{
  "schema": "cubic-scaling-finite-check/v1",
  "passed": true,
  "lesson": "cubic-scaling-and-necessary-continuity.md",
  "lesson_sha256": "95a085459a368e6d044da9e1c0d6c0056aa72227ac5e7eba2b5da49a4a93d3e4",
  "script_sha256": "a5c1a36f47a2c55d750a8fb6c9207411e52ab8659d4d4d5e7bddf23601f17a20",
  "checks": [
    {
      "name": "full homogeneous weighted Taylor model",
      "frequency_count": 2,
      "zero_two_jet_checked": true,
      "surviving_cubic": "W**3 - 3*W**2*Z + 2*W*Z**2 + Z**3",
      "leading_mixed_error": "(X1 Z^2 + X2 Z W)/r, with T=r^3",
      "quartic_and_angular_terms_included": true,
      "passed": true
    },
    {
      "name": "actual changing-rank canonical phase and the flat subtraction test",
      "common_ranks_at_w_0_and_1": [
        2,
        4
      ],
      "scaled_phase": "T X + X zeta + Z W^2 + T^(-1) zeta Z W^2",
      "flat_source_subtraction_mismatch": "X zeta (1-1/T) does not tend to zero",
      "source_observation_status": "Author consistency observation; no official erratum claimed.",
      "passed": true
    },
    {
      "name": "distinct input and output norm Jacobians",
      "models": [
        {
          "n": 1,
          "a": 0,
          "b": 0,
          "input_exponent": "-1/2",
          "output_exponent": "2*m - 1/2",
          "ratio_exponent": "2*m"
        },
        {
          "n": 1,
          "a": 1,
          "b": 1,
          "input_exponent": "-5/6",
          "output_exponent": "2*m - 1/2",
          "ratio_exponent": "2*m + 1/3"
        },
        {
          "n": 2,
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          "b": 1,
          "input_exponent": "-4/3",
          "output_exponent": "2*m - 5/6",
          "ratio_exponent": "2*m + 1/2"
        },
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          "n": 1,
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          "b": 3,
          "input_exponent": "-3/2",
          "output_exponent": "2*m - 1",
          "ratio_exponent": "2*m + 1/2"
        },
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          "input_exponent": "-3/2",
          "output_exponent": "2*m - 5/6",
          "ratio_exponent": "2*m + 2/3"
        }
      ],
      "zero_parameter_dimensions_included": true,
      "passed": true
    },
    {
      "name": "whole-frequency amplitude majorant near cancellation",
      "models": [
        {
          "mu": -2.0,
          "maximum_normalized_majorant_ratio": 0.9999999403953588
        },
        {
          "mu": -0.5,
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          "maximum_normalized_majorant_ratio": 1.095199931804691
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      ],
      "includes_zero_and_fixed_frequency_at_zeta_near_minus_T": true,
      "passed": true
    },
    {
      "name": "direct Gaussian Fourier integral and input norm",
      "kind": "Independent adaptive quadrature versus exact Gaussian scaling; Schwartz model, not a compact-input theorem proof.",
      "models": [
        {
          "T": 2.0,
          "direct_transform": 0.8657071017169558,
          "scaled_transform": 0.8657071017169556,
          "direct_norm_squared": 0.9895396786132182,
          "scaled_norm_squared": 0.9895396786132182
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          "direct_transform": 0.4328535508584779,
          "scaled_transform": 0.4328535508584778,
          "direct_norm_squared": 0.31168546769774946,
          "scaled_norm_squared": 0.31168546769775035
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      ],
      "passed": true
    },
    {
      "name": "nonzero limiting cubic integral with a smooth compact profile",
      "compact_profile_mass": 0.44399381616807937,
      "analytic_real_part_lower_bound": 0.44177569644492504,
      "models": [
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          "limit_integral_imag": 0.0,
          "independent_quadrature_error": 1.4988010832439613e-15
        },
        {
          "Z": 0.1,
          "limit_integral_real": 0.44386897918750157,
          "limit_integral_imag": 0.007462313909470812,
          "independent_quadrature_error": 1.443573725305356e-15
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        {
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          "limit_integral_imag": -0.007462313909470812,
          "independent_quadrature_error": 1.443573725305356e-15
        }
      ],
      "passed": true
    }
  ],
  "scope": "Six bounded exact weighted-phase/form/norm models and independent numerical integrals. They test the stated scaling, cancellation majorant and nonzero profile. They do not certify general FIO necessity, transitive prerequisites or fold/Airy estimates.",
  "independent_mathematical_review": false
}