Hello, and thanks for taking an interest in the pattern my Medium post describes. I don't think the pattern repeats in the full sense because, if the whole pattern repeated in the photon regime, it would imply that a particle-antiparticle pair lighter than an electron-positron pair would be created, each having an electric charge, and that hasn't been observed. However, there might be information to be gleaned from looking at photons of two particular energy levels. The first would be a photon with the energy equivalent of the electron mass. That's because of the stable proton's relation to a proton-antiproton pair, and the lead nucleus' relation to the hypothetical third point of granularity (twice the mass of a lead nucleus). Even though you can't create an electron until you have the energy of an electron-positron pair, there could still be something significant about a photon with the energy equivalent of a single electron's mass. Make sense?

In a similar vein, I feel that there is a special relationship between the Tau lepton and the second point of granularity, where a proton-antiproton pair is created. If so, then there might also be something special just below the mass of an electron-positron pair, and for similar reasons. That would be in the photon regime, since it's below the energy needed to create an electron-positron pair. So, I would examine the nature of a photon with an energy level in the ratio of the Tau mass divided by the mass of a proton-antiproton pair (and then multiplied by an electron-positron pair). A photon with that energy could conceivably be special.