Graph-correlated codeword search: A technical note in the random-oracle model

We extend Yamakawa-Zhandry codeword search to graph-correlated predicates in one iid bit oracle. Sequential preparation replaces independent-coordinate preparation; classical list recovery counts active vertices. The scalar theorem has jointly polynomial quantum cost and exp(Ω(λ/log λ)) classical queries for fixed parameters. A folded-dual block refinement replaces the squared-rate restriction by a linear-rate margin, improving the sufficient cutoff and real cap exponent. Its full cost is λO(D+1) poly(Lin+|Γ|), polynomial for fixed degree D; jointly polynomial growing-D time remains open, and its cutoff-boundary classical cap is polynomial. Large-alphabet normalization is a small-error check. These are purely asymptotic results. MSC 2020: 68Q12, 68Q17, 94B35. The accompanying package contains the manuscript source, figures, and integrity manifests.