Evolution of ⟨M_lin,3D⟩ (orange and blue lines) and ⟨M_{lin, 2D}⟩ (black, green, and navy blue lines for projections along the x, y, and z axes) for filaments that have been detected above n_th = 5000 cm⁻³ or n_th = 10²¹ cm⁻², unless specified otherwise, in M3 (left), M4 (middle), and M8 (right). The red area marks the theoretical critical line mass for isothermal gas at 10–15 K. The grey dotted line shows the time step when the first fragment forms.