Establish whether MOND theories exist outside the unit interval of scaling dimensions

Determine whether acceptable MOND theories exist with deep-MOND scaling parameter \(\eta<0\) or \(\eta>1\), thereby extending the family beyond the range from pure modified gravity to pure modified inertia.

Background

The paper develops mixed modified-gravity–modified-inertia theories whose scaling parameter is restricted to $0\leq\eta\leq1$. Within this interval, the endpoint values are associated with pure modified gravity and pure modified inertia, respectively, while intermediate values describe theories modifying both sectors.

The author does not establish whether the scaling and MOND requirements themselves exclude values below zero or above one. The unresolved question is whether physically acceptable MOND theories can be constructed outside this interval.