An Aurora PostgreSQL application uses supported pgvector functionality to search a large collection of embeddings by similarity. Exact full scans are too slow, and the team accepts an evaluated approximation tradeoff. Which approach should it investigate?

1. A B-tree on the document title as a direct replacement for embedding-distance search.
2. Use an ordinary hash index on the document ID to accelerate every nearest-neighbor query over the embeddings.
3. An index on the vector serialization length only, assuming equal length means equal meaning.
4. A supported approximate vector index such as HNSW, using the appropriate distance operator and evaluating recall and latency.