from research import *
s=begin(721,'Relate the two exact phase charts','How does the earlier positiveBC phase chart connect to the fixed-set signed chart?',{'earlier_chart':'q(Bn)=B; q(Bt)=B−1/2','signed_chart':'x(Bn)=−B+1/4; x(Bt)=−B+3/4','Short_center_labels':['2922t','2921n']},['Supplement A §§4.1,13.1–13.2; reviewer C692–C709'])
B=2939; q_t=F(B)-F(1,2); q_n=F(B); mapx=lambda q:F(1,4)-q
centerpair_q=[F(2922)-F(1,2),F(2921)]; centerpair_x=[mapx(q) for q in centerpair_q]
finish(s,{'chart_map':'x=1/4−q','sample_T_x':mapx(q_t),'sample_N_x':mapx(q_n),'center_pair_q':centerpair_q,'center_pair_x':centerpair_x,'January_center':sum(centerpair_x)/2},'The charts are related by x=1/4−q. The2922t/2921n center pair brackets the January instant−2921 by a quarter-year on either side; neither labeled phase position alone is that instant. This resolves the chart relation without changing the source phases.','Apply all independent review refinements to the final integrated manuscript.',{'T_rule':mapx(q_t)==-B+F(3,4),'N_rule':mapx(q_n)==-B+F(1,4),'center_pair':centerpair_x==[-F(11685,4),-F(11683,4)],'January_center':sum(centerpair_x)/2==-2921})