The Nodal Architecture of the 4D Manifold: The Manifold Saturation Principle and the Topological Origin of Galactic Scaling Laws

The Nodal Architecture of the 4D Manifold: The Manifold Saturation Principle and the Topological Origin of Galactic Scaling Laws | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article The Nodal Architecture of the 4D Manifold: The Manifold Saturation Principle and the Topological Origin of Galactic Scaling Laws Ashil S This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9363992/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Building upon the resolution of non-singular black hole interiors through the Order Creator Mechanism (OCM), we extend this framework to the external galactic manifold to address the mass-energy equivalence of the dark sector. We define a fundamental Topological Phase Transition occurring at the Rd inter- face, where baryonic matter shifts from a standard 3D state into a 4D nodal state. This transition is governed by a non-relativistic OCM Hamiltonian, providing a quantum-topological foundation for space-time coupling that bypasses the requirement for exotic dark particles. We introduce the Manifold Saturation Principle (S M ) as a new fundamental law of physics. As a diagnostic law, S M defines the critical topological limit where 3D space-time reaches maximum energy-density capacity, regulating both the life cycle of stellar cores and the structural evolution of galaxies. This principle replaces mathematical singularities with a physical saturation limit, providing the first purely geometric explanation for the “Hollow Core” density profiles and the universal v 4 ∝ M (Tully-Fisher) scaling. From this basis, we derive the Violet Shift—a manifold-stiffening effect (viscos- ity) that provides the physical mechanism for flat rotation curves. Furthermore, we predict specific Quasi-Periodic Oscillations (QPOs) emerging from nodal vibration frequencies, offering a novel observational signature of 4D manifold coupling. Finally, we demonstrate that galactic nodes are not isolated entities but are subject to Topological Tethering within a global Oloid-symmetric manifold. This nodal architecture and its inherent chirality provide a natural explanation for parity violations and the “Axis of Evil” observed in the Cosmic Microwave Background. By re-framing the dark sector as an emergent property of manifold dynamics, the OCM identifies the universe as a self-regulating open system in permanent exchange with a higher-dimensional reservoir. Astrophysics and Cosmology Order Creator Mechanism (OCM) Manifold Dynamics Manifold Viscosity (ηM ) Topological Phase Transitions Tully-Fisher Relation Hubble Tension Non-singular Black Holes Dark Sector Equivalence CMB Anisotropy Quantum Mechanics R_d Boundary Conditions Full Text Additional Declarations The authors declare no competing interests. Supplementary Files TopologySupplement.pdf The Nodal Architecture of the 4D Manifold: The Manifold Saturation Principle and the Topological Origin of Galactic Scaling Laws TopologyVideoLegends.pdf Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-9363992","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":620073643,"identity":"11b22109-9849-4ad5-9722-b5af39cb08ff","order_by":0,"name":"Ashil 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