This work further investigates an aspect of the phase behavior of hard circular arcs whose phase diagram has been recently calculated by Monte Carlo numerical simulations: the non-nematicity of the filamentary phase that hard minor circular arcs form. Both second-virial density-functional theory and further Monte Carlo numerical simulations find that the positional one-particle density function undulates in the direction transverse to the axes of the filaments while further Monte Carlo numerical simulations find that the mobility of the hard minor circular arcs across the filaments occurs via a mechanism reminiscent of the mechanism of diffusion in a smectic phase: the filamentary phase is not a {"modulated" ["splay(-bend)"]} nematic phase.