This research presents an empirical framework linking additive number theory with non-linear dynamics. Specifically, it explores the relationship between the distribution of Goldbach prime partitions and the synchronization thresholds ($\Gamma$) in networks of coupled oscillators governed by the Kuramoto model. Methodology: The study utilizes numerical simulations where the natural frequencies of oscillators are derived from the logarithms of primes within Goldbach pairs for a given even number $N$. Through extensive computational runs, we identify a stable, universal scaling law that governs the transition from chaos to phase-locked synchronization. Key Findings: Numerical verification across the tested range indicates a near-perfect correlation for the proposed scaling relationship: $$\Gamma(N) = \sum_{p+q=N} \frac{1}{\ln(p)\ln(q)}$$ Results suggest that prime number distributions possess inherent physical properties that can be mapped to spectral gaps in complex networks. Numerical Validation & Computational Evidence: To ensure the robustness of the hypothesis, the model was subjected to rigorous stress testing: Base Validation ($N = 10^6$): Confirms the linear scaling property of the $\Gamma(N)$ function across the first million integers. Large-Scale Stress Test ($N = 10^7$): Validation using a dataset of 664,579 prime numbers. This "Ultra Test" demonstrates that the Nedelchev Hypothesis remains stable and consistent at higher numerical scales ($10^7$). Microscopic Stability Analysis: A high-resolution check of every even integer between 9,990,000 and 10,000,000. With 5,000 consecutive points verified, this test proves the absence of local failures or "gaps" in the proposed synchronization model. Applications: The "Nedelchev Hypothesis" offers potential new methodologies for: Information Security: Analysis of prime-based synchronization for cryptographic protocols. Biomedical Engineering: Modeling pathological synchronization in neural networks (e.g., epilepsy). Power Grid Stability: Using arithmetical-physical models to predict phase transitions in energy networks. Note on Status: This work is submitted as an Empirical Hypothesis. It provides numerical evidence and a computational framework for further theoretical investigation. The author invites collaboration from the mathematical and physics communities for formal analytical proof and experimental laboratory validation. Keywords: Goldbach Conjecture, Kuramoto Model, Prime Numbers, Synchronization, Non-linear Dynamics, Computational Physics. Source Code and Simulations: https://github.com/icobug/prime-synchronization-theorem