Theorem 3 (Malicious Triad Singularity Formation):

Beyond U_c greater than 2, Prejudice J, Hostility B_θ, Malice F_∞ manifest as singularities in M_C with combined energy E_singular equals J tensor E plus B_θ tensor V_E plus F_∞ tensor R of E.

Proof: Each operator is non-invertible on invariant subspaces. Riemann curvature blows up at their loci, creating tensor singularities. For U_c less than or equal 2, flow harmonics contain singularity formation. For U_c greater than 2, submanifold tension exceeds containment capacity, hence singularities emerge.

Theorem 3 (Malicious Triad Singularity Formation): 

Beyond U_c greater than 2, Prejudice J, Hostility B_θ, Malice F_∞ manifest as singularities in M_C with combined energy E_singular equals J tensor E plus B_θ tensor V_E plus F_∞ tensor R of E.

Proof: Each operator is non-invertible on invariant subspaces. Riemann curvature blows up at their loci, creating tensor singularities. For U_c less than or equal 2, flow harmonics contain singularity formation. For U_c greater than 2, submanifold tension exceeds containment capacity, hence singularities emerge.