Peaked heads are trajectory-easy: peak mass ≥ 1−δ and relative tilts ≤ η give 1 + χ² ≤ (1 + δ e^{2η})/(1−δ)²

For all $\htmlData{mx=1}{n \in \htmlData{mx=0}{\mathbb{N}}}$, $\htmlData{mx=5}{p, t : \htmlData{mx=2}{\htmlData{mx=0}{\operatorname{Fin}}\,\htmlData{mx=1}{n}} \mathrel{\htmlData{mx=4}{\to}} \htmlData{mx=3}{\mathbb{R}}}$, $\htmlData{mx=3}{j_{0} \in \htmlData{mx=2}{\htmlData{mx=0}{\operatorname{Fin}}\,\htmlData{mx=1}{n}}}$ and $\htmlData{mx=1}{\delta, \eta \in \htmlData{mx=0}{\mathbb{R}}}$, if $\htmlData{mx=4}{\forall j,\ 0 \mathrel{\htmlData{mx=3}{\leq}} \htmlData{mx=2}{\htmlData{mx=0}{p}(\htmlData{mx=1}{j})}}$, $\htmlData{mx=3}{\sum_{j} \htmlData{mx=2}{\htmlData{mx=0}{p}(\htmlData{mx=1}{j})}} \mathrel{\htmlData{mx=4}{=}} 1$, $\htmlData{mx=1}{1 - \htmlData{mx=0}{\delta}} \mathrel{\htmlData{mx=5}{\leq}} \htmlData{mx=4}{\htmlData{mx=2}{p}(\htmlData{mx=3}{j_{0}})}$, $\htmlData{mx=0}{\delta} \mathrel{\htmlData{mx=1}{<}} 1$, $\htmlData{mx=2}{\htmlData{mx=0}{t}(\htmlData{mx=1}{j_{0}})} \mathrel{\htmlData{mx=3}{=}} 0$ and $\htmlData{mx=5}{\forall j,\ \htmlData{mx=2}{\htmlData{mx=0}{t}(\htmlData{mx=1}{j})} \mathrel{\htmlData{mx=4}{\leq}} \htmlData{mx=3}{\eta}}$, then