The loose weighted-web linkability conjecture

Let a weighted web be a directed graph with vertex sets $A$ and $B$ and vertex capacities, and call it loose when it satisfies the looseness condition defined in the paper. A loose weighted web is linkable when the paper's specified family of vertex-disjoint paths or equivalent web-flow structure exists.

Loose weighted-web conjecture. A loose weighted web is linkable.

This is a reformulation of the main vertex version of the Max-Flow Min-Cut conjecture using the paper's wave-combination machinery. The excerpt does not provide enough information to identify the exact definition of looseness or linkability, so the formulation and its precise resolved status should be checked against the full paper.