Representative CRDTs, at least Logoot and TreeDoc, were never truly proved. The correctness of Logoot and TreeDoc are claimed under the assumption that the required property of ids is preserved by the CRDT design. However, the existing id generation algorithms cannot achieve the desired property.

To be specific, I will enumerate two examples.

First, in Logoot (https://hal.inria.fr/inria-00432368/document", the function generateLinePositions in section 4.2 has a serious error, which could lead to the failure of generating new identifiers. This flawed design can be also found in the following research (Logoot-Undo, https://hal.inria.fr/hal-00450416/)

Second, in TreeDoc (https://hal.inria.fr/inria-00445975/document), the function newPosID described in section 3.2 may generate incorrect ids. This function is to generate an id r between any two ids p and q (p<q) so that p<r<q. However, in line 5, if pn=0, then we would get r<p. Readers can refer to Figure 3, in the tree, the character dY precedes the character dZ in infix order, however, the id of dY (10(0:dY)) is greater than the id of dZ (100(1:dZ)), thus their positions are inconsistent their ids.

In the literature, CRDT researchers always claim their CRDT designs are formally proved.

However, there are various scenarios whereby CRDTs would have inconsistency issues as stated above.

In my opinion, I don't think there are much validity for these claims.