This report synthesises findings from 7 peer-reviewed papers addressing the following research question: How does the performance of manifold-aware embedding projections compare to domain-adaptive fine-tuning on cross-lingual information retrieval tasks when evaluated using BEIR metrics on languages. 8 claims were extracted from source literature; 8 were independently verified against retrieved documents. An automated multi-reviewer quality assessment produced a score of 8.5/10. This report is a machine-generated literature synthesis and does not constitute original research.Research goal: How does the performance of manifold-aware embedding projections compare to domain-adaptive fine-tuning on cross-lingual information retrieval tasks when evaluated using BEIR metrics on languages with less than 100K training examples?Autonomous literature synthesis. Automated review score: 8.5/10. Full text and citation available at Assignee Research.