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# System prepended metadata

title: Shortest paths- aspect ratio

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# Shortest paths- aspect ratio

**Claim 1:** denote $v_1$ as the first vertex in the sort.
suppose that the sum of coefficinets from path starting at $v_1$ is $s$. Then for some edge $e_i=(v_1,v_i)$, the sum of coeficients is $s/d^c_{v_1}$.

**Lemma?:** if Claim 1 does not hold, then there is a different choice of coefficients $\{c_{q(s, t)}\}$ with the same coefficient sum, that gives the same dual coefficient vector $D$, 