Periodicity of Nuclear Structure and Emergent Electronic Periodicity

This working note presents a nuclear filling grammar based on the pairing of particles into structured units (clusters), and shows that it regenerates, with a restricted alphabet and no adjusted parameter, 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 justified), the hierarchy of their abundances, the observed chemical valences (number and steps, hypervalences included), and the structure of binding energies (closure steps, per-event costs, isobar depths). This version 2 extends the analysis to the complete set of catalogued radioactive isotopes of periods 1 to 4 (about 580 nuclides, attached in appendix with structural writing, resolution, cascade and half-life): unstable nuclides are written as the neutron structural equivalents of their stable isobars, and a deterministic writing algorithm (isobaric substitution in dismantling order, binder removal on the proton side) regenerates their writings reproducibly, with no arbitrary choice. Decay modes derive from the same writings, 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. Work continues towards periods 5 to 7. The present note fixes the state of the decipherment and establishes its priority.