  The linear dilaton geometry in five dimensions, rediscovered recently in the
continuum limit of the clockwork model, may offer a solution to the hierarchy
problem which is qualitatively different from other extra-dimensional scenarios
and leads to distinctive signatures at the LHC. We discuss the structure of the
theory, in particular aspects of naturalness and UV completion, and then
explore its phenomenology, suggesting novel strategies for experimental
searches. In particular, we propose to analyze the diphoton and dilepton
invariant mass spectra in Fourier space in order to identify an approximately
periodic structure of resonant peaks. Among other signals, we highlight
displaced decays from resonantly-produced long-lived states and
high-multiplicity final states from cascade decays of excited gravitons.
