A single physical system — an electron colliding with a proton — produces different outcomes depending on collision energy. At 13.6 eV the electron is captured to form hydrogen. At 100 MeV elastic scattering occurs with both particles intact. Higher energies reveal the proton’s internal quark structure: pion production at 4 GeV and deep inelastic scattering at 20 GeV. All results are derived from fundamental constants alone, as the framework expands from quaternion to octonion algebra to describe increasingly fine physical structure.