Agentic robots must turn a high-level goal into actions while keeping the physical conditions needed for future steps valid. A completed action does not ensure that its effects will persist: a later disturbance can invalidate support that the remaining plan still assumes. We present LOGIV, a graph engineering framework for agentic robot execution that uses an explicit task graph to connect symbolic planning, observation-based verification, and embodied action. LOGIV compiles a validated plan into condition-support and resource-ordering edges, checks their physical validity during execution, and uses dependency tracing to determine what must be restored after a failure. Repair is constrained by retained unfinished actions, and the combined continuation is symbolically validated before execution resumes. The framework operates above existing Vision-Language-Action (VLA) and World Action Model (WAM) policies without adding trainable components. Across 20 dual-arm tasks from RoboTwin V2 and BiCoord with three execution backbones, LOGIV improves mean task success without injected disturbances by 10.67 and 15.33 percentage points, respectively. Under predefined perturbations, it achieves higher task completion and condition restoration than three adapted recovery baselines for every backbone on both benchmarks. On three real-robot tasks, successful trials increase from 12/30 to 17/30. These results support explicit, continuously checked task dependencies as a practical interface for reliable agentic robot execution.

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