ivansalines/unified-theory-of-motion: v1.0.5

Full Changelog: https://github.com/ivansalines/unified-theory-of-motion/compare/v1.0.3...v1.0.4 Unified Theory of Motion A Research Framework on Organized Motion and Stable Toroidal Configurations Author: Ivan Salines — Independent Researcher 📧 ivan.salines@gmail.com DOI "When motion is free to organize itself according to continuity and minimal action, it may assume forms capable of sustaining themselves. Geometry does not precede motion; it can emerge from it." $$ \mathcal{L}(\rho,\theta) =\frac12(\partial_\mu\rho)^2 +\frac12\rho^2(\partial_\mu\theta)^2 -U(\rho) $$ "Geometry is not imposed on motion. It is a form motion may reveal under equilibrium conditions." 📘 Overview This repository collects a structured set of documents, numerical experiments, and computational tools developed within an ongoing research program referred to here as the Unified Theory of Motion. The term is used as a working designation, describing an exploratory framework that investigates how organized, stationary patterns of motion may give rise to mass, geometry, and particle-like structures in continuous field models. The materials are organized progressively, from conceptual foundations to more advanced theoretical and numerical explorations. 📂 Documentation Structure docs/ │ ├── 01_Foundation/ ├── 02_Framework/ ├── 03_Advanced/ └── 04_Special/ 🌱 01 — Foundation Conceptual origins and guiding ideas of the research framework. 1___The_Unified_Theory_of_Motion__A_Continuum_Bridge_Between_Relativity_and_Wave_Particle_Duality.pdf This document introduces the central working hypothesis: Organized motion may be treated as a primary object of study, with mass, energy, and geometry emerging from its stationary configurations. 🌳 02 — Framework Mathematical formulation and numerical investigation of toroidal configurations in scalar field models. Includes: A_Unified_Framework_of_Organized_Motion__Stable_Toroidal_Configurations_in_a_Complex_Scalar_Field.pdf Documents 2–6, addressing: density–phase scalar field formulations toroidal soliton-like configurations numerical relaxation procedures internal phase winding mechanisms stability properties within the explored models These documents constitute the core technical body of the framework. 🌌 03 — Advanced Extensions and exploratory applications to broader areas of fundamental physics. Documents 7–17 explore, among others: gravitational phenomenology in effective descriptions electromagnetic structure in organized motion models nonlinear stability and interaction regimes semiclassical and statistical considerations couplings to General Relativity in simplified settings effective field-theoretic interpretations Each document examines a specific domain within the limits and assumptions of the underlying models. ✨ 04 — Special Focused studies and complementary material. The_Toroidal_Law_of_Organized_Motion.pdf A formal analysis of stationary organized motion in toroidal configurations. Binary Interaction of Self-Organized Solitons in a One-Dimensional Effective Model of Motion An exploratory study of interacting soliton-like structures in reduced models. Legacy versions and preliminary drafts, retained for historical completeness. 🧮 Numerical Simulations Reproducible Python code used in the numerical investigations is available in: /code Including: relaxation solver Q-scan generator density/energy maps figure generation scripts To reproduce results: pip install -r code/requirements.txt python code/scan_Q_toroide.py python code/relaxation_solver.py Figures are stored in: /figures 🔬 Observations and Outcomes Within the explored models, the following outcomes are observed: the emergence of long-lived toroidal soliton-like configurations during numerical relaxation of a complex scalar field; confinement mechanisms associated with internal phase winding, leading to self-sustained geometric structures; stationary energy configurations interpretable as equilibria of internal motion; binary interactions exhibiting metastable bound states through nonlinear energy exchange; discrete families of configurations labeled by an integer winding number ( n ); effective attractive behavior associated with phase gradients, explored as a possible low-energy gravitational analogue; consistency with known GR and QFT descriptions in appropriate infrared regimes, discussed as emergent or effective limits. All results are obtained within simplified continuum models and are intended as controlled explorations rather than definitive physical claims. 🤝 Invitation to Collaboration This repository is shared in the spirit of open scientific inquiry. Researchers, students, and independent scholars interested in self-organization, nonlinear dynamics, field theory, or numerical modeling are welcome to examine, test, extend, or challenge the material presented here. Contributions may include: independent verification of numerical results, alternative analytical approaches, extensions of the models to related physical systems, critical feedback on assumptions or interpretations, or exploratory applications in adjacent domains. No prior agreement with the framework is expected. Constructive disagreement and falsification are considered integral parts of the research process. For discussion or collaboration, feel free to get in touch. 📜 Citation @misc{salines2025_unified_motion, author = {Ivan Salines}, title = {Unified Theory of Motion: Organized Motion and Stable Toroidal Configurations}, year = {2025}, url = {https://doi.org/10.5281/zenodo.17653903}, doi = {10.5281/zenodo.17653903} 📬 Contact For academic correspondence: 📧 ivan.salines@gmail.com 🟦 License Recommended: CC-BY 4.0 🌟 Purpose The purpose of this repository is to document and organize an extended research process, making its assumptions, methods, and numerical procedures openly accessible. The material is intended to support further analysis, independent verification, and critical discussion, rather than to present a finalized or closed theoretical system.