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The LLM has access to the full text and every translation of it ever produced, both in its corpus and on the searchable web.

Isn't this almost certainly in the training set?

The fact that a ring appears at the end proves that the model has context beyond what was in the prompt. The model clearly knows the story that the prompt was extracted from.

I haven't read the book or watched the movies and even then it looked weird as hell.

This is a rationalization. The simpler explanation is that the model failed to properly depict the passage. As the AI booster crowd would say, cope.