The hash key is only an index, and the same input always gives the same hash value, so you can retrieve your item just fine even if you can't recover the original key from the hashed value. A hash _map_ is not a hash _function_.
> the same input always gives the same hash value, so you can retrieve your item just fine
You’ll retrieve a bunch of items that hash to the same value, so not exactly. You can retrieve the set of items that have the same hash as your item just fine - which is not exactly the same.
> A hash _map_ is not a hash _function_.
This is more or less what I was getting at. I know hash functions aren’t bijective, but hashmaps are often used as if they are. I guess I’m not sure if LSHs refer to a family of functions or hashmaps, and I guess the word hashes often implies functions - my bad.