SAIM Quantum Framework V2: From Classical Kuramoto Synchronization to Noisy Quantum VQE Mass Gap Extraction

This study presents the SAIM Quantum Framework, an advanced computational approach to simulating the Electroweak Symmetry Breaking (EWSB) and the emergence of the Higgs mechanism. Using a macroscopic Kuramoto model of N=250 interacting quantum fields, we successfully map the critical slowing down (CSD) and synchronization velocity leading to the phase transition at T_EW = 35.0. By introducing a resonance boost and applying Hann-windowed Fast Fourier Transform (FFT) analysis on the post-transition order parameter, we numerically extracted the mass signature of the Higgs boson (peaking at 0.240 Hz). Furthermore, we visualize the post-transition vacuum condensate as a 3D spatial lattice (Mexican Hat potential). This computational pipeline successfully demonstrates early warning signals prior to symmetry breaking, proving the framework's viability for analyzing complex field dynamics and particle mass generation.