LLMs excel at recalling statistical patterns but degrade sharply when answers must be derived, especially on multi-hop chains. Delegating derivation to deterministic symbolic executors shifts reliability to whether model-generated premises are source-supported. We introduce CPUNeSy, a serving architecture that controls model writes to symbolic state via a task-defined predicate interface and certificate gate, abstaining when grounding passes disagree. Component analysis isolates deterministic execution, restricted grounding, agreement, and source rechecking. Experiments show deterministic execution drives most accuracy recovery on derivation-heavy tasks; controlled writes mainly improve selective reliability by withholding unsupported or inconsistent answers, at a coverage cost. On multi-hop tests in law and formal math, deterministic execution recovers most of the gap over chain-of-thought and retrieval baselines, with full-pool gains up to 35.0 points. Certification is selective-serving control, not accuracy mechanism: with grounding traces fixed on ContractNLI, source rechecking removes a quarter of DeepSeek's wrong answers surviving two-vote agreement, at measurable coverage cost. When abstention is costly, routing withheld cases to an uncertified same-model fallback raises full-pool accuracy on MedCalc-Bench Verified by 13.9 and 4.9 points for Seed and DeepSeek; these gains are not from the certified channel. On LeanDojo Benchmark 4, kernel-restricted pools match BM25 recall@15 (89.3%). Gains depend on the grounder's error regime: bias-dominated grounders benefit less, consistent with our voting bound. Certificates guarantee derivational validity relative to admitted premises; semantic faithfulness to natural-language sources remains conditional on the source checker, and prospective validation is future work.

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