Surjectivity of barcode beginning/end maps in general

Determine whether, without assuming the hypotheses of Theorem C, the beginning and end maps from the barcode of filtered symplectic homology, Beg: B→P and End: B→P, are surjective onto the set P of F-visible closed Reeb orbits.

Background

The authors construct maps that associate to each bar in the barcode its beginning and end orbits, with surjectivity established under the specific pseudo-rotation hypotheses of Theorem C. In general settings, the surjectivity of these maps remains unknown.

Surjectivity would imply that every F-visible closed orbit appears as an endpoint of some bar, strengthening the link between local homology and global filtered symplectic homology.