I beg to differ.
Mathematically resistance and conductance are reciprocal, yes. Arcs do have conductance however (in your assessment reciprocal to resistance) and this keeps growing if not controlled... hence negative conductance.
I have attached a PDF for a simulation (simulation being the operative word, which is a approximation of what catually happens) of HID lamps, the first section explains the science behind HID lamps, the other half goes into how the SPICE model was set up.
But we are now getting to a point in the thread where we are discussing applied electronics and background math to assess how long to leave between striking....