The abrupt-or-strongly-eroded dichotomy for infinite variation Lévy processes

Let $X$ be an infinite variation Lévy process. A process is abrupt or strongly eroded according to the path properties defined in the paper.

Dichotomy conjecture. Every infinite variation Lévy process is either abrupt or strongly eroded.

This dichotomy is presented as a consequence of Vigon's point-hitting conjecture and would classify all infinite variation Lévy processes according to these two behaviours. The paper establishes the dichotomy under broad sufficient conditions, but the general assertion remains open.