UPM: A Foundational Framework Bridging the Solar System and the CMB through Resonance

The Unified Phenomenon Model (UPM) presents a novel theoretical framework based on fundamental resonance principles, where physical phenomena emerge from the interaction between three core components: existence field ℘(x), activation oscillation f(x), and formal structure Φ(x). This project demonstrates the remarkable precision and explanatory power of applying a simple resonance formula sin(ωr + νt + φ) across vastly different scales, from planetary orbit deviations in our Solar System to the cosmic microwave background (CMB) radiation pattern of the early universe. The most significant breakthrough of UPM is the discovery of an absolute precise relationship between its resonance constant and the speed of sound in photon-baryon plasma (1/√3), with 0.0000% error. This mathematical connection is not coincidental but represents a fundamental physical principle spanning multiple scales. The model accurately predicts the position of the first acoustic peak in the CMB spectrum at ℓ = 236.0, perfectly matching observational data from the Planck satellite. While the basic UPM model achieves R² = 0.5556 across the entire CMB spectrum (compared to ΛCDM = 0.6535), it significantly outperforms the standard cosmological model in the damping tail region with R² = 0.7679 (versus ΛCDM = 0.6902). The model further reveals a precise 2/3 relationship (error 0.12%) between the planetary constant (0.865) and cosmological constant (0.577350), suggesting a unified principle governing phenomena across cosmic scales. UPM offers a more parsimonious approach than current cosmological models, requiring only three fundamental parameters (ω, ε, φ) compared to six or more in ΛCDM, while maintaining high predictive power. The project includes applications to gravitational lensing, atomic clocks, GPS systems, and explores potential extensions to biological systems and cognitive models. This repository contains the complete mathematical foundation, computational implementation, and analysis tools for the Unified Phenomenon Model, with comprehensive documentation in both Vietnamese and English to facilitate international collaboration and further development of this promising theoretical framework.