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We introduce a Neural-Symbolic Task Planning framework integrating Large Language Model (LLM) decomposition with category-theoretic verification for resource-aware, temporally consistent planning. Our approach represents states as objects and valid operations as morphisms in a categorical framework, ensuring constraint satisfaction through mathematical pullbacks. We employ bidirectional search that simultaneously expands from initial and goal states, guided by a learned planning distance function that efficiently prunes infeasible paths. Empirical evaluations across three planning domains demonstrate that our method outperforms existing baselines by up to 26.1% in completion rates while reducing relative resource violation rate by up to 77%. These results highlight the synergy between LLM-based operator generation and category-theoretic verification for reliable planning in domains requiring both resource-awareness and temporal consistency.
