Evidence for Internal Ternary Geometry in Nuclear Binding Energies
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| Format: | Recurso digital |
| Langue: | anglais |
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Zenodo
2025
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| _version_ | 1866901938813009920 |
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| author | LEMNARU, Cornel |
| author_facet | LEMNARU, Cornel |
| contents | <p>This work introduces a nuclear binding functional derived from a discrete ternary symmetry of the vacuum, represented by internal operators satisfying the cubic relation J^3 = -I. The resulting expression contains eight global parameters and does not rely on shell, pairing, deformation or region-dependent corrections. </p> <p><strong>A central result of the model is the emergence of a sixth-order periodicity in N − Z</strong>. This periodic structure arises from the phase sector of the ternary symmetry and manifests as a regular oscillatory pattern in the residuals. The effect is not predicted by liquid-drop approaches or macroscopic-microscopic models and does not originate from parameter optimisation. Instead, it follows analytically from the internal cubic relation and persists uniformly from light to heavy nuclei. <br>Its presence suggests that nuclear binding may encode a discrete geometric imprint of the vacuum.</p> <p><strong>The functional decomposes into three contributions associated with internal components of the symmetry: </strong>a geometric cohesion term combining volume, surface and Coulomb behaviour; an isospin coupling term accounting for mixing and asymmetry; and a phase term generating the sixth-order oscillation in N − Z. <br>The parameter structure further implies a modified effective equation of state for dense neutron matter, potentially affecting neutron-star mass–radius relations.</p> <p>These results indicate that the ternary symmetry may represent either an underlying microstructure of the vacuum or an emergent organisational principle governing nuclear binding. The present work establishes priority for the formulation, interpretation and numerical validation of the ternary nuclear functional.</p> <p>Interactive numerical exploration is available on the <strong>J3 ATOMIC</strong> platform: <a href="https://www.j3atomic.com" target="_new" rel="noopener">https://www.j3atomic.com</a></p> <p>In <strong>Free Low-Res</strong> mode, the calculation reproduces exactly the function (Eq. 11) from the preprint:<br><strong>Evidence for Internal Ternary Geometry in Nuclear Binding Energies</strong> — <a href="https://doi.org/10.5281/zenodo.17847017" target="_new" rel="noopener">https://doi.org/10.5281/zenodo.17847017</a></p> <p>In <strong>High-Res</strong> mode (contractual), the platform extends this formalism for deterministic calculations, with a global precision on the order of:<br><strong>RMS ≈ 0.002625 eV/n (per nucleon)</strong></p> <p>Direct precision verification is available at:<br><a href="https://www.j3atomic.com">https://www.j3atomic.com</a> → <strong>LABORATORY → VERIFY PRECISION</strong></p> <p>The probability that a formula depending exclusively on <strong>Z</strong> and <strong>N</strong> would reproduce exactly the first <strong>8 significant digits</strong> for all <strong>3558 nuclei</strong> in AME2020 is <strong>≈ 10⁻²⁸⁴⁶⁴</strong>; <br><strong>this result strongly refutes the hypothesis of a global overfit.</strong></p> <p>The platform provides a demonstrative and exploratory implementation of the formalism and parameter set described in this preprint, <br>intended to illustrate the structure of the model and its qualitative behaviour across the nuclear chart.</p> <h3>Observation</h3> <p>This preprint forms part of a broader research programme examining a ternary internal structure of the vacuum and its projections across physical domains. <br>Related studies include:</p> <ul> <li> <p>Unified Vacuum Dynamics from a Ternary Internal Symmetry</p> </li> <li> <p>Photon Emergence from a Discrete Ternary Vacuum Symmetry</p> </li> <li> <p>Photon, Neutrinos and the Higgs Boson as Emergent Structures of a Ternary Symmetry of the Vacuum</p> </li> <li> <p>Einstein--Cartan Cosmology with Scalar Torsion and Dark-Sector Coupling</p> </li> <li> <p>Ternary Unified Physics: Internal Torsion, Phase Geometry, and Emergent Correspondence Limits</p> </li> </ul> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_17847018 |
| institution | Zenodo |
| language | eng |
| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Evidence for Internal Ternary Geometry in Nuclear Binding Energies LEMNARU, Cornel ternary vacuum symmetry nuclear binding energy mass model neutron stars emergent geometry isospin coupling phase oscillations nuclear structure finite-range functional hadronic phenomenology <p>This work introduces a nuclear binding functional derived from a discrete ternary symmetry of the vacuum, represented by internal operators satisfying the cubic relation J^3 = -I. The resulting expression contains eight global parameters and does not rely on shell, pairing, deformation or region-dependent corrections. </p> <p><strong>A central result of the model is the emergence of a sixth-order periodicity in N − Z</strong>. This periodic structure arises from the phase sector of the ternary symmetry and manifests as a regular oscillatory pattern in the residuals. The effect is not predicted by liquid-drop approaches or macroscopic-microscopic models and does not originate from parameter optimisation. Instead, it follows analytically from the internal cubic relation and persists uniformly from light to heavy nuclei. <br>Its presence suggests that nuclear binding may encode a discrete geometric imprint of the vacuum.</p> <p><strong>The functional decomposes into three contributions associated with internal components of the symmetry: </strong>a geometric cohesion term combining volume, surface and Coulomb behaviour; an isospin coupling term accounting for mixing and asymmetry; and a phase term generating the sixth-order oscillation in N − Z. <br>The parameter structure further implies a modified effective equation of state for dense neutron matter, potentially affecting neutron-star mass–radius relations.</p> <p>These results indicate that the ternary symmetry may represent either an underlying microstructure of the vacuum or an emergent organisational principle governing nuclear binding. The present work establishes priority for the formulation, interpretation and numerical validation of the ternary nuclear functional.</p> <p>Interactive numerical exploration is available on the <strong>J3 ATOMIC</strong> platform: <a href="https://www.j3atomic.com" target="_new" rel="noopener">https://www.j3atomic.com</a></p> <p>In <strong>Free Low-Res</strong> mode, the calculation reproduces exactly the function (Eq. 11) from the preprint:<br><strong>Evidence for Internal Ternary Geometry in Nuclear Binding Energies</strong> — <a href="https://doi.org/10.5281/zenodo.17847017" target="_new" rel="noopener">https://doi.org/10.5281/zenodo.17847017</a></p> <p>In <strong>High-Res</strong> mode (contractual), the platform extends this formalism for deterministic calculations, with a global precision on the order of:<br><strong>RMS ≈ 0.002625 eV/n (per nucleon)</strong></p> <p>Direct precision verification is available at:<br><a href="https://www.j3atomic.com">https://www.j3atomic.com</a> → <strong>LABORATORY → VERIFY PRECISION</strong></p> <p>The probability that a formula depending exclusively on <strong>Z</strong> and <strong>N</strong> would reproduce exactly the first <strong>8 significant digits</strong> for all <strong>3558 nuclei</strong> in AME2020 is <strong>≈ 10⁻²⁸⁴⁶⁴</strong>; <br><strong>this result strongly refutes the hypothesis of a global overfit.</strong></p> <p>The platform provides a demonstrative and exploratory implementation of the formalism and parameter set described in this preprint, <br>intended to illustrate the structure of the model and its qualitative behaviour across the nuclear chart.</p> <h3>Observation</h3> <p>This preprint forms part of a broader research programme examining a ternary internal structure of the vacuum and its projections across physical domains. <br>Related studies include:</p> <ul> <li> <p>Unified Vacuum Dynamics from a Ternary Internal Symmetry</p> </li> <li> <p>Photon Emergence from a Discrete Ternary Vacuum Symmetry</p> </li> <li> <p>Photon, Neutrinos and the Higgs Boson as Emergent Structures of a Ternary Symmetry of the Vacuum</p> </li> <li> <p>Einstein--Cartan Cosmology with Scalar Torsion and Dark-Sector Coupling</p> </li> <li> <p>Ternary Unified Physics: Internal Torsion, Phase Geometry, and Emergent Correspondence Limits</p> </li> </ul> |
| title | Evidence for Internal Ternary Geometry in Nuclear Binding Energies |
| topic | ternary vacuum symmetry nuclear binding energy mass model neutron stars emergent geometry isospin coupling phase oscillations nuclear structure finite-range functional hadronic phenomenology |
| url | https://doi.org/10.5281/zenodo.17847018 |