{
  "schemaVersion": 1,
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  "exhibitId": "spectral",
  "slug": "spectral-bridge",
  "title": "Spectral: bridge weight and heat diffusion",
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      "numericalMethod": "Unnormalized L = D − W; double-precision cyclic Jacobi (maximum 100 sweeps), followed by the modal matrix exponential. Observation sampling 0.1 on [0,200] is not an integration step. Node layout is excluded from L. Eigenvector signs and repeated-eigenvalue bases are not unique.",
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      "diagnostics": {
        "method": "Unnormalized L = D − W; double-precision cyclic Jacobi (maximum 100 sweeps), followed by the modal matrix exponential. Observation sampling 0.1 on [0,200] is not an integration step. Node layout is excluded from L. Eigenvector signs and repeated-eigenvalue bases are not unique.",
        "warnings": [
          "Raw heat contains a minimum value of -7.511352650979575e-16. Negative values within floating-point error are retained in data; colors use the nonnegative heat scale."
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      "csvPath": "/studies/spectral/run-20260917003910210-62944-005.csv",
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      "plotSampleCounts": [
        {
          "title": "Laplacian eigenvalue spectrum",
          "series": "Computed eigenvalues",
          "samples": 32
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        {
          "title": "Heat decay over a fixed observation window",
          "series": "Distance from global mean",
          "samples": 2001
        },
        {
          "title": "Heat decay over a fixed observation window",
          "series": "Distance from component means",
          "samples": 2001
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  "results": [
    "This saved batch contains 5 completed calculations. The table and downloads below refer to those actual runs.",
    "The largest recorded absolute diagnostic residual was 9.15329e-13. 5 of 5 residual-bearing cases were within their own reported numerical tolerance.",
    "Across 5 recorded readings, Second eigenvalue λ₂ ranged from -3.75699e-16 to 0.06190975.",
    "Across 5 recorded readings, Selected eigenvalue ranged from -3.75699e-16 to 0.06190975.",
    "Across 5 recorded readings, Total heat mass ranged from 1 to 1.",
    "Across 5 recorded readings, Eigensystem residual ranged from 1.14475e-15 to 9.15329e-13.",
    "Bridge weight 0: λ₂ = -3.75699e-16; distance from the global mean at t = 200 was 0.1767767; connected bound Not applicable; first observed 10% crossing: Not observed by t = 200.",
    "Bridge weight 0.01: λ₂ = 0.001238157; distance from the global mean at t = 200 was 0.1383664; connected bound 0.7683532; first observed 10% crossing: Not observed by t = 200.",
    "Bridge weight 0.05: λ₂ = 0.005963459; distance from the global mean at t = 200 was 0.05431949; connected bound 0.2986252; first observed 10% crossing: 100.4.",
    "Bridge weight 0.2: λ₂ = 0.02091855; distance from the global mean at t = 200 was 0.002814583; connected bound 0.01500181; first observed 10% crossing: 30.1.",
    "Bridge weight 1: λ₂ = 0.06190975; distance from the global mean at t = 200 was 8.36409e-7; connected bound 4.12756e-6; first observed 10% crossing: 11.5."
  ],
  "interpretation": [
    "The bridge comparisons above are readings from the saved runs, including the cases where no crossing was observed. Near-zero eigenvalues are reported with their numerical sign; connectivity is decided from edge weights.",
    "Use component counts from the positive-weight edge data when interpreting the zero-weight case.",
    "Changing one bridge modifies a bottleneck. Scaling every weight would instead rescale the whole time axis; that is not the operation studied here."
  ],
  "summaryCsvPath": "/studies/spectral/summary-20260917003910210-62944.csv"
}