Inversion of all decomposable cobordisms using Lagrangian moves

Determine whether every decomposable Lagrangian cobordism can be inverted using Lagrangian diagram moves, producing a Lagrangian cobordism in the reverse direction after any necessary stabilizations.

Background

The paper develops Lagrangian diagram moves as a method for constructing weak and genuine Lagrangian cobordisms and applies them to reverse a specific decomposable concordance from a stabilized mirror of the knot $9_{46}$ to a stabilized unknot. The construction shows that one particular decomposable concordance can be inverted after stabilization, but it does not establish that the method works for arbitrary decomposable cobordisms.

The unresolved issue is whether the move-based inversion procedure extends from the examples and restricted settings treated in the paper—such as cobordisms without 0-handles and selected concordances—to all decomposable cobordisms.