Good examples of Hall's conjecture: the complete list below 10^45 and 24 new examples

A good example of Hall's conjecture is a pair of positive integers (x, y) with 0 < |x3 − y2| < √x. This data release gives the complete list for x < 1045 (78 values, 23 of them new; previously complete only for x < 1029) and 24 new examples in total. They include x = 759633455495182253123802839538155831 with Hall ratio r = √x/|x3−y2| = 20.413, the second-largest known after Elkies' 46.600. Version 2.0 extends version 1.0 (complete below 1042) to 1045 and adds 2 new examples. Every example can be checked exactly with the included verify.py. The completeness claim is computational, resting on an exact GPU implementation of the Aanderaa–Kristiansen–Ruud sieve. The method, source code and run records will follow with a preprint. AI disclosure: the algorithm improvements, implementation, computations, audits and literature checks were carried out by AI systems (Anthropic Claude, OpenAI Codex) under the author's direction. The author takes responsibility for the content.