The central vein sign (CVS) is a supportive imaging biomarker for multiple sclerosis (MS), but its manual assessment on susceptibility-weighted imaging with phase enhancement (SWIp) is time-consuming and reader-dependent. Existing automated methods rely on multi-contrast volumetric data and prerequisite lesion masks. We study a deliberately different formulation: a structured end-to-end pipeline operating on a single axial SWIp sequence with sparse slice-wise annotations and no prerequisite volumetric mask, combining anatomical tiling, tiled lesion detection, cross-slice reconstruction of lesion identity, and two complementary branches that independently assess the same lesion crops—direct CVS classification (Pathway A) and vein-presence gating, vein segmentation, and geometric centrality (Pathway B). A cohort of 64 clinical studies annotated by four readers was merged into a consolidated reference. The main contribution is an explicit decomposition of where such a pipeline fails. On an eight-study evaluation, the pipeline recovered 78 of 111 reference lesions (70.3%); lesion-level F1 was 0.667 for Pathway A and 0.706 for Pathway B, rising to 0.785 and 0.818 when restricted to detected lesions, and a paired test found no significant difference between the pathways ($p=1.00$). Detection is therefore the binding constraint, and a threshold sweep shows the associated overcounting of CVS-positive lesions is not separable from it by detector confidence alone. All operating thresholds were selected on these same eight studies, which were acquired on a single scanner, so the figures are single-centre development-set estimates rather than measures of clinical performance and are likely optimistic. Larger-cohort, acquisition-diverse independent evaluation is required before clinical use.