{
  "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\u2212Q_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"
  ]
}