{
  "A": {
    "module": "R = F_11[[t]] (truncated), free of rank 1",
    "map": "multiplication by t^2 * u with u(0) = 2",
    "map_nonzero": true,
    "vanishing_order": 2,
    "value_at_zero": 0,
    "annihilates_anything": false,
    "D_style_nonannihilation": "PASS",
    "E_style_leading_coefficient": "NOT CERTIFIED — this gate emits no leading-coefficient equality",
    "requirement_enforced": true,
    "ok": true
  },
  "B": {
    "module": "Z_11, free of rank 1",
    "map": "multiplication by 11",
    "rational_isomorphism": true,
    "integral_image": "11^1 * Z_11",
    "integral_index": 11,
    "integral_unit_isomorphism": false,
    "requirement_enforced": true,
    "ok": true
  },
  "what_A_separates": "a nonzero map with positive vanishing order from an annihilating map",
  "what_B_separates": "a rational isomorphism from an integral unit isomorphism",
  "switching_a_requirement_off_is_itself_a_defect": true,
  "agrees": true
}