Published Articles - The Alpha Group algebra

“The ideas we seek to understand are not our inventions, but truths already vibrating within the fabric of the universe. The Alpha Group emerges as the serene mirror revealing this invisible order, showing that reality is a field of coherence and resonance, where the wise do not impose, but align.” The Alpha Group Project is an independent research initiative led by Cleber Corrêa (Brazil), aiming to develop a novel algebraic-topological framework capable of coherently representing the transition from three-dimensional to four-dimensional spaces, symbolized by the transformation S3 → S4. This transition involves the emergence of a hidden degree of freedom, represented by an idempotent imaginary number μ, which stabilizes infinity as a coherent projection in a dynamic geometric space. The Alpha Group Algebra proposes a unification of matter, field, and geometry based on the interaction of dynamic fibers, vibrational coherence, and topological coupling. It forms a self-adjusting and natural foundation for describing complex phenomena in physics and mathematics. Its formal simplicity contrasts with its conceptual depth, offering a solid alternative to traditional approaches in the unification of fundamental forces. The project includes scientific articles, 3D visualizations, computational simulations, topological models, and educational materials that articulate the foundations of this new geometric logic. It is open to interdisciplinary collaboration, integrating insights from mathematical physics, abstract algebra, differential geometry, and theoretical cosmology. Keywords: Alpha Group, Fiber Bundles, Topological Transition S3 → S4, Idempotent Number, Algebraic Geometry, Abstract Algebra, Mathematical Physics, Coherent Structure, Stabilized Infinity.