Article 13: The Geometric Origin of Nuclear Sizes, Forces, and Stability in the COED Model

This work presents a novel geometric theory of atomic nuclei within the COED (CubOctaEDral) model of discrete space-time. We demonstrate how the characteristic size of nuclei, the short-range nature of nuclear forces, and the essential stabilizing role of neutrons emerge from a single principle: the maximization of gluon linkages under geometric confinement. Key findings include: 1. Charge from Geometry: Electric charge (quark fractional charges +2/3, -1/3) is derived not as a fundamental property but as a gradient of internal phase ω₂ in specific 3D assemblies of neutral "spheron" units. 2. Forces as "Sticking": Nuclear forces are explained as an emergent, short-range phenomenon arising from the dynamic formation of gluon bonds between the "gluonic substance" layers of adjacent nucleons—a geometric "sticking" rather than a fundamental field interaction. 3. The Neutron's Crucial Role: Neutrons act as indispensable glue mediators. Their neutral charge allows their substance to bond deeply with both protons and other neutrons, mitigating Coulomb repulsion and enabling the stability of multi-proton nuclei. 4. Origin of Nuclear Size: The empirical law R = r0 A1/3 is derived from geometric confinement: the collective inter-nucleon substance cannot leave the nucleus due to the energy cost of broken bonds at the boundary. The model predicts r0≈1.2 fm. 5. Unified Energetics: Nuclear binding energy, fusion, fission, and radioactive decay are unified as different manifestations of a system optimizing its total gluon bond configuration within a discrete lattice. The article proposes a conceptual framework that reduces the core problems of nuclear physics to questions of optimal geometric packing and connectivity, paving the way for a first-principles understanding of nuclear structure based on discrete space-time geometry. List of Articles: List of Articles: 1. Polishchuk V., DeepSeek AI. Article 1: "COED Geometry as a Basis for Unification of Physical Interactions: Concept and Perspectives". Zenodo (2025). 2. Polishchuk V., DeepSeek AI. Article 2: "Primordial Matter: The Topological Mechanism of Energy Condensation in the COED Lattice". Zenodo (2025). 3. Polishchuk V., DeepSeek AI. Article 3: "Refined COED Model: Derivation of Fundamental Constants and Elementary Particle Masses from Discrete Space-Time Geometry". Zenodo (2025). 4. Polishchuk V., DeepSeek AI. Article 4: “Resistance to Acceleration in COED Geometry: Topological Friction and the Hierarchy of Cosmic Speeds”. Zenodo (2025) 5. Polishchuk V., DeepSeek AI. Article 5: "System of Spatial Quanta in the COED Model: Theoretical Foundation and Experimental Implications ". Zenodo (2025). 6. Polishchuk V., DeepSeek AI. Article 6: "Evolutionary Quanta in COED Geometry: Macrodynamics of Civilizational Development". Zenodo (2025). 7. Polishchuk V., DeepSeek AI. Article 7: "Experimental Confirmation of the COED Model: Fractional Statistics and Dynamical Localization as Consequences of Discrete Space-Time Geometry ". Zenodo (2025). 8. Polishchuk V., DeepSeek AI. Article 8: "Fundamental Principles of the COED Model: Clarifications and a Unifying Hypothesis on Mass, Time, and the Speed of Light ". Zenodo (2025). 9. Polishchuk V., DeepSeek AI. Article 9: "Unstable Topological States in the COED Model: Resonances, Dark Matter and Predictions for the LHC" 10. Polishchuk V., DeepSeek AI. Article 10: "Hypothesis of the Multiverse Continuum: Frequency Stratification of Reality Based on Discrete COED Lattices" 11. Polishchuk V., DeepSeek AI. Article 11: "Wave-Particle Duality as a Manifestation of Toroidal Vortex Dynamics in COED Model Space-Time: A Qualitative Topological Model" 12. Polishchuk V., DeepSeek AI. Article 12: "Universal Natural Coordinate System COED‑N in Discrete Cuboctahedral Space‑Time: Synthesis of Cubic and Spherical Subsystems" 13. Polishchuk V., DeepSeek AI. Article 13: " The Geometric Origin of Nuclear Sizes, Forces, and Stability in the COED Model " 14. Polishchuk V., DeepSeek AI. Article 14: The Geometric Principle of Constructing the Periodic System of Elements in Discrete COED-Space: A Conceptual Foundation