Zeolite synthesis requires a structured recipe that specifies an organic structure-directing agent (OSDA), gel composition, crystallization temperature, and reaction time. General-purpose language models can draft such recipes, but their outputs often fail domain checks, producing invalid SMILES strings, missing condition fields, or temperature–time schedules inconsistent with local Arrhenius trends. We present ZeoAgent, a closed-loop compiler for machine-checkable zeolite synthesis recipes. ZeoAgent represents each generated recipe as a typed record and verifies it through deterministic field-level checks. At each iteration, a compact yet diverse set of retrieved synthesis precedents guides the next draft. When a field fails validation, the corresponding error code is returned to the model for targeted revision. Recipes passing these checks are calibrated with a local Arrhenius fit before final ranking. In condition-only experiments, the recorded OSDA is supplied and only the hydrothermal-condition fields are predicted. On the archived model outputs, ZeoAgent attains 99.7% RDKit parseability, compared with 81.7% for Qwen3-8B. Typed feedback raises repair pass@5 from 68.3% to 72.0%, and PGC reduces high-residual schedules under its fitted local Arrhenius self-consistency diagnostic from 77.0% to 5.4%.