We construct a one-parameter family of zeta-type functions ZR (s) = sqrt (3) + b (R) ^s-1/2 + b (R) ^1/2-s, with b (R) = (4/3) R², 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 ZR (s) = ZR (1-s) and that all non-trivial zeros lie on the critical line Re (s) = 1/2. The proof reduces to a quadratic w² + 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 10⁹. 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.
William Butler (Wed,) studied this question.