## A symmetry sought for an ad hoc conservation law

The Noether Theorem states that for every symmetry (with sufficient properties) there is a conservation law.

Playing with some formulas, I made up a conservation law rather ad hoc and wonder if in this case there might be, conversely, a symmetry in the sense of the Noether Theorem. The conservation law I am playing with is $$\sum_{i} 1/v_i(t)=\text{const,}$$where the v_i are some functions of time. You may consider them as velocities of points i.

Is there a symmetry that would lead to this conservation law?
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