Maximal non-interleaving of Eg-walker’s Yjs-variant insertion ordering

Prove that the variant of the Yjs list CRDT algorithm (based on YATA) used within Eg-walker’s internal state to order concurrent insertions is maximally non-interleaving, meaning that concurrent sequences of insertions at the same position are placed contiguously rather than interleaved.

Background

Eg-walker maintains an internal CRDT structure to order concurrent insertions consistently across replicas. The implementation uses a variant of the Yjs algorithm, itself based on YATA, to determine the ordering of concurrently inserted characters.

The paper asserts that this ordering should be maximally non-interleaving—a property ensuring that concurrent runs of insertions at the same position appear consecutively rather than being interleaved. However, the authors do not provide a formal proof and explicitly conjecture this property, deferring a detailed analysis to future work.

Establishing this property would strengthen Eg-walker’s guarantees beyond the strong list specification by aligning its behavior with non-interleaving principles desirable for collaborative text editing semantics.