Gangmu: Quotient-Based Consolidation of Mathematical Knowledge Across Documents

Mathematical statements often appear in different forms across documents, yet systematically identifying and consolidating equivalent statements remains underexplored. We formulate Mathematical Knowledge Consolidation (MKC) using the Quotient-Based Graph Structure, which maps document-level statement nodes to canonical mathematical entities under strict semantic equivalence while preserving source evidence. Building on this structure, we introduce Gangmu, a two-stage framework that constructs an Evidence Graph of statements and relations and recovers a Canonical Graph through Mathematical Entity Resolution (MathER) in an open-world setting that permits unmatched statements. Gangmu uses semantic normalization, multi-evidence representations, uncertainty handling, and consistency checks to restrict linking and merging to confirmed equivalence. We also introduce MathER-Alg, a benchmark built from 50 algebra texts, comprising a reference knowledge base and 512 expert-annotated queries for open-world mathematical entity resolution. Experiments on MathER-Alg show that Gangmu achieves the highest overall accuracy among the evaluated methods.