= Noncontact of ROF level boundaries
{title2=$\mathcal H^{n-1}((\partial^*E_s\cap\partial^*E_t)\setminus J_f)=0$}
For bounded <BV space> data and $s<t$, nested <ROF level-set formulation> minimizing sets cannot share an interface of positive surface <measure> away from data jumps. On regular graph patches, upward and downward <first variations> use the <BV traces on a hypersurface>. At contacts outside $J_f$ the forcing <BV trace on a hypersurface> agrees, whereas the two levels differ by $t-s$. Graph regularity and contact differentiation give the contradiction. Bounded forcing is a hypothesis of this argument; arbitrary unbounded $L^2\cap BV$ data are not covered by this statement.
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