CERTIFICATE OF RECOGNITION The Organizing Committee of the VI International Virtual Congress of Education (VICIVE) hereby grants this CERTIFICATE to: Jonathan Rangel Castaño Independent Researcher Distinguished in Mathematics and Theoretical Physics (Colombia, 2025) In recognition of his outstanding academic trajectory and his original scientific contributions to mathematics and theoretical physics in Colombia. In 2025, his work received formal international recognition and was officially acknowledged by the Ministry of the Interior of Colombia. This recognition does not constitute a copyright claim, but rather an institutional acknowledgment of authorship and academic contribution both internationally and before the Ministry of the Interior of Colombia. The registered work entitled: "Geometric Representation of Particle Flows Associated with Normal Curvature Generated by Three New Transcendental Numbers, with Applications in Solar Energy and Artificial Energy" was created in 2025 and constitutes the foundational applied research article within his broader research program. That same year, he developed a new book on prime numbers titled: PRIMAL DYNAMICS: A New Approach to the D Set of Prime Numbers This work presents an original structural reinterpretation of prime numbers through a dynamic and geometric framework. Within this theory, he introduces innovative concepts such as the D set, primal dynamics, the prime core, residual trace, primal blocks, discontinuity zones, numerical trajectories, and a stability index. The book proposes that prime numbers are not isolated arithmetic entities, but manifestations of deep modular symmetries and structured numerical dynamics. This contribution establishes a coherent theoretical architecture integrating number theory, dynamical systems, and differential geometry. Additionally, his more recent article titled: "The Discontinuity Map of Prime Numbers and the Modular Structure of Prime Gaps" extends this framework and is projected as a foundational reference for future mathematicians, particularly in the study of prime distribution, discontinuities, modular structures within number theory, and statistical applications related to prime number behavior. As of 2026, his research is focused on the development of statistical frameworks applied to prime numbers, particularly in relation to discontinuity maps and modular structures. His current work explores probabilistic behaviors, statistical distributions, and structural patterns within prime number sequences, aiming to strengthen the analytical understanding of prime gaps and their geometric and dynamic representations. Jonathan Rangel Castaño is recognized as a highly distinguished independent researcher, noted for the originality, rigor, and conceptual depth of his scientific framework. He holds a Bachelor's degree in Mathematics and a Master's degree in Education, with strong academic training in mathematical reasoning, scientific methodology, and intercultural processes. This foundation has enabled him to build an autonomous research program integrating number theory, dynamical systems, and differential geometry. Among his main contributions are: A structural reinterpretation of prime numbers through Primal Dynamics and the Structure of the D Set, introducing a unified dynamic model of numerical stability. The development of the Trivariate Misk Geometric–Differential methodology applied to bands and energy flows, integrating differential geometry, discrete energy sequences, and curvature theory. The formal definition of three new transcendental rational invariants (Misk constants): θM(n) ≈ 1.6025 ψM(n) ≈ 0.6240 ΦM(n) ≈ 2.6600001 Within this framework, geometry is presented as a governing structural principle for energy modulation, curvature dynamics, and vibrational stability, establishing connections between discrete numerical sequences and continuous geometric curvature through the Gauss map and the Weingarten operator. His scientific production demonstrates independence, internal coherence, and a solid rigorous mathematical foundation, contributing original perspectives to number theory, energy geometry, and contemporary mathematical science in Colombia.
