  By quantifying the distance between two collider events, one can triangulate
a metric space and reframe collider data analysis as computational geometry.
One popular geometric approach is to first represent events as an energy flow
on an idealized celestial sphere and then define the metric in terms of optimal
transport in two dimensions. In this paper, we advocate for representing events
in terms of a spectral function that encodes pairwise particle angles and
products of particle energies, which enables a metric distance defined in terms
of one-dimensional optimal transport. This approach has the advantage of
automatically incorporating obvious isometries of the data, like rotations
about the colliding beam axis. It also facilitates first-principles
calculations, since there are simple closed-form expressions for optimal
transport in one dimension. Up to isometries and event sets of measure zero,
the spectral representation is unique, so the metric on the space of spectral
functions is a metric on the space of events. At lowest order in perturbation
theory in electron-positron collisions, our metric is simply the summed squared
invariant masses of the two event hemispheres. Going to higher orders, we
present predictions for the distribution of metric distances between jets in
fixed-order and resummed perturbation theory as well as in parton-shower
generators. Finally, we speculate on whether the spectral approach could
furnish a useful metric on the space of quantum field theories.
