Extensive Finite-Momentum Instabilities of the Uniformly Frustrated SU(2) Vacuum on the Diamond Lattice in Granular Entropic Physics

We compute the full momentum-dependent Hessian K(p) of the Wilson plaquette action for SU(2) gauge field fluctuations above the uniformly frustrated vacuum on the GEP diamond lattice. The Bloch-folded 9x9 Hessian reproduces the published zero-momentum spectrum exactly and reveals extensive negative eigenvalues across the entire Brillouin zone. At the most unstable wavevector, five of nine eigenvalues are negative, with lambda_min = -6.02. A control test with the trivial vacuum (phi = 0) confirms zero instability everywhere, establishing that the negative modes originate specifically from geometric frustration. The dominant unstable mode is a rank-3 colour-space mixed collective reorganization with characteristic wavelength of approximately 3-4 lattice spacings. These results strongly suggest that the uniformly frustrated vacuum is not the ground state and that any stable vacuum configuration is likely non-uniform and spatially structured.