HammingWeightClaimReduction
$\displaystyle\sum$ over: $X_k \in \{0,1\}^{\log_2 N_{\text{instr}}}$
Opening point $(r_{\text{addr}}^{(7)})$
RHS (input claim)
$$\sum_{j\in instr\cup bc} \gamma^{3j} + \sum_{j\in ram} \gamma^{3j} \cdot \textcolor{BurntOrange}{\textsf{RamHammingWeight}}(r_{\text{cycle}}^{(6)}) + \sum_{j=0}^{N_ra-1} \gamma^{3j+1} \cdot \textcolor{ForestGreen}{\textsf{Ra}_{j}}(r_{\text{addr}}^{(6)}, r_{\text{cycle}}^{(6)}) + \sum_{j=0}^{N_ra-1} \gamma^{3j+2} \cdot \textcolor{ForestGreen}{\textsf{Ra}_{j}}(r_{\text{addr}_{j}}^{(6)}, r_{\text{cycle}}^{(6)})$$
Integrand
$$\sum_{j=0}^{N_ra-1} \textcolor{ForestGreen}{\textsf{Ra}_{j}}(X_k, r_{\text{cycle}}^{(6)}) \cdot \left(\gamma^{3j} + \gamma^{3j+1} \cdot \widetilde{\text{eq}}(r_{\text{addr}}^{(6)}, X_k) + \gamma^{3j+2} \cdot \widetilde{\text{eq}}(r_{\text{addr}_{j}}^{(6)}, X_k)\right)$$
Openings produced
- $\textsf{Ra}_{j}(r_{\text{addr}}^{(7)}, r_{\text{cycle}}^{(6)}) \text{ for } j=0,\ldots,N_{\text{ra}}-1 (N_{\text{ra}} = d_{\text{instr}} + d_{\text{bc}} + d_{\text{ram}})$