Finite-Field Basis Obstructions for Zero Link Turan Density

For a finite r-uniform hypergraph H, let H_k be its k-fold suspension and let pi_infinity(H) be the limiting Turan density of these suspensions. For a prime power q and m>=0, let B(q,m,r) be the r-graph of linearly independent r-sets in the vector space of dimension r+m over F_q. We prove that the absence of a hypergraph homomorphism from H to B(q,m,r) gives the explicit positive lower bound pi_infinity(H)>=productⱼ₌ₘ₊₁^infinity(1-q^(-j)). We apply the theorem to a six-vertex three-graph and its dual: every vertex link is tripartite, while both graphs have link Turan density at least productj>=1(1-2^(-j)), approximately 0.288788. Status: Public Beta; internally verified candidate proof; external mathematical review pending.