{
  "data": "reduced prefix products c_j=p_j/q_j; input h*m",
  "each_stage": "stage j stays in hZ iff q_j divides m",
  "all_stages": "lcm(q_1,...,q_r) divides m",
  "final_only": "q_r divides m",
  "distinction": "equal final products can have different prefix denominators",
  "authorization": "a diagnostic word is not automatically an admitted chronology route"
}