{
  "schema": "AN02-L156-geometry181/v1",
  "coordinate_conventions": "z=xi+i*eta; Euclidean complex coordinates; Levi coefficient isDelta/4 in dimension1; Hermitian forms use w*Lw.",
  "first_figure": {
    "proof_locators": [
      "formalNW1-NW3,NW5-NW8",
      "learnerexamples1-2,L156.1-L156.6"
    ],
    "naive_carrier": "K=[-R,R],R>0; displayed smooth half-plane has zero support-term Levi",
    "naive_parameters": {
      "kappa": 4,
      "xi": 0,
      "eta_interval": [
        0.1,
        4
      ],
      "samples": 700
    },
    "naive_coefficient": "-1/[eta*(1+eta)^2]",
    "strict_parameters": {
      "a": 2,
      "t": 4096,
      "xi": 0,
      "q_interval": [
        0.02,
        4
      ],
      "samples": 700
    },
    "strict_carriers": "K=[-1/128,1/128],L=[-3/128,3/128],X=(-1/32,1/32)",
    "strict_display": "q=eta/t; plotted values are t^(3/2) times the actual Levi coefficient; support function is affine at every displayed point",
    "strict_coefficient": "s^(-3/4)/4*(q0^(3/4)+1/4-3*q0/4)-a*t^2/(t^2+xi^2+eta^2)^2; s=t^2+eta^2,q0=t^2/s",
    "bound": "s^(-3/4)/32; no ordinary smooth coefficient claimed on the nonsmooth support ridge"
  },
  "second_figure": {
    "proof_locators": [
      "formalNW10-NW11",
      "learnerexample3,L156.7,solutions8-9"
    ],
    "map": "h(z)=z^2",
    "target": "varphi(w)=|w|^2",
    "pullback": "|z|^4",
    "radius_interval": [
      0,
      1.5
    ],
    "samples": 700,
    "target_radius": "r^2",
    "derivative_norm": "2r",
    "target_Levi": 1,
    "pullback_Levi": "4r^2",
    "critical_point": "z=0",
    "displayed_compact_annulus": {
      "epsilon": 0.4,
      "outer_radius": 1.5,
      "strict_lower_bound": 0.64
    },
    "qualifications": "Radial values in actual complex coordinates; chosen inverse charts are local away from0. No global chart, systems theorem or global manifold estimate is depicted."
  },
  "authorship": "GPT-6.1 Sol (OpenAI), Ultra; original exact scientific plots; CC0 1.0",
  "human_source": "Lars Hormander, The Analysis of Linear Partial Differential Operators II, Notes on printedp300-301.",
  "Blender_assessment": "Exact one-dimensional curvature profiles and coordinate radii fully display these findings. A3D embedding would add no mathematical information.",
  "protected_source_body_or_images_used": false
}