from research import *
s=begin(673,'Test one-map compression of the phase family','Can one affine function change34 to40 while preserving every half-year phase separation?',{'width_change':[34,40],'phase_change':[F(1,2),F(1,2)]},['C672','Supplement A §4.3'])
width_slope=F(40,34); phase_slope=F(1,2)/F(1,2)
predicted_phase=width_slope*F(1,2)
finish(s,{'required_width_slope':width_slope,'required_phase_slope':phase_slope,'false_global_phase_gap':predicted_phase,'role_specific_rule':'C+epsilon+(20/17)(x−C−epsilon)'},'A single affine date map is impossible: width demands slope20/17, while the preserved phase separation demands slope1. The valid expression dilates around each phase’s own center. This explains why the full object needs a phase coordinate.','Compare the scalar34.5 Key input with the coordinate34-to40 construction.',{'incompatible':width_slope!=phase_slope,'phase_miss':predicted_phase==F(10,17) and predicted_phase!=F(1,2),'phase_specific':F(20,17)*34==40})