Abstract:
This paper introduces The Particle Framework (TPF), a comprehensive theoretical structure derived from the principles of Relativity Particles (RP) Theory. TPF is founded on the Postulate of Universal Dimensional Curvature, which posits that energy density induces geometric curvature in all associated dimensions. This principle is formalized through an axiomatic system, Yıldırım’s Geometry, which generates a novel class of polytopes ({Yn}) via a unique ternary production mechanism. We demonstrate how this framework provides a hierarchical, bottom-up construction of matter, from 0D puncta governed by non-commutative matrix dynamics to composite fermions whose properties—such as mass, generation, and confinement—emerge as solutions to self-consistent geometrodynamic equations. Critically, we extend the implications of TPF beyond fundamental physics into materials engineering. We establish a novel conceptual bridge, arguing that the principles governing particle stability and complexity in TPF are analogous to the phenomena of topological protection and geometric frustration observed in quantum materials. This suggests a new paradigm for materials design, where the fundamental rules of particle construction can inform the engineering of materials with programmable, emergent properties.
Yıldırım, E. (2025). The Particle Framework (TPF): A Geometrodynamic Approach to Emergent Matter and its Implications for Materials Engineering. Zenodo. https://doi.org/10.5281/zenodo.17041028
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