s880.py

from research import *
s=begin(880,'Derive the prefix-denominator theorem','What must hold for every stage of a finite Key word to preserve a grid?',{},['C873','Strategy partial actions'])
proof={'data':'reduced prefix products c_j=p_j/q_j; input h*m','each_stage':'stage j stays in hZ iff q_j divides m','all_stages':'lcm(q_1,...,q_r) divides m','final_only':'q_r divides m','distinction':'equal final products can have different prefix denominators','authorization':'a diagnostic word is not automatically an admitted chronology route'}
a=artifact('model/key_word_domain_theorem.json',json.dumps(proof,indent=2)+'\n')
finish(s,{'theorem':a},'The exact all-stage domain is h times the least common multiple of reduced prefix denominators. Final integrality is a weaker condition whenever cancellation occurs only later.','Evaluate the complete fixed inventory of nine two-Key words.',{'criterion':proof['all_stages'].startswith('lcm'),'authorization_retained':bool(proof['authorization'])})