How do you perform a basic nearest-neighbour search with pgvector?

-- K-Nearest Neighbour (KNN) query: find 5 most similar documents
-- Replace '[...]' with the actual query embedding from your ML model
SELECT id, content, embedding <-> '[0.1,0.2,0.3]' AS distance
FROM documents
ORDER BY distance          -- ORDER BY the distance expression
LIMIT 5;                   -- return only the top-5 nearest

-- Using cosine distance (common for text embeddings):
SELECT id, content, 1 - (embedding <=> '[0.1,0.2,0.3]') AS similarity
FROM documents
ORDER BY embedding <=> '[0.1,0.2,0.3]'
LIMIT 10;

-- Self-similarity: find items similar to a known row (not itself)
SELECT b.id, b.content, a.embedding <-> b.embedding AS distance
FROM documents a
CROSS JOIN documents b
WHERE a.id = 42 AND b.id != 42
ORDER BY distance
LIMIT 5;

-- Or using a subquery:
SELECT id, content,
       embedding <-> (SELECT embedding FROM documents WHERE id = 42) AS distance
FROM documents
WHERE id != 42
ORDER BY distance
LIMIT 5;

-- With a parameter placeholder (Python + psycopg2):
-- cur.execute(
--     'SELECT id, content, embedding <-> %s AS dist FROM documents ORDER BY dist LIMIT 5',
--     (query_embedding,)
-- )