Ramification breaks from a reduced ramification polygon ($\mathrm{length}(-m)=|G_m|-|G_{m+1}|$)

In a totally ramified Galois extension, the uniformizer criterion for lower ramification groups gives $\sigma \in G_m\setminus G_{m+1}$ exactly when $v_L((\sigma (\pi )-\pi )/\pi )=m$. The Newton polygon root valuation theorem therefore identifies a slope $-m$ in the coefficient-index convention with a lower ramification jump at $m$. Its horizontal length is the number of automorphisms in that difference. Under the reflected Newton polygon convention the same jump has slope $+m$.