Extension of the deformed Pachner relation to the 2-to-4 move

A Pachner move is a local bistellar transformation between triangulations; here the relevant $3\to 3$ move has associated algebraic relations whose terms may be deformed using $x$-chains. Theorems previously established that the modified $3\to 3$ relation holds when the $x$-chains on both sides arise from the same boundary tetrahedron chain, and that adding a boundary $x$-chain does not change either side.

Extension conjecture. The analogues of these two theorems hold also for a $2\to 4$ Pachner move.

This would extend the deformation framework from the $3\to 3$ move to another four-dimensional Pachner move. The source states the extension without providing a proof or further indication of its status.