s493.py

from research import *
lifes=[930,912,905,910,895,962,365,969,777,950,600,438,433,464,239,239,230,148,205,175,180,147,137,133,137,120]
s=begin(493,'Cumulative residuals and completion selection','Does cumulative rounding itself create the −2 change used in C481?',{'MT_26_lifespans':lifes,'terminal_anchor':1406,'actual_completion':14004},['File51a §§16.1–16.2','File22 §5.1'])
rounded=[5*((x+2)//5) for x in lifes];res=[b-a for a,b in zip(lifes,rounded)]
finish(s,{'actual_sum':sum(lifes),'rounded_sum':sum(rounded),'positive_rounding':sum(x for x in res if x>0),'negative_rounding':sum(x for x in res if x<0),'Moses_line_heads':[1406+sum(lifes),1406+sum(rounded)],'completion_offset':14004-(1406+sum(lifes))},
 'Cumulative rounding preserves12600 and the14006 Moses-line head exactly. The−2 is the selected lower completion endpoint14004, not a cumulative rounding error. The bridge uses both row residuals and explicit endpoint selection.',
 'Combine the two separately explained shifts and test which endpoint alternatives preserve the anchor.',{'total':sum(lifes)==sum(rounded)==12600,'residuals':sum(x for x in res if x>0)==12 and sum(x for x in res if x<0)==-12})