{
  "schema": "AN02-affine-projective-cycle-exact-geometry267/v1",
  "license": "CC0-1.0",
  "canonical_disc": {
    "F": "tau",
    "N": [
      1,
      0,
      0
    ],
    "x": [
      0,
      0,
      1
    ],
    "epsilon": "7/20",
    "disc_map": "D(u,v)=(u-i*epsilon,v,0),u^2+v^2<=1",
    "domain_orientation": "negative du wedge dv",
    "boundary_orientation": "decreasing theta",
    "constant_imaginary_coordinates": {
      "Im(tau)": "-epsilon",
      "Im(eta)": 0,
      "sigma": 0
    },
    "canonical_circle": "(cos(theta)-i*epsilon,sin(theta),0)",
    "projective_coordinate": "y=eta/tau=sin(theta)/(cos(theta)-i*epsilon)",
    "nonvanishing": "|F(D)|>=epsilon",
    "proof_locator": "Learner Example3;formal logarithm and reduced-cycle argument"
  },
  "multiplicity": {
    "antipodal_degree": "(-1)^(n-1)",
    "second_center_weight": "(-1)^(n-1)",
    "signed_center_class": "2[kminus]",
    "projectivized_actual_contour": "2*tau(p_*[kminus])",
    "positive_normal_tube_coefficient": 1,
    "polynomial_degree": "m is distinct from both factors",
    "proof_locator": "Formal equations3–15 and chain-cap naturality"
  },
  "scalar_fiber": {
    "M": "Cstar times C",
    "F": "a",
    "cycle": "(exp(i*t),0),0<=t<=2*pi",
    "projected_point": "[1:0]",
    "vartheta": "da/a",
    "period": "2*pi*i",
    "scope": "Explicit noncanonical scalar-fiber model;canonical whole-sphere logarithm forbids its winding.",
    "proof_locator": "Learner Example2;formal affine splitting and logarithm"
  }
}