{'fraction_non_alphanumeric': 0.01589242053789731, 'fraction_numerical': 0.0012224938875305623, 'mean_word_length': 5.022058823529412, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Evolution of algebraic terms 3: Term continuity and beam algorithms

The first paper in this series introduced the notion of term to term operation continuity for finite groupoids, and proved that two testable conditions on a finite groupoid imply that it is term continuous (TC). The second presented an evolution inspired algorithm for finding terms for operations, and gave experimental evidence that, in general, it was successful exactly when the groupoid was both idemprimal and TC. In this paper, we describe a new class of algorithms for finding terms which brings these results together. Theorems about idemprimality and term continuity show how each of these two properties impact our algorithms. They lead to a final explanation for the success of our algorithms when the groupoid is both idemprimal and TC.