{
  "fibre": {
    "R": 2,
    "r": 1,
    "a": [
      1.5,
      0
    ],
    "t": [
      0.6,
      0.2
    ],
    "roots": [
      [
        -0.4,
        0
      ],
      [
        0.1,
        0.25
      ],
      [
        0.25,
        -0.3
      ]
    ],
    "segment_avoids_roots": true,
    "example_m": 3
  },
  "ranks": {
    "input": "q",
    "period": "q*m",
    "relative": "q*(m+1)",
    "output_envelope": "q*(m+2)",
    "annihilator_codimension_bound": "q^2*(m+2)^2"
  },
  "cusp": {
    "polynomial": "s^2-x^3",
    "x": "1/4",
    "roots": [
      "-1/8",
      "1/8"
    ],
    "positive_root_loop_radius": "1/25",
    "orientation": "counterclockwise",
    "period": "pi*i*x^(-3/2)",
    "period_at_x": "8*pi*i"
  },
  "proof_locators": [
    "PM.1",
    "PM.5\u2013PM.7",
    "PM.9\u2013PM.19",
    "PM.20\u2013PM.21"
  ],
  "nature": "Exact illustrative fibres and proved maps/bounds; no numerical solution of a holonomic module."
}