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There is no such magical hash. Any hash splits the space of words into equivalence classes and unless there's only one equivalence class, there must be words that are edit distance one apart that are in different classes since you can get from any word to any other by a sequence of single edits.

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Any single hash will be suboptimal; the "magic" would be to use a bunch of different hashes to partition your space into suboptimal buckets, and use all of them at once to get very good (though still approximative) query results.

This is what Spotify's excellent Annoy library does. [1]

[1] https://github.com/spotify/annoy

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