Holomorphic-curve lower bounds for unobstructed unknotting number

Establish whether counts of $J$-holomorphic curves with boundary on a connected immersed Lagrangian cobordism that is cylindrical over embedded Legendrians provide a lower bound for the unobstructed Legendrian unknotting number.

Background

The paper introduces an unobstructed unknotting number by forbidding regular homotopies through embedded loose Legendrians. It then asks whether holomorphic-curve counts associated with connected immersed Lagrangian cobordisms can detect or bound this quantity from below.