A family of zeta functions with provable critical-line zeros from four-element partition combinatorics

We construct a one-parameter family of zeta-type functions Z_R(s) = sqrt(3) + b(R)s-1/2 + b(R)1/2-s, with b(R) = (4/3)R^2, arising from the partition combinatorics of a four-element cell with a k <-> 4-k symmetry. We prove that every member of this family satisfies a functional equation Z_R(s) = Z_R(1-s) and that all non-trivial zeros lie on the critical line Re(s) = 1/2. The proof reduces to a quadratic w^2 + sqrt(3)w + 1 = 0 whose roots have unit modulus - a consequence of an exact combinatorial identity c(R) = sqrt(3) that is independent of scale. We connect this construction to prime-number density through an information-theoretic mapping and show that the resulting model reproduces pi(N)/N to ~1% accuracy over N = 500 to 10^9. Numerical evidence reveals that 8 of the first 10 Riemann zeta zeros correspond to near-vanishing of individual partition zeta product factors. Paper 5a in the EDCE series.