Dear Ed Unverricht,
In my search for pieces to the Great Cosmic Puzzle and for mathematical toolsets with which to assemble a Cosmological Model based on a True Understanding. Your paper impresses me as being 100% relevant and MOST useful to Quantum Mechanics. I hope to apply these understandings to my idea of Combinatorial Quantum-wave Mechanics (CQM).
Your paper stands above most in that it clearly lifts up the understanding of anyone who reads it.
You have earned my respect BIG TIME! First, you realized the importance and relevance of the subject matter to have studied it so well! Second, you have presented a clearest and most concise description of Group Theory I've ever seen. Third, and to me the most important, is your description of quarks fits nicely into the 4D Space~Time "framework" of my paradigm called the Cosmic Onion Model. In the context of this model quarks are NOT entities in-and-of themselves but are the geometric interactions of three wave functions interacting with a 4th wavefunction type (wave-icle) which are the root-causes of protons and neutrons. (These interactions manifest as quarks -- that's why neutrons decay into electron, proton and photon energy - NEVER into quarks. The wavefunction of a decaying neutron twists into the wavefunction of a proton plus splits into an electron and anti-neutrino and sometime with gamma ray emission. Not to mention other "bounded" decay modes.)
Just as challenge to anyone reading this, maybe there exists a physicist who can explain the Electromagnetic Wave diagram showing the electric field and magnetic fields perpendicular to each other, yet perfectly in-phase with each other. Why would they propagate one way or the other? (Nature does not include the little arrow.) Without the help of the little arrow what "propels" the wave one way or the other? (My best guess is that the wave is constructed from photons (h*c) (packet of energy in the form of angular momentum moving at c) temporally spaced so that they construct the overall EM wave -- at the photon level there must be a phase shift between E vs. M.)
Not to worry, I don't hold that against you. I only mention it as a challenge to anyone who can offer an better explanation.
Overall, your paper desires more than 4.8 so here is a boost to 5.1.