Independent Theoretical Physics Research

Vibrational Ontology
& Multiverse Topology

Exploring the mathematical foundations of inter-universal dynamics, dark matter cosmology, and the spectral architecture of existence.

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Research Program

Our research develops a unified theoretical framework for understanding the structure of the Multiverse through vibrational dynamics and membrane topology.

Topological Permeability

Developing the NFU metric for quantifying membrane permeability at multi-universal vertices using quantum foam geometry.

Hexahedral Cosmology

Investigating the hexahedral brane packing model and its implications for the 5:1 dark matter ratio through temporal exclusion.

Spectral Domains

Establishing the mathematical hierarchy of nested spectral domains and the fractal inheritance principle.

Cross-Brane Transport

Modeling transient stability and active frequency shielding for theoretical inter-universal dynamics.

Publications

Vibrational Ontology Series (2025) - A four-part theoretical framework

I

Topological Permeability Index (NFU): Resonant Tunneling in Multi-Universal Membrane Dynamics

Francisco Molina-Burgos

We propose a topological solution to inter-brane transit based on quantum foam geometry. The NFU index quantifies metric fragility at multi-universal vertices, demonstrating that membrane permeability is a function of vibrational signature matching rather than energy density. Dark Matter halos are reinterpreted as regions of high membrane tension.

December 2025 brane cosmology, multiverse topology, dark matter
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II

Nested Spectral Domains: A Set-Theoretic Hierarchy for the Multiverse, Universes, and Dimensions

Francisco Molina-Burgos

We propose a rigorous ontological hierarchy based on Vibrational Set Theory. Universes are defined by unique vibrational signatures acting as band-pass exclusion filters, while dimensions represent internal degrees of freedom. The framework establishes Fractal Inheritance as a mathematical property of self-similar spectral containment.

December 2025 multiverse ontology, spectral domains, dimensional hierarchy
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III

Hexahedral Brane Packing: Deriving the 5:1 Dark Matter Ratio from Cubic Multiverse Topology

Francisco Molina-Burgos

We derive the Dark Matter to Baryonic Matter ratio of 5:1 as a direct consequence of hexahedral multiverse topology. The Temporal Exclusion Principle identifies the timelike axis as self-referential, leaving 5 spatial neighbors whose gravitational projection manifests as dark matter. This provides a geometric explanation without exotic particles.

December 2025 dark matter, hexahedral packing, temporal exclusion
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IV

Transient Stability in Cross-Brane Transport: Active Frequency Shielding and the Generalized Impedance Limit

Francisco Molina-Burgos

We propose Active Frequency Shielding (AFS) as the mechanism enabling transient inter-universal existence. The Generalized Bulk Impedance derives from spectral mismatch, and the Autonomy Horizon defines maximum visit duration. This explains the transient nature of extra-universal phenomena through thermodynamic constraints.

December 2025 cross-brane transport, vibrational shielding, transient stability
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Core Equations

NFU Master Equation

φnfu = Ageom ηR · ΨDM · exp ( - |εlocal-εtarget|2 2σ2 )

Topological permeability as a function of geometric factors, dark matter coupling, and vibrational resonance.

Dark Matter Ratio

ΩDM Ωb 5

Derived from hexahedral topology with temporal exclusion (6 faces - 1 temporal = 5 spatial neighbors).

Autonomy Horizon

τmax Etotal Evac ( 1-R 1+R )

Maximum duration of cross-brane visitation based on energy reserves and spectral reflection coefficient.

About

Principal Investigator

Francisco Molina-Burgos

Independent Researcher

Mexico

ORCID: 0009-0008-6093-8267

Avermex Research Division focuses on developing rigorous mathematical frameworks for theoretical physics questions that lie at the intersection of cosmology, quantum mechanics, and multiverse theory.

Our approach combines classical brane cosmology (Randall-Sundrum), quantum foam geometry, and information-theoretic principles to construct falsifiable models of inter-universal dynamics.

"The distinction between a Universe and a Dimension is a distinction of signal processing: Carrier Frequency vs. Modulation." - Nested Spectral Domains, 2025

Contact

For academic inquiries and collaboration proposals:

pako.molina@gmail.com