Relate the whole-line contact model to the full knot problem

Establish whether the local whole-line contact functional with obstacle |H|≥2, prescribed odd phase increment, and affine-tail freedoms yields the correct asymptotic selection constant for the corresponding geometric hard-thickness knot problem.

Background

The paper introduces and analyzes a specified whole-line variational model for a switched tangency, including coercivity and minimizers for odd phase classes with |q|≥3. It explicitly separates these results from the full knot problem: the model does not account for the outer strands or establish that its obstacle and constants coincide with geometric thickness asymptotics. A rigorous matching result would require both a lower bound and a recovery construction for the complete knot geometry.