Recorded data and provenance for the associated calculation.

Download recorded JSON

statuspassed
timestamp20261014T061244Z
gaussian_tangent_checks28
source_sha256e5ebcd08865c525b02ab88d265859aa804f208cd124f811c7981914841adbbd1
scopePeriodic variation and covariance controls, exact Gaussian tangent and dispersion identities; no general evolution theorem.
View complete data
{
  "status": "passed",
  "timestamp": "20261014T061244Z",
  "gaussian_tangent_checks": 28,
  "numerical": [
    {
      "size": 96,
      "profile": "positive",
      "minimum_covariance_remainder": 0.01702290627184122,
      "energy": 42.31078654128145,
      "variation_error": 1.0076051104590533e-11,
      "flux_error": 1.0631968867371578e-13,
      "finite_differences": [
        {
          "epsilon": 0.001,
          "relative_error": 1.504987724720852e-08
        },
        {
          "epsilon": 0.0003,
          "relative_error": 1.363639923201987e-09
        },
        {
          "epsilon": 0.0001,
          "relative_error": 1.320325099252173e-10
        },
        {
          "epsilon": 3e-05,
          "relative_error": 2.4692362043943206e-10
        },
        {
          "epsilon": 1e-05,
          "relative_error": 1.0076051104590533e-11
        }
      ]
    },
    {
      "size": 96,
      "profile": "nodal",
      "minimum_covariance_remainder": 0.22375368797947104,
      "energy": 27.00448713512698,
      "variation_error": 5.181688411681762e-12,
      "flux_error": 5.2364187012257416e-14,
      "finite_differences": [
        {
          "epsilon": 0.001,
          "relative_error": 1.498697529966897e-08
        },
        {
          "epsilon": 0.0003,
          "relative_error": 1.3433705536858298e-09
        },
        {
          "epsilon": 0.0001,
          "relative_error": 1.4729026331927741e-10
        },
        {
          "epsilon": 3e-05,
          "relative_error": 5.4030196983134715e-11
        },
        {
          "epsilon": 1e-05,
          "relative_error": 5.181688411681762e-12
        }
      ]
    },
    {
      "size": 96,
      "profile": "oscillatory",
      "minimum_covariance_remainder": 12.073283669692394,
      "energy": 36.030754980848585,
      "variation_error": 7.027605372091593e-12,
      "flux_error": 3.498120960126563e-14,
      "finite_differences": [
        {
          "epsilon": 0.001,
          "relative_error": 2.1071652296568866e-10
        },
        {
          "epsilon": 0.0003,
          "relative_error": 7.027605372091593e-12
        },
        {
          "epsilon": 0.0001,
          "relative_error": 1.6657152477543395e-11
        },
        {
          "epsilon": 3e-05,
          "relative_error": 6.623950002328412e-11
        },
        {
          "epsilon": 1e-05,
          "relative_error": 5.2184289265548404e-11
        }
      ]
    },
    {
      "size": 192,
      "profile": "positive",
      "minimum_covariance_remainder": 0.017015102455315234,
      "energy": 42.310786541281445,
      "variation_error": 1.0076273149195458e-11,
      "flux_error": 5.556961339364109e-13,
      "finite_differences": [
        {
          "epsilon": 0.001,
          "relative_error": 1.505342972496493e-08
        },
        {
          "epsilon": 0.0003,
          "relative_error": 1.3517973129761884e-09
        },
        {
          "epsilon": 0.0001,
          "relative_error": 1.3203227400282458e-10
        },
        {
          "epsilon": 3e-05,
          "relative_error": 1.0076273149195458e-11
        },
        {
          "epsilon": 1e-05,
          "relative_error": 7.206190227870835e-10
        }
      ]
    },
    {
      "size": 192,
      "profile": "nodal",
      "minimum_covariance_remainder": 0.22375369369782394,
      "energy": 27.00448713736498,
      "variation_error": 1.1658474186049261e-10,
      "flux_error": 1.4009017854096306e-13,
      "finite_differences": [
        {
          "epsilon": 0.001,
          "relative_error": 1.498363264018643e-08
        },
        {
          "epsilon": 0.0003,
          "relative_error": 1.3577914625972909e-09
        },
        {
          "epsilon": 0.0001,
          "relative_error": 1.261840354427335e-10
        },
        {
          "epsilon": 3e-05,
          "relative_error": 1.1658474186049261e-10
        },
        {
          "epsilon": 1e-05,
          "relative_error": 1.7947471286916539e-10
        }
      ]
    },
    {
      "size": 192,
      "profile": "oscillatory",
      "minimum_covariance_remainder": 12.073283669692458,
      "energy": 36.030754980848585,
      "variation_error": 1.886971037323021e-11,
      "flux_error": 7.773460143970746e-14,
      "finite_differences": [
        {
          "epsilon": 0.001,
          "relative_error": 2.0361082167085626e-10
        },
        {
          "epsilon": 0.0003,
          "relative_error": 1.886971037323021e-11
        },
        {
          "epsilon": 0.0001,
          "relative_error": 1.886971037323021e-11
        },
        {
          "epsilon": 3e-05,
          "relative_error": 5.218456320277981e-11
        },
        {
          "epsilon": 1e-05,
          "relative_error": 3.030868046772703e-10
        }
      ]
    }
  ],
  "motion": [
    {
      "depth": 2,
      "width_index": 75,
      "count": 2926,
      "inertia_per_norm": 2926
    },
    {
      "depth": 2,
      "width_index": 80,
      "count": 3321,
      "inertia_per_norm": 3321
    },
    {
      "depth": 2,
      "width_index": 94,
      "count": 4560,
      "inertia_per_norm": 4560
    },
    {
      "depth": 3,
      "width_index": 0,
      "count": 1,
      "inertia_per_norm": 1
    },
    {
      "depth": 3,
      "width_index": 3,
      "count": 20,
      "inertia_per_norm": 20
    },
    {
      "depth": 4,
      "width_index": 2,
      "count": 15,
      "inertia_per_norm": 15
    },
    {
      "depth": 4,
      "width_index": 19,
      "count": 8855,
      "inertia_per_norm": 8855
    },
    {
      "depth": 4,
      "width_index": 71,
      "count": 1215450,
      "inertia_per_norm": 1215450
    },
    {
      "depth": 5,
      "width_index": 9,
      "count": 2002,
      "inertia_per_norm": 2002
    },
    {
      "depth": 5,
      "width_index": 14,
      "count": 11628,
      "inertia_per_norm": 11628
    },
    {
      "depth": 5,
      "width_index": 21,
      "count": 65780,
      "inertia_per_norm": 65780
    },
    {
      "depth": 6,
      "width_index": 12,
      "count": 18564,
      "inertia_per_norm": 18564
    },
    {
      "depth": 6,
      "width_index": 34,
      "count": 3838380,
      "inertia_per_norm": 3838380
    },
    {
      "depth": 10,
      "width_index": 22,
      "count": 64512240,
      "inertia_per_norm": 64512240
    }
  ],
  "source_sha256": "e5ebcd08865c525b02ab88d265859aa804f208cd124f811c7981914841adbbd1",
  "scope": "Periodic variation and covariance controls, exact Gaussian tangent and dispersion identities; no general evolution theorem."
}