s672.py

from research import *
s=begin(672,'Generate the complete phase bracket','Can center, width and suffix offset recover all eight supplied endpoints?',{'base_center':2871,'widths':[34,40],'phase_offsets':{'n':0,'t':F(1,2)},'BC_label_rule':'coord(tY)=Y−1/2'},['Supplement A §§4.1,4.3'])
rows=[]
for w in [34,40]:
    for phase,eps in [('n',F(0)),('t',F(1,2))]:
        coords=[2871+eps+F(w,2),2871+eps-F(w,2)]
        labels=[x+(F(1,2) if phase=='t' else 0) for x in coords]
        rows.append({'width':w,'phase':phase,'coordinates':coords,'labels':labels})
finish(s,{'phase_rows':rows,'formula':'x=C+epsilon±w/2'},'One center/width/phase formula generates all eight before/after positions. Corresponding suffix widths are34 and40; Tishri and Nisan centers remain separated by half a year in exact coordinates.','Test whether one global affine date map can perform this entire phase change.',{'source_labels':[r['labels'] for r in rows]==[[2888,2854],[2889,2855],[2891,2851],[2892,2852]],'fixed_phase':[rows[i+1]['coordinates'][0]-rows[i]['coordinates'][0] for i in [0,2]]==[F(1,2)]*2})