This is probably the most "hackernews" conversation I've ever had but as far as I've ever seen the term used, "memoization" is not restricted to temporarily tabling the results during a single run of the algorithm but used to mean any caching of results of an expensive pure function for future use. You seem to call that a "semi-permanent database of answers". Here is the original memoization paper [1] where he is using a constant-time table lookup exactly as I envisage in this case rather than only tabling results during a single invocation of the algorithm. Ironically he uses it to memoize a recursively-defined factorial function.

[1] https://www.cs.utexas.edu/users/hunt/research/hash-cons/hash...