s1298.py

from research import *
s=begin(1298,'Register the lifted Rounded source shift','What enablesoff-grid sourcechanges toactcoherently?',{},['C1297','C1218–C1221'])
op={'id':'translate_with_residual','input':'(y,rho),y in5Z,rho in[-2,2],x=y+rho;source-authorizedintegerd','action':'(y+Q_Z(rho+d),rho+d−Q_Z(rho+d))','output':'losslessRoundedplusresidualencodingofx+d','preserved':'exactreconstructedvalueunderknownshift;T_eT_d=T_(d+e)','lost':'nonewhilebothcoordinatesretained','without_residual':'Universalactiononroundedcellsexistsonlyfor d in5Z','source_domain':'Algebraicnegativeauxiliaryresidualallowed;originaldurationandchronologystatesremain source-qualified.','evidence':['C1218','C1219 all105measurements','C1220','C1221']}
a=artifact('model/operation_rounded_residual_lift.json',json.dumps(op,indent=2)+'\n')
finish(s,{'lift_operation':a},'Theliftedoperation connects exactsourcechanges toRoundedcoordinates bycarrying theresidual. Itpreservesinformation ratherthan derivingmissing residuals orreducingtheprimitive sourcecost.','Register anchoredKeys andscopedtranslations withtheircompositiondomain.',{'composition_stated':'T_eT_d' in op['preserved'],'scope_retained':'source-qualified' in op['source_domain']})