The No-Vacuum Principle and an Explicit Seifert Matrix for the Riemann Zeta Function

We establish a direct connection between knot theory and the Riemann Hypothesis. We prove that any complex matrix S satisfying S + S^T = I has all eigenvalues with real part 1/2. We then construct an explicit sequence of such Seifert matrices S_N from the prime numbers, where S_N = 1/2 I_N + i/2 K_N with K_N[i,j] = tan(π ln p_j) for i < j. The Alexander polynomials det(tS_N - S_N^T) of this sequence are shown to converge to 1/ζ(s) after the change of variable t = exp(2π(s-1/2)). This construction provides a topological mechanism for the Riemann Hypothesis: the non-trivial zeros of ζ(s) correspond to the eigenvalues of the limiting matrix, which by the No-Vacuum Principle must lie on the critical line Re(s) = 1/2. Numerical verification for N=59 shows agreement with the first Riemann zeros to within 0.02. This work reduces the Riemann Hypothesis to a problem in linear algebra and knot theory.