arXiv:2610.16158v1 Announce Type: cross Abstract: Conflict-graph search can stagnate despite effective operators when interventions fail to address the conflicts blocking progress. A disruptive intervention may also require further search before its value emerges. We propose CIPHEUR, a large language model (LLM)-guided framework that connects conflict evidence to coordinated intervention and recovery through Structured Intervention Units (SIUs). The shared control interface supports offline synthesis of executable policies and online contextual decisions. Asynchronous online control sustains native search during inference, while all policies preserve the original objective and feasibility constraints. Across eight satellite-ground scheduling conflict views with five runs per view and a 900-second evaluation cap, CIPHEUR-online achieves the highest mean objective among 11 configurations and increases mean scheduled contact duration by 14.84% over the greedy baseline GWMIN. It exceeds the strongest external per-view mean in seven of eight views and outperforms CHILS in all 40 paired runs. Within the same runs, its normalized objective improvement from 360 to 900 seconds is 1.50 to 1.86 times that of the two programmatic controllers. A separately frozen, one-shot LLM-generated controller also improves the mean objective over CHILS without runtime model calls. Together, these results demonstrate how structural search control translates LLM design knowledge and contextual reasoning into improved solution quality and sustained search progress.