arXiv:2601.20482v3 Announce Type: replace Abstract: Column matching is a central task in reconciling schemas for data integration. Column names and descriptions are valuable for this task. LLMs can leverage such natural-language schema metadata. However, in many datasets, correct matching requires additional evidence beyond the column itself. Because providing complete schema metadata remains impractical for most LLMs and can obscure the relevant evidence even when it fits, the core challenge becomes to select and organize the most useful contextual information. We present ConStruM, a structure-guided framework for budgeted evidence packing in schema matching. ConStruM constructs a lightweight, reusable structure in which, at query time, it assembles a small context pack emphasizing the most discriminative evidence. ConStruM is designed as an add-on: given a shortlist of candidate targets produced by an upstream matcher, it augments the matcher's final LLM prompt with structured, query-specific evidence so that the final selection is better grounded. For this purpose, we develop a context tree for budgeted multi-level context retrieval and a global similarity hypergraph for grouping and differentiating confusable columns. Across HRS-B and PSID-B, ConStruM achieves a mean combined accuracy of 95.4%, compared with 51.6% for the no-context LLM, and ranks first among all eleven evaluated methods on both benchmarks. On MIMIC--OMOP and Synthea--OMOP, attaching it to our Matchmaker reconstruction produces no statistically significant accuracy change. Together, these results show that ConStruM can deliver large gains when matching depends on context while remaining compatible with a strong matcher in the other tested settings.