  In this simple note, we suggest a way to rigorously establishing constraints
on the form of the ground states of the Hubbard and t-J models and extended
longer (yet finite) range variants for various dopings, once exact numerical
results are established for these Hamiltonians on finite size clusters with two
different (both open and periodic) boundary conditions. We demonstrate that
strong bounds will be established if non-uniform minima subject periodic
boundary conditions are found. An offshoot of our proposal might enable
rigorously establishing the strong tendency toward especially stable stripe
formation at the magical commensurate doping of 1/8 on the infinite lattice, as
well as at other dopings.
