of inverse transformations; determine a location within the document to perform the 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 collection of local edits.