Inference-time search can substantially improve LLM reasoning when tasks admit deterministic verification, but existing methods largely refine single trajectories and lack a reliable mechanism for composing partial solutions across candidates. We propose contract-checked graph editing: represent each candidate as an interface-typed reasoning DAG and validate every nontrivial edit with a deterministic structural gate (acyclicity, namespace closure, schema validity, terminal constraints) before invoking the verifier. The gate certifies runnability only and emits auditable rejection reasons; semantic correctness is determined solely by the verifier. Instantiated in Genetic Inference Search (GIS) with Qwen2.5-32B-Instruct under strictly matched token budgets (8K tokens), contract-checked grafting increases verifier-runnable recombination from 41.2% to 92.8% and improves accuracy over rStar (+6.1 on MATH, +9.1 on MATH L5) while using 42% fewer verifier calls. The same operators transfer across outer loops (beam, best-first, MCTS) and to structured generation and code, outperforming execution-guided beam search on Spider (+2.8) and improving multi-file code generation on HumanEval-MF (+9.2).