Dependency Hierarchy Governs Curvature Gains in Structured Latent Repair

Dependency hierarchy conditions when curved geometry improves structured latent repair: branching traces provide metric expansion for selective updates, whereas flat connectivity offers little structure to exploit. We test this prediction with CurvRepair through a confound-closed audit that fixes graph source, support retrieval, locator, pullback, update norm, trigger, and selection rule while changing only the latent metric. On the strict released-only ProofWriter-OWA+GSM-Hard+MATH-500 endpoint ($n=1242$), CurvRepair gains $+1.55$ percentage points over its edit-rule-matched Euclidean control (95% CI $[+1.29,+1.81]$, paired-bootstrap $p=6.8\times 10^{-6}$) while satisfying the prespecified $0.15$ pp harm tolerance. Matched rewiring separates the structural regimes: depth-preserving rewiring retains 85.2% of the whole-set gain, hierarchy destruction removes 68.4%, and random edges leave an 11.6% residual whose interval includes zero. The effect replicates across the complete 23-task BIG-Bench-Hard release ($n=6511$; $+1.68$ pp), the complete MMLU-Pro release ($n=12,032$; +1.46 pp, 95% CI [+1.19,+1.73]), and a fixed-anchor repair workflow (+0.94 pp). At equal end-to-end token budgets, CurvRepair leads Self-Consistency-Rewrite, Reflexion-Plus, and Constrained-Regeneration, with all three paired intervals above zero. Confound closure and structural intervention therefore turn hierarchy into an actionable criterion for choosing curved geometry in latent repair.