s1199.py

from research import *
s=begin(1199,'Derive the row rounding carry from the hidden residual sum','How does the joint observation control the difference between rounded life and rounded parts?',{},['C1191','C1192'])
def Q(x):return 5*((x+2)//5)
rows=json.loads((ROOT/'model/ordinary_joint_rounding_fibres.json').read_text())['rows'];branches={z:Q(z) for z in range(-4,5)};out=[{'row':x['tradition']+':'+x['name'],'z':x['z'],'carry':Q(x['L'])-x['B']-x['R']} for x in rows]
a=artifact('model/joint_rounding_carry_bridge.json',json.dumps({'identity':'Q(L)-Q(b)-Q(r)=Q(z), z=L-Q(b)-Q(r)','branches':branches,'rows':out,'proof':'Q commutes with translation by multiples of5; B+R is such a multiple.'},indent=2)+'\n')
finish(s,{'carry_bridge':a,'branches':branches},'The same residual sum that measures joint ambiguity determines the carry between rounded lifespan and rounded parts. Carry is−5 for z≤−3, zero for |z|≤2, and+5 for z≥3.','Check whether the carry by itself retains the exact joint recovery information.',{'all_rows':all(o['carry']==Q(x['z']) for o,x in zip(out,rows)),'three_branches':set(branches.values())=={-5,0,5}})