{
  "schema": "AN02-derivative-class-exact-figure-geometry/v1",
  "angular": {
    "distribution": "|x|^lambda*f_2(x1/|x|), Re(lambda)>-2, dimension2",
    "class_range": "Gevrey1<=s<2",
    "physical_class_singular_bases": "x1=0,x2!=0",
    "Fourier_class_singular_bases": "xi1>0,xi2=0",
    "source_bases": [
      [
        "0",
        "1"
      ],
      [
        "0",
        "-1"
      ]
    ],
    "source_covectors": [
      [
        "1",
        "0"
      ],
      [
        "1",
        "0"
      ]
    ],
    "target_bases": [
      [
        "1",
        "0"
      ],
      [
        "1",
        "0"
      ]
    ],
    "target_covectors": [
      [
        "0",
        "-1"
      ],
      [
        "0",
        "1"
      ]
    ],
    "marked_circle": "|x|=1;only to locate the two exact marked bases",
    "covectors_drawn_via": "Euclidean identification",
    "display_scale": "3/5",
    "coordinate_scales_equal": true,
    "origins": "outlined;excluded from homogeneous interchange",
    "higher_Gevrey_orders": "s>=2 has no nonzero-base class fibers on either side",
    "proof_locators": [
      "complete-proof Theorem4.1",
      "learner Example3",
      "learner Solution5"
    ]
  },
  "growth": {
    "exact_derivative_modulus": "2*(2*k+1)!",
    "normalization": "|f^(k)(0)|^(1/k)/(k+1)^s",
    "integer_orders": {
      "first": 1,
      "last": 128
    },
    "s_values": [
      "1",
      "3/2",
      "2"
    ],
    "connected_lines": "connect integer samples;not a continuous-order assertion",
    "positive_packet_position": "0",
    "positive_packet_covector": "1",
    "p_definition": "1/sqrt(h)",
    "p_values": [
      "4.0",
      "6.0",
      "8.0",
      "12.0",
      "16.0",
      "24.0",
      "32.0",
      "48.0"
    ],
    "scaled_packet_values_90_digit_arithmetic": [
      {
        "p": "4.0",
        "h": "0.0625",
        "scaled_packet": "7.51771225005268529326222511711594952661060749"
      },
      {
        "p": "6.0",
        "h": "0.027777777777777777777777777777777778",
        "scaled_packet": "7.34506915922433951845876916277238667482590474"
      },
      {
        "p": "8.0",
        "h": "0.015625",
        "scaled_packet": "7.27880641671702511432316674540338077655836104"
      },
      {
        "p": "12.0",
        "h": "0.0069444444444444444444444444444444444",
        "scaled_packet": "7.22052193683305755190264267904246784324251061"
      },
      {
        "p": "16.0",
        "h": "0.00390625",
        "scaled_packet": "7.19362996903249565044810021389330666992930961"
      },
      {
        "p": "24.0",
        "h": "0.0017361111111111111111111111111111111",
        "scaled_packet": "7.16797308522093391252177731865028330134936262"
      },
      {
        "p": "32.0",
        "h": "0.0009765625",
        "scaled_packet": "7.1555591897716793628237425905794713359267986"
      },
      {
        "p": "48.0",
        "h": "0.00043402777777777777777777777777777778",
        "scaled_packet": "7.14339918901866106712789053900723011716572269"
      }
    ],
    "proved_limit": "2*pi*exp(1/8)",
    "proof_locators": [
      "learner Example2,equations27/28/32a/32b",
      "learner Solution3",
      "complete-proof Example8.2"
    ]
  },
  "Blender": "Not used: exact two-dimensional covectors and scientific plots are clearer here."
}