{
  "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."
}