from research import *
s=begin(1063,'Allocation identity versus available source cuts','Can the1/6 or1/26 allocation be made from whole components of the completed paths?',{'duration':14720,'fractions':['1/6','1/26']},['C991','C1058–C1062'])
amounts=[14720*F(x) for x in s['inputs']['fractions']];p=json.loads((ROOT/'model/completed_path_inputs.json').read_text())
finish(s,{'required_selected_amounts':amounts,'whole_component_realization':False,'proof':'All original components and their one-pass values are integers; any sum of whole components is integral, while both required amounts are nonintegral.','scope':'does not refute source allocations on other paths; a new fractional cut would need source support'},'The factor identities transfer algebraically, but neither allocation can select whole components of these four paths. A named subdivision is additional source information.','Use paired endpoint gaps to test common-pivot integrality without searching pivots.',{'noninteger_amounts':all(x.denominator>1 for x in amounts),'values':amounts==[F(7360,3),F(7360,13)],'integer_source_components':all(isinstance(x,int) for v in p['original_paths'].values() for x in v)})