s1213.py

from research import *
s=begin(1213,'Test row operations that translate by the five-year lattice','Which changes pass through nearest-five rounding without changing their amplitude?',{},['C1182','C1199','prep/review1182_1201 pending independent review'])
def Qz(x):return 5*((x+2)//5)
checks=[Qz(x+5*k)==Qz(x)+5*k for x in range(-12,33) for k in range(-5,6)]
a=artifact('model/round_lattice_equivariance.json',json.dumps({'law':'Q_Z(x+5k)=Q_Z(x)+5k for integer x,k','proof':'floor((x+5k+2)/5)=floor((x+2)/5)+k','duration_domain':'Original row durations remain nonnegative. Q_Z is the algebraic integer extension used only for signed residuals or translations.','C1199_clarification':'Its Q(z) is Q_Z(z), with z in [-4,4]; it is not a newly admitted negative chronological duration.','row_consequence':'If both d and e are multiples of5, rounded b,r,L each retain the corresponding R_d/A_e translation.'},indent=2)+'\n')
finish(s,{'equivariance':a},'All translations by multiples of five pass through rounding exactly, including the century, half-century, forty and sixty changes. The signed carry notation uses an algebraic extension, not negative source durations.','Locate the only whole-genealogy amplitudes outside that lattice.',{'all_translation_cases':all(checks),'two_off_lattice':[x for x in [100,-24,27,40,60] if x%5]!=[]})