{
  "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."
}