s1220.py

from research import *
s=begin(1220,'Prove coherence of consecutive rounded-residual translations','Does the lifted action depend on how an admitted total shift is decomposed?',{},['C1218','C1219'])
def Qz(x):return 5*((x+2)//5)
def T(y,rho,d):
 k=Qz(rho+d);return y+k,rho+d-k
cases=[]
for rho in range(-2,3):
 for a,b in [(100,27),(-100,100),(100,-60),(-24,27),(27,-24)]:
  y1,r1=T(1000,rho,a);end=T(y1,r1,b);cases.append(end==T(1000,rho,a+b))
a=artifact('model/rounded_translation_composition.json',json.dumps({'law':'T_d2 composed with T_d1 = T_(d1+d2)','proof':'Each T changes the reconstructed exact value y+rho by its stated d and re-encodes that unique result as nearest-five value plus residual.','carry_identity':'Q_Z(rho+d1+d2)=Q_Z(rho+d1)+Q_Z(rho+d1-Q_Z(rho+d1)+d2)','scope':'Algebraic composition does not authorize intermediate source states or chronology routes.'},indent=2)+'\n')
finish(s,{'composition':a,'diagnostic_cases':len(cases)},'The lifted translations compose exactly because they retain the full original value. Their coherence is mathematical; source authorization of each intermediate state remains separate.','Determine precisely when the residual may be dropped without breaking a universal shift rule.',{'all_cases':all(cases),'25cases':len(cases)==25})