{
  "schema": "space-time-color-observed-orbit-audit-v1",
  "orbitId": "wallpaper:g6:731aa45654d4d690",
  "fieldUrl": "../../scott-gray/data/orbits/g96-F0p00395000-k0p02000000-N48-M128.f32",
  "metadataUrl": "../../scott-gray/data/orbits/g96-F0p00395000-k0p02000000-N48-M128.json",
  "fieldSha256": "731aa45654d4d690f202dc48818e47c8fe023bfd5462284a8601f4bed6563483",
  "fieldByteLength": 2359296,
  "fieldShape": [
    128,
    2,
    48,
    48
  ],
  "fieldLayout": "Float32 little-endian; q[frame,channel,y,x], planar U then V; converted to Float64 for reductions.",
  "period": 398.9774322342758,
  "sourceGroupId": "g96",
  "sourceKind": "audited-subgroup",
  "operationConvention": "Compare q(R*x, t+tau*T) against q(x,t); x,y are periodic coordinates i/N. R90(x,y)=(-y,x) in mathematical coordinates, modulo the square lattice. All rotations have center (0,0).",
  "normalization": "RMS = sqrt(mean(error^2)) over all 128 frames and 48*48 nodes separately for each channel; normalized RMS divides by that channel's global maximum-minus-minimum over the full saved movie.",
  "testedScope": "All 16 combinations of rotations 0,90,180,270 degrees about the lattice origin and phases 0,1/4,1/2,3/4, without translation or color change. Additionally test scalar color reversal and best affine fit at T/2 with no rotation, and three specified binary thresholds. This is not an exhaustive search over centers, phase shifts, nonlinear palette permutations, or the maximal symmetry group.",
  "exactnessScope": "Maximum 0 means byte-exact equality of the saved samples. Grid-aligned quarter-turn and frame-aligned quarter-period identities also commute with the site's periodic linear/bilinear interpolation. This audit does not rerun the PDE solver or establish a continuum existence theorem.",
  "paletteInterpretation": {
    "ember": "A multistop gradient of U, normalized by the orbit's full U range; not two species, two labels, or an RGB complement operation.",
    "concentration": "The grayscale-like concentration palette displays V, normalized by the orbit's full V range.",
    "source": "../../scott-gray/render.mjs"
  },
  "speciesInterpretation": {
    "equations": "U_t=Du*lap(U)-U*V^2+F*(1-U); V_t=Dv*lap(V)+U*V^2-(F+k)*V",
    "colorSwap": "Relabeling a displayed color does not interchange U and V or change the chemical state.",
    "noSpeciesSwapSymmetry": "At the saved parameters Du=0.16 differs from Dv=0.08, and the feed/kill reaction terms differ. Exchanging U and V is not an equivariance of these equations.",
    "noConservationAssumption": "On a periodic domain, d mean(U+V)/dt = F*(1-mean(U))-(F+k)*mean(V), which is generally nonzero. A two-color complement must not be inferred from conservation of total concentration.",
    "source": "../../scott-gray/research/gray_scott_rk4.cpp"
  },
  "existingSourceValidationNotRerun": {
    "candidateSymmetryMax": 0,
    "refinedReturnRms": 7.967024695721742e-09,
    "refinedTrajectoryRms": 1.4103014136263861e-08,
    "refinedDt": 0.19481319933314248
  },
  "spaceTimeOperations": [
    {
      "rotationDegrees": 0,
      "matrix": [
        [
          1,
          0
        ],
        [
          0,
          1
        ]
      ],
      "translation": [
        0,
        0
      ],
      "phaseShift": 0.0,
      "maximumAbsolute": 0.0,
      "rmsByChannel": [
        0.0,
        0.0
      ],
      "rmsOverChannelRange": [
        0.0,
        0.0
      ]
    },
    {
      "rotationDegrees": 0,
      "matrix": [
        [
          1,
          0
        ],
        [
          0,
          1
        ]
      ],
      "translation": [
        0,
        0
      ],
      "phaseShift": 0.25,
      "maximumAbsolute": 0.32409002259373665,
      "rmsByChannel": [
        0.13846933652729534,
        0.08512773483923078
      ],
      "rmsOverChannelRange": [
        0.42709538202666036,
        0.39595010862130925
      ]
    },
    {
      "rotationDegrees": 0,
      "matrix": [
        [
          1,
          0
        ],
        [
          0,
          1
        ]
      ],
      "translation": [
        0,
        0
      ],
      "phaseShift": 0.5,
      "maximumAbsolute": 0.2608790844678879,
      "rmsByChannel": [
        0.1800920731639162,
        0.1035317476593813
      ],
      "rmsOverChannelRange": [
        0.555476719372842,
        0.4815517153005974
      ]
    },
    {
      "rotationDegrees": 0,
      "matrix": [
        [
          1,
          0
        ],
        [
          0,
          1
        ]
      ],
      "translation": [
        0,
        0
      ],
      "phaseShift": 0.75,
      "maximumAbsolute": 0.32409002259373665,
      "rmsByChannel": [
        0.13846933652729534,
        0.08512773483923078
      ],
      "rmsOverChannelRange": [
        0.42709538202666036,
        0.39595010862130925
      ]
    },
    {
      "rotationDegrees": 90,
      "matrix": [
        [
          0,
          -1
        ],
        [
          1,
          0
        ]
      ],
      "translation": [
        0,
        0
      ],
      "phaseShift": 0.0,
      "maximumAbsolute": 0.32409002259373665,
      "rmsByChannel": [
        0.13846933652729534,
        0.08512773483923078
      ],
      "rmsOverChannelRange": [
        0.42709538202666036,
        0.39595010862130925
      ]
    },
    {
      "rotationDegrees": 90,
      "matrix": [
        [
          0,
          -1
        ],
        [
          1,
          0
        ]
      ],
      "translation": [
        0,
        0
      ],
      "phaseShift": 0.25,
      "maximumAbsolute": 0.0,
      "rmsByChannel": [
        0.0,
        0.0
      ],
      "rmsOverChannelRange": [
        0.0,
        0.0
      ]
    },
    {
      "rotationDegrees": 90,
      "matrix": [
        [
          0,
          -1
        ],
        [
          1,
          0
        ]
      ],
      "translation": [
        0,
        0
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      "phaseShift": 0.5,
      "maximumAbsolute": 0.32409002259373665,
      "rmsByChannel": [
        0.13846933652729534,
        0.08512773483923078
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      "rmsOverChannelRange": [
        0.42709538202666036,
        0.39595010862130925
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    },
    {
      "rotationDegrees": 90,
      "matrix": [
        [
          0,
          -1
        ],
        [
          1,
          0
        ]
      ],
      "translation": [
        0,
        0
      ],
      "phaseShift": 0.75,
      "maximumAbsolute": 0.2608790844678879,
      "rmsByChannel": [
        0.1800920731639162,
        0.1035317476593813
      ],
      "rmsOverChannelRange": [
        0.555476719372842,
        0.4815517153005974
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    },
    {
      "rotationDegrees": 180,
      "matrix": [
        [
          -1,
          0
        ],
        [
          0,
          -1
        ]
      ],
      "translation": [
        0,
        0
      ],
      "phaseShift": 0.0,
      "maximumAbsolute": 0.2608790844678879,
      "rmsByChannel": [
        0.1800920731639162,
        0.1035317476593813
      ],
      "rmsOverChannelRange": [
        0.555476719372842,
        0.4815517153005974
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    },
    {
      "rotationDegrees": 180,
      "matrix": [
        [
          -1,
          0
        ],
        [
          0,
          -1
        ]
      ],
      "translation": [
        0,
        0
      ],
      "phaseShift": 0.25,
      "maximumAbsolute": 0.32409002259373665,
      "rmsByChannel": [
        0.13846933652729534,
        0.08512773483923078
      ],
      "rmsOverChannelRange": [
        0.42709538202666036,
        0.39595010862130925
      ]
    },
    {
      "rotationDegrees": 180,
      "matrix": [
        [
          -1,
          0
        ],
        [
          0,
          -1
        ]
      ],
      "translation": [
        0,
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      ],
      "phaseShift": 0.5,
      "maximumAbsolute": 0.0,
      "rmsByChannel": [
        0.0,
        0.0
      ],
      "rmsOverChannelRange": [
        0.0,
        0.0
      ]
    },
    {
      "rotationDegrees": 180,
      "matrix": [
        [
          -1,
          0
        ],
        [
          0,
          -1
        ]
      ],
      "translation": [
        0,
        0
      ],
      "phaseShift": 0.75,
      "maximumAbsolute": 0.32409002259373665,
      "rmsByChannel": [
        0.13846933652729534,
        0.08512773483923078
      ],
      "rmsOverChannelRange": [
        0.42709538202666036,
        0.39595010862130925
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    },
    {
      "rotationDegrees": 270,
      "matrix": [
        [
          0,
          1
        ],
        [
          -1,
          0
        ]
      ],
      "translation": [
        0,
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      "phaseShift": 0.0,
      "maximumAbsolute": 0.32409002259373665,
      "rmsByChannel": [
        0.13846933652729534,
        0.08512773483923078
      ],
      "rmsOverChannelRange": [
        0.42709538202666036,
        0.39595010862130925
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    },
    {
      "rotationDegrees": 270,
      "matrix": [
        [
          0,
          1
        ],
        [
          -1,
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        ]
      ],
      "translation": [
        0,
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      ],
      "phaseShift": 0.25,
      "maximumAbsolute": 0.2608790844678879,
      "rmsByChannel": [
        0.1800920731639162,
        0.1035317476593813
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      "rmsOverChannelRange": [
        0.555476719372842,
        0.4815517153005974
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    },
    {
      "rotationDegrees": 270,
      "matrix": [
        [
          0,
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        [
          -1,
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        ]
      ],
      "translation": [
        0,
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      "phaseShift": 0.5,
      "maximumAbsolute": 0.32409002259373665,
      "rmsByChannel": [
        0.13846933652729534,
        0.08512773483923078
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      "rmsOverChannelRange": [
        0.42709538202666036,
        0.39595010862130925
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    },
    {
      "rotationDegrees": 270,
      "matrix": [
        [
          0,
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        ],
        [
          -1,
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        ]
      ],
      "translation": [
        0,
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      "phaseShift": 0.75,
      "maximumAbsolute": 0.0,
      "rmsByChannel": [
        0.0,
        0.0
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      "rmsOverChannelRange": [
        0.0,
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    }
  ],
  "channels": [
    {
      "channel": "U",
      "range": [
        0.059269435703754425,
        0.3834811747074127
      ],
      "rangeSpan": 0.3242117390036583,
      "globalMean": 0.2167068786874956,
      "spatialStdOfPerNodeTemporalMean": 0.010485996631955026,
      "halfPeriodIdentity": {
        "rms": 0.1800920731639162,
        "rmsOverRange": 0.555476719372842
      },
      "halfPeriodReversalAboutGlobalMean": {
        "map": "z -> 2*globalMean-z",
        "rms": 0.05940675657125095,
        "rmsOverRange": 0.18323444041173545
      },
      "halfPeriodReversalAboutRangeMidpoint": {
        "map": "z -> minimum+maximum-z",
        "rms": 0.06013600877124301,
        "rmsOverRange": 0.18548374884897198
      },
      "halfPeriodBestAffineFit": {
        "map": "z -> slope*z+offset (least squares; not required to be an involution)",
        "slope": -0.8037299613899269,
        "offset": 0.390880689927928,
        "rms": 0.0564165602818733,
        "rmsOverRange": 0.17401146687423527
      },
      "binaryThresholds": [
        {
          "thresholdName": "full-range midpoint",
          "threshold": 0.22137530520558357,
          "highLabelFraction": 0.4956190321180556,
          "swapMismatchFraction": 0.05807834201388889,
          "minimumPhaseMismatchFraction": 0.027777777777777776,
          "maximumPhaseMismatchFraction": 0.08854166666666667
        },
        {
          "thresholdName": "global mean",
          "threshold": 0.2167068786874956,
          "highLabelFraction": 0.5075954861111112,
          "swapMismatchFraction": 0.06141493055555555,
          "minimumPhaseMismatchFraction": 0.03125,
          "maximumPhaseMismatchFraction": 0.09375
        },
        {
          "thresholdName": "global median",
          "threshold": 0.21958519518375397,
          "highLabelFraction": 0.4999864366319444,
          "swapMismatchFraction": 0.05856662326388889,
          "minimumPhaseMismatchFraction": 0.033854166666666664,
          "maximumPhaseMismatchFraction": 0.0920138888888889
        }
      ],
      "temporalFourierEnergy": {
        "normalization": "Fraction of all non-DC real-DFT energy, summed over spatial nodes; DC means per-node temporal mean.",
        "firstHarmonicFraction": 0.8965292851887883,
        "evenHarmonicFraction": 0.08696850812975938,
        "firstEightHarmonics": [
          {
            "harmonic": 1,
            "fraction": 0.8965292851887883
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          {
            "harmonic": 2,
            "fraction": 0.08294360666967272
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            "harmonic": 3,
            "fraction": 0.015385090572396742
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            "harmonic": 4,
            "fraction": 0.0036885582170836286
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          {
            "harmonic": 5,
            "fraction": 0.00100987514258663
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          {
            "harmonic": 6,
            "fraction": 0.00030064658166871694
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          {
            "harmonic": 7,
            "fraction": 9.49532032635416e-05
          },
          {
            "harmonic": 8,
            "fraction": 3.135173501354837e-05
          }
        ]
      },
      "derivedOddTemporalPart": {
        "definition": "b(x,t) = (q(x,t)-q(x,t+T/2))/2",
        "halfPeriodSignReversalMax": 0.0,
        "quarterTurnThreeQuarterPeriodSignReversalMax": 0.0,
        "zeroValueFraction": 0.001736111111111111,
        "scope": "An exact algebraic projection of the saved movie, not a Gray-Scott concentration or independently evolved solution. A binary sign label is undefined at zero if exact label complementation is required."
      }
    },
    {
      "channel": "V",
      "range": [
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      "rangeSpan": 0.2149961143732071,
      "globalMean": 0.12918613066004683,
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      "halfPeriodIdentity": {
        "rms": 0.1035317476593813,
        "rmsOverRange": 0.4815517153005974
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      "halfPeriodReversalAboutGlobalMean": {
        "map": "z -> 2*globalMean-z",
        "rms": 0.04494268165773473,
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      "halfPeriodReversalAboutRangeMidpoint": {
        "map": "z -> minimum+maximum-z",
        "rms": 0.10318011932572263,
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      },
      "halfPeriodBestAffineFit": {
        "map": "z -> slope*z+offset (least squares; not required to be an involution)",
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        "offset": 0.21740472452528115,
        "rms": 0.04122593633468363,
        "rmsOverRange": 0.19175200656473457
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      "binaryThresholds": [
        {
          "thresholdName": "full-range midpoint",
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          "highLabelFraction": 0.2216254340277778,
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        {
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        {
          "thresholdName": "global median",
          "threshold": 0.10719567909836769,
          "highLabelFraction": 0.5,
          "swapMismatchFraction": 0.072265625,
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      ],
      "temporalFourierEnergy": {
        "normalization": "Fraction of all non-DC real-DFT energy, summed over spatial nodes; DC means per-node temporal mean.",
        "firstHarmonicFraction": 0.8057421719745237,
        "evenHarmonicFraction": 0.15739620404099464,
        "firstEightHarmonics": [
          {
            "harmonic": 1,
            "fraction": 0.8057421719745237
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          {
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            "fraction": 0.14756321601805916
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            "fraction": 0.034002557231393345
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            "harmonic": 4,
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            "harmonic": 5,
            "fraction": 0.002572187551079149
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            "harmonic": 6,
            "fraction": 0.0007879875063280283
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            "harmonic": 7,
            "fraction": 0.00025339158711726583
          },
          {
            "harmonic": 8,
            "fraction": 8.46573089884619e-05
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        ]
      },
      "derivedOddTemporalPart": {
        "definition": "b(x,t) = (q(x,t)-q(x,t+T/2))/2",
        "halfPeriodSignReversalMax": 0.0,
        "quarterTurnThreeQuarterPeriodSignReversalMax": 0.0,
        "zeroValueFraction": 0.001736111111111111,
        "scope": "An exact algebraic projection of the saved movie, not a Gray-Scott concentration or independently evolved solution. A binary sign label is undefined at zero if exact label complementation is required."
      }
    }
  ]
}