Abstract The central result of this paper is the structural equality: $$\sum_{i=1}^{\infty} w_i \cdot L_{T_i}(s) = \prod_p \left(1 - p^{-s}\right)^{-1} = \zeta(s)$$ 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 foundation of this equality is the relational inversion framework, which is shown to constitute a generative function over the space of primality certificate theorems themselves. The framework does not merely apply to existing theorems --- it generates new ones by the same method. Fifteen theorems $T_1$--$T_{15}$ are demonstrated in full, establishing the method and revealing fifteen algebraic layers of the prime distribution. Five further theorems $T_{16}$--$T_{20}$ are presented as demonstrations of the framework's productive extent: $T_{16}$ and $T_{19}$ are genuine proposed extensions; $T_{17}$, $T_{18}$, and $T_{20}$ are unverified open research directions. The architecture extends to $T_{\infty}$ by the method itself, not by assertion. The structural equality is simultaneously the central result and the verification criterion of the framework. A primality certificate theorem $T_i$ belongs to the architecture if and only if its partial L-function $L_{T_i}(s)$ is consistent with $\zeta(s)$ and forces its zeros to the critical line $\mathrm{Re}(s) = \tfrac{1}{2}$. The Riemann Hypothesis is therefore not a property to be proved about $\zeta(s)$ from outside. It 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. The critical line is not an output of the framework --- it is the requirement every generated theorem must meet. The central geometric object is the symmetric-pair construction of the Brillhart--Lehmer--Selfridge combined test $T_{10}$: for each prime $p$ and even multiplier $U < p$, the pair $N_f = pU + 1$ and $N_b = pU - 1$ satisfies the exact identity $$N_f - 1 = N_b + 1 = pU$$ unconditionally for every pair. This encodes a deterministic mirror symmetry between the $N-1$ algebraic geometry in $(\mathbb{Z}/N\mathbb{Z})^*$ and the $N+1$ algebraic geometry in $(\mathbb{Z}/N\mathbb{Z})[\sqrt{D}]^*$. The certified sets $C_{T_2}$ and $C_{T_8}$ are both determined by the primality condition on the shared anchor $pU$, independently in their respective domains. No correspondence between the fields $K_{T_2}/\mathbb{Q}$ and $K_{T_8}/\mathbb{Q}$ is required. Three previously identified gaps are resolved by the Generative Consistency Theorem. Gap~1 (Mirror Symmetry of Frobenius Conditions) is closed by the anchor co-determination argument, which replaces the Frobenius correspondence with the shared arithmetic source $pU$ verified by $\zeta(s)$. Gap~2 (Exact Factorisation $E(s) = E(1-s)$) is closed because $E(s)$ as a component of the structural equality must satisfy the consistency condition. Gap~3 (Residual Symmetry $R(s) = R(1-s)$) is closed because the residual shrinks to empty at $T_{\infty}$ and is verified by $\zeta(s)$ at every stage. The framework establishes a precise two-directional relationship. In the forward direction, the relational inversion operator generates primality certificate theorems, each contributing an exact algebraic layer to the prime distribution. In the reverse direction, $\zeta(s)$ verifies every generated theorem. The Riemann Hypothesis and the generative architecture are equivalent statements about the same mathematical object. The critical line $\mathrm{Re}(s) = \tfrac{1}{2}$ is the unique locus of arithmetic consistency between the independent accountings of the flat and curved domains, both drawing from the shared anchor $pU$ --- not approximately, not by symmetry, but by arithmetic.