[
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    "n_materials": 4,
    "n_properties": 5,
    "potential": "Adams-1989",
    "eigenvalues": [
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    "eigenvectors": [
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    "effective_dimensionality": 1.9906942374940468,
    "fractional_dimensionality": 0.39813884749880935,
    "cumulative_variance": [
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    "log_slope": -0.9392177035994594,
    "log_intercept": 4.078116632741848,
    "log_r_squared": 0.9980948402706267,
    "decay_monotonicity": -1.0,
    "width_ratios": [
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    ],
    "mean_width_ratio": 2.564442970300341,
    "is_hyper_ribbon": true,
    "interpretation": "Hyper-ribbon structure confirmed (PR = 1.99 / 5) Errors are strongly confined: only ~2.0 effective dimensions control all 5 properties. Log-spacing is highly linear (R² = 0.998), consistent with Vandermonde universality class. First principal direction captures 65.9% of error variance.",
    "pr_ci_lower": 1.0,
    "pr_ci_upper": 1.9906942374940473,
    "log_r2_ci_lower": 0.0,
    "log_r2_ci_upper": 1.0
  },
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    "n_materials": 4,
    "n_properties": 5,
    "potential": "Foiles-1986",
    "eigenvalues": [
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    "eigenvectors": [
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      ],
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    "effective_dimensionality": 1.6847865118795993,
    "fractional_dimensionality": 0.33695730237591986,
    "cumulative_variance": [
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    "log_slope": -1.11391497711905,
    "log_intercept": 4.310380403663343,
    "log_r_squared": 0.9686767805065148,
    "decay_monotonicity": -1.0,
    "width_ratios": [
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    ],
    "mean_width_ratio": 3.2314444558213378,
    "is_hyper_ribbon": true,
    "interpretation": "Hyper-ribbon structure confirmed (PR = 1.68 / 5) Errors are strongly confined: only ~1.7 effective dimensions control all 5 properties. Log-spacing is highly linear (R² = 0.969), consistent with Vandermonde universality class. First principal direction captures 74.6% of error variance.",
    "pr_ci_lower": 1.0,
    "pr_ci_upper": 1.972246228383309,
    "log_r2_ci_lower": 0.0,
    "log_r2_ci_upper": 1.0
  },
  {
    "n_materials": 5,
    "n_properties": 5,
    "potential": "Zhou-2004",
    "eigenvalues": [
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    ],
    "eigenvectors": [
      [
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      [
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      ],
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        0.25571033983365393,
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      ],
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        -0.13343986488026832,
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        0.18958586318434384,
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        -0.12578434074896389
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    ],
    "effective_dimensionality": 1.1498940321391153,
    "fractional_dimensionality": 0.22997880642782306,
    "cumulative_variance": [
      0.9302274976331378,
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      1.0,
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    ],
    "log_slope": -3.773047066790872,
    "log_intercept": 4.064218037461151,
    "log_r_squared": 0.9493400587720295,
    "decay_monotonicity": -1.0,
    "width_ratios": [
      14.177744299981875,
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    ],
    "mean_width_ratio": 181.82520177355215,
    "is_hyper_ribbon": true,
    "interpretation": "Hyper-ribbon structure confirmed (PR = 1.15 / 5) Errors are strongly confined: only ~1.1 effective dimensions control all 5 properties. Log-spacing is highly linear (R² = 0.949), consistent with Vandermonde universality class. First principal direction captures 93.0% of error variance.",
    "pr_ci_lower": 1.0,
    "pr_ci_upper": 1.3693640115003824,
    "log_r2_ci_lower": 0.0,
    "log_r2_ci_upper": 1.0
  },
  {
    "n_materials": 4,
    "n_properties": 5,
    "potential": "Ackland-1987",
    "eigenvalues": [
      1611.423261110456,
      390.7102903958159,
      0.1764980965212706,
      0.0
    ],
    "eigenvectors": [
      [
        -0.5589061786365787,
        -0.5852877522035276,
        -0.5874198200115239,
        -0.0002926761962231178,
        8.197102134986836e-7
      ],
      [
        -0.3245614658240722,
        0.8062782363818417,
        -0.49454505114892405,
        0.000672815681886569,
        0.000011928222469233629
      ],
      [
        -0.7626993708492288,
        0.08568610228080013,
        0.640286881689441,
        0.03129400985492018,
        -0.0009775815705461521
      ],
      [
        0.023945894703140954,
        -0.0033975206192432203,
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    ],
    "effective_dimensionality": 1.4582577202031295,
    "fractional_dimensionality": 0.2916515440406259,
    "cumulative_variance": [
      0.8047820872846945,
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      1.0,
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    ],
    "log_slope": -4.559659133915052,
    "log_intercept": 8.432457211715937,
    "log_r_squared": 0.8632925139254519,
    "decay_monotonicity": -1.0,
    "width_ratios": [
      4.124343025309048,
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    ],
    "mean_width_ratio": 1108.902126437408,
    "is_hyper_ribbon": true,
    "interpretation": "Hyper-ribbon structure confirmed (PR = 1.46 / 5) Errors are strongly confined: only ~1.5 effective dimensions control all 5 properties. Moderate log-linearity (R² = 0.863) — may be an intermediate regime. First principal direction captures 80.5% of error variance.",
    "pr_ci_lower": 1.0,
    "pr_ci_upper": 1.697249414364924,
    "log_r2_ci_lower": 0.0,
    "log_r2_ci_upper": 1.0
  }
]