Abstract The central result of this paper is the structural equality: $$\sum_{i=1}^{\infty} w_i \cdot L_{T_i}(s) = \prod_{p}(1 - p^{-s})^{-1} = \zeta(s)$$ where $T_i$ ranges over the sequence of primality certificate theorems generated by the relational inversion framework, $w_i$ is the Chebotarev weight of $T_i$, and $L_{T_i}(s)$ is the partial Euler product over the certified set $C_{T_i}$. Every term on the left side is exact and deterministic. The right side is the Riemann zeta function in its Euler product form. The equality between them is an equality between two exact objects. The left side is active: the relational inversion framework generates a deterministic geometric architecture of the primes, each theorem contributing an exact algebraic layer. The right side is reactive: the zeta function provides analytic verification equal and opposite to whatever the geometry produces. Both sides are algebraically perfect. Their equality is a consequence of that perfection, not a definition. The foundation of this equality is the relational inversion framework, shown to constitute a generative function over the space of primality certificate theorems themselves. Fifteen theorems $T_1$--$T_{15}$ are demonstrated in full. Five further theorems $T_{16}$--$T_{20}$ are presented as demonstrations of productive extent. The kernels of these theorems are identified as the geometric seeds of the entire architecture. Each kernel defines a rigid algebraic rule, not a probabilistic filter. The kernels for the flat domain ($N_f = pU+1$) and the curved domain ($N_b = pU-1$) are exact mirrors around the shared anchor $pU$ — the discrete, deterministic precursor to the analytic reflection $s \mapsto 1-s$ that defines the critical line $\mathrm{Re}(s) = \tfrac{1}{2}$. The Riemann Hypothesis is the internal consistency condition of the generative framework: every theorem the framework generates must satisfy $\mathrm{Re}(s) = \tfrac{1}{2}$ to belong to the architecture.