Eid's Prime-Edge Principle: A Theoretical Framework for Prime-Sensitive Resonance Collapse

This observational numerical note reports a novel phenomenon in finite residual matrix models where resonances are governed by the upper projection edge Kedge=m+WK_{\text{edge}} = m + WKedge=m+W, rather than individual frequency bands. The core contribution is the formulation of the Moving Prime-Edge Resonance Principle, which suggests that resonance survival and collapse occur within LLL-dependent “destructive edge regions.” Numerical evidence across multiple scales ( L=4.5,5.0,5.5L = 4.5, 5.0, 5.5L=4.5,5.0,5.5) reveals a striking correlation: these destructive regions tend to cluster near prime numbers or prime-neighboring locations. In an extended analysis, 87.5%87.5\%87.5% of observed “death edges” were found within a distance of 2 from a prime number. This work provides a new framework for studying the intersection of finite matrix theory, oscillatory modes, and arithmetic signatures, offering specific conjectures for future theoretical and numerical validation.