Periodicity of Nuclear Structure and Emergent Electronic Periodicity

Version 6 — 19/09/2026 Main text (Note, v4 FR/EN): unchanged. New: complete Structural Atlas (French and English versions), replacing the partial atlas (vol. 1, periods 1-4) of version 5. The atlas now covers all six periods, from hydrogen to lead: 292 plates (all stable and quasi-stable isotopes, including the ¹⁸⁰Ta/¹⁸⁰ᵐTa isomeric pair), each with its structural notation and its abundance or status. All notations have been verified at the nucleon level (exact Z and N for every isotope). This note demonstrates that nuclear structures follow recurring, periodic patterns, and that electronic periodicity (the Mendeleev table and the chemical bonding capacities) emerges from this nuclear structuring. This is the central fact established here, and it is independent of notation choices, segmentation conventions and ongoing developments. The demonstration rests on a filling grammar based on the structured arborescence of the particles (chains of alternating nucleons connected from the central α), which regenerates, with a restricted alphabet and no adjusted parameter, four independent registers over periods 1 to 6: the list of stable and quasi-stable isotopes of each element, the hierarchy of their abundances, the observed chemical valences, and the structure of binding energies. Versions 2 and 3 covered the radioactive nuclides of periods 1 to 4 (appendices A and B) and the derivation of period 5. The present version 4 marks the completion point of the sequencing: period 6 is derived from caesium to lead (about 70 canonical writings), including the lanthanide crown, dissolved into ordinary structure: a widened crown of twelve protons (three per axis), filled by intercalated insertions that mature in place along the common alphabet: the constant trivalence derives from saturation, and its measured deviations (Ce, Eu, Tb, Yb) fall at the expected positions. The analysis is conducted from caesium to lead, the last brick reliably certifying the periodicity, and this segment decomposes into gestures marked out by the bricks: 12+2+8+4+2. Three recurring bricks form along the segment (¹⁶⁰Dy, ¹⁶⁶Er, ¹⁹⁰Os), each immediately followed by an exact replica of the entry gestures: the structural periodicity is tighter than the chemical periodicity of the table. The N = 126 line (²⁰⁸Pb) translates into double maturation above the third brick, and the analysis stops where the periodicity is clean: beyond bismuth, two readings remain open (the real end of stability, or stable writings never assembled by the pathways of our cosmic history), constituting a distinct programme. Added to this is a new reading of nuclear isomers as differential writings (demonstrated on ¹⁸⁰ᵐTa, the « eternal isomer », elucidated). This result realizes, over six periods, the prediction stated in the « Lattice Mechanics » framework [3]. A vocabulary refinement enacted by the sequencing itself: the initial term of « pairing into structured units » (clusters), inherited from the prediction [3] and versions 1 to 3, proves to be a scaffolding approximation: the demonstrated structure is a connected arborescence: the present version adopts this vocabulary, the notation remaining unchanged. The rest of the programme is extension and deepening: complete tables, period 7 as diagnosis, the isomer register. The present note fixes the state of the decipherment and establishes its priority.