Linking implicit scientific claims made on social media to their original publications is crucial for evidence-based fact-checking and scholarly discourse, yet it is hindered by lexical sparsity, very short queries, and domain-specific language. Team AIRwaves ranked second in Subtask 4b of the CLEF-2025 CheckThat! Lab with an evidence-retrieval approach that markedly outperforms the competition baseline. The optimized sparse-retrieval baseline(BM25) achieves MRR@5 = 0.5025 on the gold label blind test set. To surpass this baseline, a two-stage retrieval pipeline is introduced: (i) a first stage that uses a dual encoder based on E5-large, fine-tuned using in-batch and mined hard negatives and enhanced through chunked tokenization and rich document metadata; and (ii) a neural re-ranking stage using a SciBERT cross-encoder. Replacing purely lexical matching with neural representations lifts performance to MRR@5 = 0.6174, and the complete pipeline further improves to MRR@5 = 0.6828. The findings demonstrate that coupling dense retrieval with neural re-rankers delivers a powerful and efficient solution for tweet-to-study matching and provides a practical blueprint for future evidence-retrieval pipelines.