Hessian Analysis of the Frustrated SU(2) Vacuum on the Diamond Lattice in Granular Entropic Physics

We compute the 9x9 Hessian of the Wilson plaquette action for SU(2) gauge field fluctuations above the frustrated vacuum on the GEP diamond lattice. The vacuum holonomies U_0 = i sigma dot e_k (pi-rotations geometrically selected by parity obstruction) produce a non-trivial background with Tr(W_0) = -10/27 and frustration energy S_0 = 64/27 per hexagonal plaquette. The Hessian is constructed via background-field expansion U = U_0 V, using the adjoint rotation R_kᵃᵇ = 2 e_k^a e_k^b - deltaᵃᵇ. After summing over all four hexagon classes, numerical diagonalisation yields eigenvalues {-1.12, -0.06, +0.19, +0.19, +0.30, +1.78, +1.78, +2.04, +10.90}: two negative and seven positive. The frustrated vacuum is therefore a saddle point of the Wilson action, not a minimum. Colour-space factorisation Kᵃᵇ{mu nu} = A deltaᵃᵇ delta{mu nu} does not hold even after S_4 tetrahedral averaging. The two unstable eigenvectors are intrinsically colour-space mixed, confirming that the frustration genuinely entangles internal gauge and external spatial degrees of freedom. The saddle-point structure is consistent with the known tension between the Wilson action (which prefers trivial holonomy phi = 0) and the parity obstruction (which geometrically enforces phi = pi). The paper explicitly states what is not claimed: no proof of mass gap, confinement, cosmological constant, or 4D recovery. The full Hessian matrix and reproducible computation script are provided.