Periodicity of Nuclear Structure and Emergent Electronic Periodicity

This working note presents a grammar of nuclear filling based on the pairing of particles into structured units (clusters), and shows that it regenerates, with a restricted alphabet and no fitted parameters, four independent registers over periods 1 to 4 of the periodic table: the list of stable and quasi-stable isotopes of each element (every Z and every N accounted for), the hierarchy of their abundances (the dominant isotope as a shell saturation, the logic of the relative proportions following the filling rules, and the unstable isotopes as rule violations, with their products), the observed chemical valences (numbers and steps, hypervalences included), and the structure of the binding energies (closure steps, tariffs by event type, isobar depths). The main decay modes of the region derive from the same writing, including double beta decays, whose arrival isotope is predicted by the filling order. This result realizes, over four periods, the prediction stated in the “Lattice Mechanics” framework [3]: electronic periodicity should emerge from the cluster structure of the nucleus. The work continues: systematic validation over all recorded radioactive isotopes, extension to periods 5 to 7, and a complete atlas in preparation. The present note fixes the state of the decipherment and establishes its priority.