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 5 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). Version 2 extended the analysis to the complete set of catalogued radioactive isotopes of periods 1 to 4 (about 580 nuclides, appendices A and B: writings, resolutions, cascades, half-lives), with the deterministic writing algorithm for unstable nuclides (isobaric substitution) and the differential notation {X;Y}. The present version 3 adds the complete derivation of period 5 (89 canonical writings from Rb to Xe, derived valences, a single maturation alphabet), a four-tier taxonomy of stability grounded in measured half-lives, competitive stability, and the principles consolidated by this decipherment: β decay as the finishing step of nucleosynthesis, isobaric lineages, the nn→np assembly law. About 1300 nuclides are now written. This result realizes, over five 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 6 and 7. The present note fixes the state of the decipherment and establishes its priority.