  The nucleus $^{29}$Ne is situated at the border of the island of inversion.
Despite significant efforts, no bound low-lying intruder $f_{7/2}$-state, which
would place $^{29}$Ne firmly inside the island of inversion, has yet been
observed. Here, the first investigation of unbound states of $^{29}$Ne is
reported. The states were populated in $^{30}\mathrm{Ne}(p,pn)$ and
$^{30}\mathrm{Na}(p,2p)$ reactions at a beam energy of around $230$
MeV/nucleon, and analyzed in terms of their resonance properties, partial cross
sections and momentum distributions. The momentum distributions are compared to
calculations using the eikonal, direct reaction model, allowing
$\ell$-assignments for the observed states. The lowest-lying resonance at an
excitation energy of 1.48(4) MeV shows clear signs of a significant
$\ell$=3-component, giving first evidence for $f_{7/2}$ single particle
strength in $^{29}$Ne. The excitation energies and strengths of the observed
states are compared to shell-model calculations using the sdpf-u-mix
interaction
