| _version_ | 1866901607037272064 |
|---|---|
| author | Smith, Jason Borabon, Charles |
| author_facet | Smith, Jason Borabon, Charles |
| contents | <p><br><strong>A Scale-Free Coherence Invariant Linking Atomic and Orbital Energy Structures</strong><br><br></p> <p>Description</p> <p>This preprint extends the RMAχτ coherence invariant—originally developed for planetary, orbital, and galactic-scale systems—into the atomic domain. The framework was first introduced in Smith & Borabon (2025), Coherence Metrics and Gradient Dynamics Across Planetary and Galactic Scales: A Three-Paper Series (https://doi.org/10.5281/zenodo.17645297<br>). In the present work, the same invariant is applied to fundamental atomic energetics without modification of its governing structure. Hydrogenic systems emerge naturally from the suppression law, helium is reproduced to near-exact accuracy through multiplicative coherence interference, and lithium is predicted across three ionization states with errors below 0.1%. No potentials, operator formalisms, or wavefunction assumptions are invoked; energy levels arise directly from coherence-density suppression along a topological coordinate.</p> <p>The consistency of results across such disparate scales—astronomical and atomic—suggests that the RMAχτ invariant may represent a deeper structural principle linking how coherence forms, persists, and degrades across physical regimes. While this work does not claim a completed unification, the cross-domain stability of the invariant and its ability to generate correct energy structures from minimal assumptions indicate that it may be capturing an underlying generative relationship shared by many physical systems. This possibility is presented cautiously and empirically: the invariant is evaluated by its predictive performance across domains, not by assertion.</p> <p>All data, figures, and source materials required to reproduce the results are included in this deposit. The authors anticipate further exploration into whether this coherence-based formulation can serve as a bridge between large-scale dynamical systems and microscopic quantum behavior, potentially offering a unified lens for understanding structured energy across scales.</p> <p>contact@coherence.institute</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_17849551 |
| institution | Zenodo |
| language | |
| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | A Scale-Free Coherence Invariant Linking Atomic and Orbital Energy Structures Smith, Jason Borabon, Charles coherence invariant RMAχτ suppression law coherence density atomic energy structure hydrogenic scaling helium interference lithium ionization energies scale-free dynamics <p><br><strong>A Scale-Free Coherence Invariant Linking Atomic and Orbital Energy Structures</strong><br><br></p> <p>Description</p> <p>This preprint extends the RMAχτ coherence invariant—originally developed for planetary, orbital, and galactic-scale systems—into the atomic domain. The framework was first introduced in Smith & Borabon (2025), Coherence Metrics and Gradient Dynamics Across Planetary and Galactic Scales: A Three-Paper Series (https://doi.org/10.5281/zenodo.17645297<br>). In the present work, the same invariant is applied to fundamental atomic energetics without modification of its governing structure. Hydrogenic systems emerge naturally from the suppression law, helium is reproduced to near-exact accuracy through multiplicative coherence interference, and lithium is predicted across three ionization states with errors below 0.1%. No potentials, operator formalisms, or wavefunction assumptions are invoked; energy levels arise directly from coherence-density suppression along a topological coordinate.</p> <p>The consistency of results across such disparate scales—astronomical and atomic—suggests that the RMAχτ invariant may represent a deeper structural principle linking how coherence forms, persists, and degrades across physical regimes. While this work does not claim a completed unification, the cross-domain stability of the invariant and its ability to generate correct energy structures from minimal assumptions indicate that it may be capturing an underlying generative relationship shared by many physical systems. This possibility is presented cautiously and empirically: the invariant is evaluated by its predictive performance across domains, not by assertion.</p> <p>All data, figures, and source materials required to reproduce the results are included in this deposit. The authors anticipate further exploration into whether this coherence-based formulation can serve as a bridge between large-scale dynamical systems and microscopic quantum behavior, potentially offering a unified lens for understanding structured energy across scales.</p> <p>contact@coherence.institute</p> |
| title | A Scale-Free Coherence Invariant Linking Atomic and Orbital Energy Structures |
| topic | coherence invariant RMAχτ suppression law coherence density atomic energy structure hydrogenic scaling helium interference lithium ionization energies scale-free dynamics |
| url | https://doi.org/10.5281/zenodo.17849551 |