{
  "R_d": "(b,r,L)->(b+d,r-d,L)",
  "A_e": "(b,r,L)->(b,r+e,L+e)",
  "normal_form": "A_deltaL R_deltab; Delta r=Delta L-Delta b",
  "R_invariant": "lifespan",
  "A_invariant": "begetting",
  "diagonal_Rd_Ad": "(b+d,r,L+d), preserving remainder",
  "claim": "unique integer coordinate description of compatible row changes; source masks and admissible domains remain extra premises"
}