Skip to main Communities My dashboard Log in Sign up Published April 15, 2026 | Version 2.0 Preprint Open Gravitational Resonance Linking: A Complete Framework for Galactic Dynamics Authors/Creators Vogl, Brian Contributors Researcher: Vogl, Brian Description This paper presents Gravitational Resonance Linking (GRL), a complete, parameter-free theoretical framework for galactic dynamics in which flat rotation curves arise from gravitational standing waves accumulated over hundreds of resonance cycles spanning billions of years of galactic evolution. Statistically opposed stellar mass distributions across galactic cores couple gravitationally, building a standing wave field that organizes the outer disk. The mass participation fraction f_locked = (1/π) × η follows from the solid angle geometry of disk opposition, where η is measurable directly from near-infrared photometry. The gravitational amplification A = 1 + N × f²/2 predicts an apparent dark mass fraction of 82% for a typical 4 Gyr disk — consistent with the cosmologically observed 84% to within 2 percentage points — with no free parameters. Key results include: (1) A physical saturation limit A_max = 8× beyond which no GRL-organized galaxy can amplify, corresponding to an apparent dark fraction ceiling of 87.5%; (2) Natural emergence of the MOND acceleration constant a₀ from GRL parameters to within 0.4% of the observed value; (3) Mathematical equivalence to the Gross-Pitaevskii coherence equation, identifying f²/2 as the vortex self-interaction energy in galactic variables and establishing the galaxy as a quantized gravitational vortex; (4) A galactic action scale ℏ_grav = 3.85×10⁷⁴ J·s that agrees to within 35% with an independent derivation from Eddington's number and the galactic-to-proton mass ratio across 108 orders of magnitude; (5) Decoherence analysis showing the coherent state survives approximately 6×10¹⁵ years through energy gap protection and power-law decoherence. An independent kinematic analysis of 203,940 stars from the APOGEE DR17 catalog reveals a new empirical law: every bound stellar group at every organizational scale orbits a dynamical center displaced inward by δ = k × R_gc, where k = 1.00229 ± 0.002 and R² = 0.97 across 37,828 groups spanning six orders of magnitude. The six-level gravitational tree hierarchy is shown to be self-correcting against all sub-galactic perturbations. Five specific predictions distinguish GRL from dark matter halo theory and are testable with existing and near-future instruments including JWST, Rubin Observatory, and Gaia. A galactic center wobble signature is already detected at 9σ in APOGEE data. GRL predicts galactic and cosmological dark phenomena are physically distinct; the Meissner effect at void scales is identified as a candidate dark energy mechanism in a companion paper in preparation. This work is submitted for peer review and scientific discussion. Comments and critical feedback are welcomed. KEYWORDS galactic dynamics, flat rotation curves, dark matter alternative, gravitational resonance, standing waves, Gross-Pitaevskii equation, superfluid vortex, healing length, vortex self-interaction energy, APOGEE DR17, stellar kinematics, hierarchical gravitational structure, galactic coherence, power-law decoherence, energy gap protection, MOND, baryonic Tully-Fisher relation, near-infrared photometry, Fourier decomposition, galactic morphology, mass participation fraction, JWST, Rubin Observatory, Gaia, dark energy, Meissner effect, cosmic voids, galactic rotation, astrophysics, theoretical physics, preprint Abstract This paper presents Gravitational Resonance Linking (GRL), a complete, parameter-free theoretical framework for galactic dynamics in which flat rotation curves arise from gravitational standing waves accumulated over hundreds of resonance cycles spanning billions of years of galactic evolution. Statistically opposed stellar mass distributions across galactic cores couple gravitationally, building a standing wave field that organizes the outer disk. The mass participation fraction f_locked = (1/π) × η follows from the solid angle geometry of disk opposition, where η is measurable directly from near-infrared photometry. The gravitational amplification A = 1 + N × f²/2 predicts an apparent dark mass fraction of 82% for a typical 4 Gyr disk — consistent with the cosmologically observed 84% to within 2 percentage points — with no free parameters. Key results include: (1) A physical saturation limit A_max = 8× beyond which no GRL-organized galaxy can amplify, corresponding to an apparent dark fraction ceiling of 87.5%; (2) Natural emergence of the MOND acceleration constant a₀ from GRL parameters to within 0.4% of the observed value; (3) Mathematical equivalence to the Gross-Pitaevskii coherence equation, identifying f²/2 as the vortex self-interaction energy in galactic variables and establishing the galaxy as a quantized gravitational vortex; (4) A galactic action scale ℏ_grav = 3.85×10⁷⁴ J·s that agrees to within 35% with an independent derivation from Eddington's number and the galactic-to-proton mass ratio across 108 orders of magnitude; (5) Decoherence analysis showing the coherent state survives approximately 6×10¹⁵ years through energy gap protection and power-law decoherence. An independent kinematic analysis of 203,940 stars from the APOGEE DR17 catalog reveals a new empirical law: every bound stellar group at every organizational scale orbits a dynamical center displaced inward by δ = k × R_gc, where k = 1.00229 ± 0.002 and R² = 0.97 across 37,828 groups spanning six orders of magnitude. The six-level gravitational tree hierarchy is shown to be self-correcting against all sub-galactic perturbations. Five specific predictions distinguish GRL from dark matter halo theory and are testable with existing and near-future instruments including JWST, Rubin Observatory, and Gaia. A galactic center wobble signature is already detected at 9σ in APOGEE data. GRL predicts galactic and cosmological dark phenomena are physically distinct; the Meissner effect at void scales is identified as a candidate dark energy mechanism in a companion paper in preparation. This work is submitted for peer review and scientific discussion. Comments and critical feedback are welcomed. KEYWORDS galactic dynamics, flat rotation curves, dark matter alternative, gravitational resonance, standing waves, Gross-Pitaevskii equation, superfluid vortex, healing length, vortex self-interaction energy, APOGEE DR17, stellar kinematics, hierarchical gravitational structure, galactic coherence, power-law decoherence, energy gap protection, MOND, baryonic Tully-Fisher relation, near-infrared photometry, Fourier decomposition, galactic morphology, mass participation fraction, JWST, Rubin Observatory, Gaia, dark energy, Meissner effect, cosmic voids, galactic rotation, astrophysics, theoretical physics, preprint Files GRL_GP_final.pdf Files (395.1 kB) Name Size Download all GRL_GP_final.pdf md5:f12d34b90f09afe965bf333c43d3c956 395.1 kB Preview Download Additional details Dates Created 2025-09-28 Completion Date Updated 2026-04-15 Update to the document 197 Views 236 Downloads Show more details All versions This version Views Total views 197 88 Downloads Total downloads 236 38 Data volume Total data volume 78.8 MB 17.8 MB More info on how stats are collected.... Versions External resources Indexed in OpenAIRE Communities Keywords and subjects Keywords galactic dynamics modified gravity quantum gravity gravitational resonance macroscopic quantum coherence rotation curves MOND theoretical physics EuroSciVoc Theoretical physics Details DOI DOI Badge DOI 10.5281/zenodo.19561311 Markdown [](https://doi.org/10.5281/zenodo.19561311) reStructuredText .. image:: https://zenodo.org/badge/DOI/10.5281/zenodo.19561311.svg :target: https://doi.org/10.5281/zenodo.19561311 HTML <a href="https://doi.org/10.5281/zenodo.19561311"><img src="https://zenodo.org/badge/DOI/10.5281/zenodo.19561311.svg" alt="DOI"></a> Image URL https://zenodo.org/badge/DOI/10.5281/zenodo.19561311.svg Target URL https://doi.org/10.5281/zenodo.19561311 Resource type Preprint Publisher Zenodo Rights License Creative Commons Attribution 4.0 International The Creative Commons Attribution license allows re-distribution and re-use of a licensed work on the condition that the creator is appropriately credited. Read more Copyright Copyright (C) 2026 Brian Vogl Citation Export Technical metadata Created April 15, 2026 Modified April 15, 2026 Jump up About About Policies Infrastructure Principles Projects Roadmap Contact Blog Blog Support Help FAQ Developers REST API OAI-PMH Contribute GitHub Donate Funded by Powered by CERN Data Centre & InvenioRDM Status Privacy policy Cookie policy Terms of Use This site uses cookies. Find out more on how we use cookies Accept all cookies Accept only essential cookies