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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, whichwould place $^{29}$Ne firmly inside the island of inversion, has yet beenobserved. Here, the first investigation of unbound states of $^{29}$Ne isreported. 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 crosssections and momentum distributions. The momentum distributions are compared tocalculations using the eikonal, direct reaction model, allowing$\ell$-assignments for the observed states. The lowest-lying resonance at anexcitation energy of 1.48(4) MeV shows clear signs of a significant$\ell$=3-component, giving first evidence for $f_{7/2}$ single particlestrength in $^{29}$Ne. The excitation energies and strengths of the observedstates are compared to shell-model calculations using the sdpf-u-mixinteraction

Border of the Island of Inversion: Unbound states in $^{29}$Ne