CogExtract: Test-Time Search with Execution-Grounded Verification for Web Information Extraction on Dynamic Pages

Web information extraction systems must generate reusable rules that remain reliable across pages with locally varying structures. Existing approaches typically generate a single rule and reuse it without external verification, making errors difficult to detect and repair. We introduce CogExtract, a test-time search framework that couples three mechanisms: Diversity-Conditioned Generation constructs structurally distinct XPath candidates; Execution-Grounded Verification ranks them using deterministic execution signals from a seed page and a sibling verification page; and Failure-Conditioned Reflection uses the resulting failure evidence to guide targeted regeneration when no candidate passes verification. We evaluate CogExtract on LiveWeb-IE, covering 14 websites, 312 page groups, and 50,524 URLs, with 11 vision-language model backbones. CogExtract achieves the best F1 for every backbone and improves over VGS by 14.5 points on average, while increasing model calls by only 13%; GPT-5 reaches the highest overall F1 of 76.6. Mechanism-level analyses show that execution-grounded scoring outperforms LLM self-evaluation in candidate discrimination (AUC 0.840 vs. 0.640; best-selection P@1 96.2% vs. 77.9%). Within the audited a/c failure subset, structured execution-grounded diagnosis also achieves 91.0% accuracy, compared with 59.0% for LLM judgment. These results demonstrate that external execution evidence provides an effective basis for both rule selection and targeted repair on dynamic web pages.