> In the notebook, I compute a MiniLM embedding of every real Wayfair classification. I compute the embedding of the fake, hypothetical embedding from the LLM. I then dot product the fake embedding into the real ones to find the most similar. Producing: [the right answer]

Isn't this begging the question that the hallucinated classification will be more selective with respect to the real schema than the query itself? What would the dot product of <E(search query), E(schema)> have given?

Even if that is too vague, smaller LLMs are capable rerankers; return the top N matching true categories and ask for a contextual ordering.