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This work aims to establish a new foundation for fundamental physics through Topological 0-Matrix Mechanics (TSM), replacing traditional concepts with a mechanical framework.

June 12, 2026Open Access

Topological 0-Matrix (Substrate) Mechanics (TSM) Theory

Key Points

This work aims to establish a new foundation for fundamental physics through Topological 0-Matrix Mechanics (TSM), replacing traditional concepts with a mechanical framework.
Completion of the first seven chapters detailing TSM theory covering axioms, mechanics, and particle structure.
Translation of these chapters into English and Polish to facilitate international collaboration and peer review.
Development of a coherent theoretical framework including definitions and mechanics of oscillation spheres.
Gravity is redefined as a result of classical 4-dimensional Navier-Cauchy equations, eliminating the need for curved spacetime.
Elementary particles are modeled as non-linear topological knots within a substrate, offering a mechanical explanation of their properties.
The theory simplifies complex models, removing dark matter and dark energy from consideration.

Abstract

Topological 0-Matrix (Substrate) Mechanics (TSM) This monograph presents a complete, alternative foundation for fundamental physics, achieving a radical simplification of the description of reality by eliminating the abstract concept of empty spacetime in favor of continuum mechanics. Topological 0-Matrix (Substrate) Mechanics (TSM) proves that the entire observable Universe emerges as a macroscopic, elasto-dynamic manifestation of a sub-Planckian, geometrically jammed network of oscillators—the titular 0-Matrix. The TSM theory fulfills the grand dream of theoretical physics for complete unification, delivering unprecedented simplifications in two key areas: Derivation of General Relativity (GR): Gravity is not the magic of curved spacetime invented by Einstein. It is directly derived from classical, 4-dimensional engineering Navier-Cauchy equations! Space is a tangible medium, its metric is the state of internal stresses, and attraction is a mere pressure gradient. TSM uncompromisingly eliminates singularities (no black holes) and, through a single, fundamental elasto-dynamic mechanism, erases the mythical dark matter and dark energy from physics. Simplification and Demystification of the Standard Model: No more absurd, dimensionless material points and quantum mysticism! In TSM, elementary particles are reduced to stable, non-linear topological knots (solitons) within the 0-Matrix substrate. Rest mass, spin 1/2, and charge are pure geometry of standing waves trapped in the network. Consequently, the model explains the internal structure of fermions with rigorous, mechanical precision. It explains and derives the puzzling mass relations of particles, including the famous Koide formula. We are pleased to announce the completion of the first 7 coherent chapters of the Topological 0-Matrix (Substrate) Mechanics (TSM) theory. These chapters have been fully translated into English and now serve as a solid, unified foundation for understanding the core mechanics of the model. Highlights Foundational Completeness: Chapters 1–7 establish the necessary axiomatic framework, including the definition of the 0-Matrix, the mechanics of oscillation spheres, and the emergent nature of time and matter. Bilingual Documentation: All seven chapters are available in both Polish and English. We have ensured that the terminology remains consistent across both languages to facilitate international peer review. Conceptual Basis: This block serves as an essential entry point for anyone looking to grasp the fundamental physics of the TSM model, from the basic 0-particle interaction to the topological emergence of physical fields. Detailed Structure For a detailed breakdown of the topics, definitions, and specific concepts covered within these chapters, please refer to the Table of Contents located in the main README.md file of this repository. Feedback As these chapters represent the core of the theory, we welcome any feedback regarding the clarity of definitions, mathematical notation, or conceptual consistency. Please use the GitHub Issues tab to report any findings, missing symbols, or ambiguities in definitions.

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