 Solution

No stereochemical information need survive from the starting carbinol. Ionization converts that tetrahedral stereocentre into a planar, delocalized propargyl/allenyl cation before cyclization. In achiral conditions the two enantiomeric pathways to the new stereocentre in the tert-butyl-derived product are equivalent, so an enantiopure alcohol is expected to give racemic product. A claim of retained enantiopurity would require evidence for unusually effective conformational memory or ion-pair control.