{
  "status": "PASS",
  "checks": 3498,
  "groups": {
    "primitive_identity": 1,
    "pulse_mass": 1,
    "endpoint_smoothness": 14,
    "double_pulse_table": 8,
    "piecewise_polynomial_grid": 287,
    "window_derivative_identity": 4,
    "quiet_window_identity": 3,
    "window_C2_join": 18,
    "wall_boundary": 404,
    "complete_reflection_cancellation": 167,
    "missing_image_rejected": 1,
    "wrong_wave_speed_rejected": 1,
    "forced_polynomial_PDE_identity": 252,
    "forced_zero_initial_data": 252,
    "source_model_coefficients": 1,
    "source_model_value": 1,
    "temporal_only_source_rejected": 1,
    "energy_integrals": 1,
    "integer_square_root_enclosure": 144,
    "energy_budget_outward": 1,
    "displacement_budget_outward": 1,
    "coarse_rational_energy_bound": 1,
    "exact_energy_norm": 101,
    "residual_norm_identity": 101,
    "residual_triangle_majorant_grid": 101,
    "residual_bound_rational_comparison": 101,
    "candidate_data_and_wall_contract": 1,
    "constant_offset_initial_data_rejected": 1,
    "initial_velocity_mismatch_rejected": 1,
    "spherical_polynomial_PDE_identity": 32,
    "spherical_polynomial_initial_velocity": 32,
    "off_center_first_value": 1,
    "off_center_peak_value": 1,
    "off_center_window_grid": 201,
    "positive_velocity_contribution": 656,
    "sphere_misses_support": 438,
    "positive_displacement_negative_solution": 1,
    "normal_derivative_counterexample": 1,
    "dimension_two_radical_crosscheck": 1,
    "dimension_two_outward_interval": 1,
    "dimension_one_three_at_two": 1,
    "two_dimensional_positive_grid": 80,
    "early_two_dimensional_polynomial": 20,
    "two_dimensional_tail_outward_grid": 60,
    "tail_mass_constant": 1
  },
  "results": {
    "reflection": {
      "times": [
        "2",
        "3",
        "7/2",
        "9/2",
        "11/2",
        "6",
        "7",
        "8"
      ],
      "values": [
        "-4/35",
        "-8/35",
        "-4/35",
        "0",
        "-4/35",
        "-8/35",
        "-4/35",
        "0"
      ],
      "windows": [
        [
          "0",
          "1"
        ],
        [
          "1",
          "3"
        ],
        [
          "3",
          "4"
        ],
        [
          "4",
          "5"
        ],
        [
          "5",
          "6"
        ],
        [
          "6",
          "8"
        ],
        [
          "8",
          "10"
        ]
      ],
      "piece_coefficients": [
        [
          "0"
        ],
        [
          "-97/70",
          "27/4",
          "-27/2",
          "57/4",
          "-17/2",
          "57/20",
          "-1/2",
          "1/28"
        ],
        [
          "944128/35",
          "-55296",
          "48384",
          "-23424",
          "6776",
          "-5856/5",
          "112",
          "-32/7"
        ],
        [
          "0"
        ],
        [
          "-4705000/7",
          "864000",
          "-475200",
          "144960",
          "-26488",
          "14496/5",
          "-176",
          "32/7"
        ],
        [
          "944128/35",
          "-27648",
          "12096",
          "-2928",
          "847/2",
          "-183/5",
          "7/4",
          "-1/28"
        ],
        [
          "0"
        ]
      ]
    },
    "source": {
      "solution": {
        "t^3*x^2": "1/6",
        "t^5": "1/15"
      },
      "u(1,2)": "11/15"
    },
    "energy": {
      "Q(1)^2": "11/75000",
      "Q(1)_interval": [
        "12110601416389966661690131238872774796778943333906717995888867748424029/1000000000000000000000000000000000000000000000000000000000000000000000000",
        "1211060141638996666169013123887277479677894333390671799588886774842403/100000000000000000000000000000000000000000000000000000000000000000000000"
      ],
      "energy_budget_interval": [
        "2594677322938192139404040761670008891469769562491596892612060207218722/85581649610182205227651528562625333430116358593434883472952257770702075",
        "124544511501033222691393956560160426790548938999596650845378889946498654/4107919181288745850927273371006016004645585212484874406701708372993699525"
      ],
      "displacement_interval": [
        "6250000000000000000000000000000000000000000000000000000000000000000/3423265984407288209106061142505013337204654343737395338918090310828083",
        "100000000000000000000000000000000000000000000000000000000000000000000/54772255750516611345696978280080213395274469499798325422689444973249327"
      ],
      "displacement_budget_interval": [
        "484529553823032023234006793611668148578294927081932815435343367869787/57054433073454803485101019041750222286744239062289922315301505180468050",
        "69772255750516611345696978280080213395274469499798325422689444973249327/8215838362577491701854546742012032009291170424969748813403416745987399050"
      ]
    },
    "spherical": {
      "off_center_3/2": "81/8192",
      "off_center_2": "1/32",
      "positive_displacement_at_1/2": "-135/256",
      "sphere_value_only_rejected": true
    },
    "tails": {
      "u1(2)": "16/35",
      "u3(2)": "0",
      "u2(2)_interval": [
        "20053114908526703605864460094079129636534550411468136786684063600313/312500000000000000000000000000000000000000000000000000000000000000000",
        "1403718043596869252410512206585539074557418528802769575067884452021937/21875000000000000000000000000000000000000000000000000000000000000000000"
      ],
      "strict_outer_interval": [
        "1/16",
        "3/40"
      ],
      "limit_t_times_u2": "1/8"
    }
  },
  "scope": "Finite exact polynomial/rational certificates; grid diagnostics are explicitly labelled. General theorems are proved in the companion pages."
}