arXiv:2611.13820v1 Announce Type: cross Abstract: Logical Anomaly Detection (LAD) requires verifying whether all category-specific constraints, such as object counts, pairing relations, and measurement ranges, are satisfied by a query image given only a few normal references. Recent LAD methods based on Large Vision-Language Models (LVLMs) formulate this as checklist verification, decomposing the decision into independent textual checks. This decomposition, however, is text-only. Every item still reads the same unmodified query image, so the LVLM must extract different forms of visual evidence from one raw image. We identify this text-image mismatch as a constraint-specific perception gap, the source of two failure modes: instance conflation for binding constraints and scale drift for calibration constraints. To diagnose whether these failures stem from insufficient reasoning or insufficient perception, we compare textual reasoning guides and visual perception guides in a training-free setting. Our analysis shows that reasoning over the same image provides little benefit, whereas adapting the visual input to each constraint substantially improves verification accuracy. Based on this finding, we propose CASCADE, a training-free framework that extends checklist decomposition using constraint-specific visual scaffolds. We further introduce CASCADE++, which adapts these scaffolds at the object level by deriving their configurations from the constraint structure and reference distribution. Across MVTec-LOCO and VID-AD, CASCADE++ surpasses the full-shot state of the art by 3.9 AUROC points with only three references, and improves over the strongest VID-AD baseline by 11.4, transferring across multiple LVLM backbones without any training.