s1204.py

from research import *
s=begin(1204,'Separate the two loss types by the known cap branch','Are rounding residual and cap excess independent missing quantities on every row?',{},['C1202','C1203'])
d=json.loads((ROOT/'model/SP_capacity_slack_transfer.json').read_text());L=[930,912,905,910,895,962,365,969,777];out=[]
for l,c in zip(L,d['SP_capacities']):
 y=min(l,c);q=5*((y+2)//5);out.append({'L':l,'c':c,'y':y,'Q_y':q,'excess':l-y,'rounding_residual':y-q,'branch':'clipped' if l>c else 'unclipped','missing_if_branch_known':'excess only; y=c fixes residual' if l>c else 'residual only; excess=0'})
a=artifact('model/cap_round_branch_information.json',json.dumps({'rows':out,'identity':'L=Q(y)+(y-Q(y))+(L-y)','qualification':'Branch status is additional information; at L=c excess0 is a boundary case.'},indent=2)+'\n')
finish(s,{'branch_information':a},'The two loss registers are not two independent unknowns per row. A known clipped row has y=c, fixing its rounding residual; a known unclipped row has zero excess and needs only its rounding residual.','Verify reconstruction of all nine baseline lives using the branch-appropriate register.',{'identity_all':all(x['L']==x['Q_y']+x['rounding_residual']+x['excess'] for x in out),'three_clipped':sum(x['branch']=='clipped' for x in out)==3,'branch_constraints':all(x['y']==x['c'] if x['branch']=='clipped' else x['excess']==0 for x in out)})