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      "family": "split",
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      "mean_rms": 0.35355339059327373,
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        "half_plane": {
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      "n_members": 96,
      "psi_deg": 90
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    {
      "A": 0.5,
      "case": 20,
      "family": "split",
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      "geometry": "warped",
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      "methods": {
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          "flag_count": 182,
          "flag_fraction": 0.7109375,
          "flag_wilson95": [
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          "refused_or_nonfinite": 0,
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          "zero_amplitude": 0
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        "regression": {
          "finite_fits": 256,
          "flag_count": 183,
          "flag_fraction": 0.71484375,
          "flag_wilson95": [
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      },
      "n_members": 96,
      "psi_deg": 135
    },
    {
      "A": 1.0,
      "case": 21,
      "family": "split",
      "g": 7,
      "geometry": "warped",
      "mean_rms": 0.7071067811865475,
      "methods": {
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          "flag_count": 256,
          "flag_fraction": 1.0,
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          "refused_or_nonfinite": 0,
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        "regression": {
          "finite_fits": 256,
          "flag_count": 256,
          "flag_fraction": 1.0,
          "flag_wilson95": [
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          "n": 256,
          "refused_or_nonfinite": 0,
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          "sine_direction_wilson95": null,
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          "zero_amplitude": 0
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      },
      "n_members": 96,
      "psi_deg": 0
    },
    {
      "A": 1.0,
      "case": 22,
      "family": "split",
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      "geometry": "warped",
      "mean_rms": 0.7071067811865475,
      "methods": {
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          "flag_count": 256,
          "flag_fraction": 1.0,
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          "refused_or_nonfinite": 0,
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          "zero_amplitude": 0
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        "regression": {
          "finite_fits": 256,
          "flag_count": 256,
          "flag_fraction": 1.0,
          "flag_wilson95": [
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          "n": 256,
          "refused_or_nonfinite": 0,
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          "sine_direction_wilson95": null,
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          "threshold": 0.37330623545629554,
          "zero_amplitude": 0
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      },
      "n_members": 96,
      "psi_deg": 45
    },
    {
      "A": 1.0,
      "case": 23,
      "family": "split",
      "g": 7,
      "geometry": "warped",
      "mean_rms": 0.7071067811865475,
      "methods": {
        "half_plane": {
          "finite_fits": 256,
          "flag_count": 256,
          "flag_fraction": 1.0,
          "flag_wilson95": [
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          "n": 256,
          "refused_or_nonfinite": 0,
          "sine_direction_count": null,
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          "threshold": 0.3683746438477797,
          "zero_amplitude": 0
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        "regression": {
          "finite_fits": 256,
          "flag_count": 256,
          "flag_fraction": 1.0,
          "flag_wilson95": [
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          "n": 256,
          "refused_or_nonfinite": 0,
          "sine_direction_count": null,
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          "sine_direction_wilson95": null,
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          "threshold": 0.37330623545629554,
          "zero_amplitude": 0
        }
      },
      "n_members": 96,
      "psi_deg": 90
    },
    {
      "A": 1.0,
      "case": 24,
      "family": "split",
      "g": 7,
      "geometry": "warped",
      "mean_rms": 0.7071067811865475,
      "methods": {
        "half_plane": {
          "finite_fits": 256,
          "flag_count": 256,
          "flag_fraction": 1.0,
          "flag_wilson95": [
            0.9852161435741286,
            0.9999999999999999
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          "n": 256,
          "refused_or_nonfinite": 0,
          "sine_direction_count": null,
          "sine_direction_fraction": null,
          "sine_direction_wilson95": null,
          "sine_error_p50_p90_deg": null,
          "threshold": 0.3683746438477797,
          "zero_amplitude": 0
        },
        "regression": {
          "finite_fits": 256,
          "flag_count": 256,
          "flag_fraction": 1.0,
          "flag_wilson95": [
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            0.9999999999999999
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          "n": 256,
          "refused_or_nonfinite": 0,
          "sine_direction_count": null,
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          "sine_direction_wilson95": null,
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          "threshold": 0.37330623545629554,
          "zero_amplitude": 0
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      },
      "n_members": 96,
      "psi_deg": 135
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  ],
  "thresholds": [
    [
      0.9679424501921808,
      0.9691720931452162
    ],
    [
      1.0471260911528721,
      1.0524070894467399
    ],
    [
      0.6876147801683802,
      0.6976068022273257
    ],
    [
      0.6925868218202706,
      0.6863086856197451
    ],
    [
      0.49826628628375746,
      0.49575870966326085
    ],
    [
      0.5106982633271427,
      0.5068707617254209
    ],
    [
      0.35279645340633803,
      0.35599020747502336
    ],
    [
      0.37330623545629554,
      0.3683746438477797
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  ],
  "limitations": [
    "Pure synthetic ring geometries and independent Gaussian unit scatter; not realistic cluster simulations or the full catalogue pipeline.",
    "Current group-estimator code only; cluster-specific code and selection are not validated. N values are toy sizes, not sample-matched bins.",
    "Sine is a projected velocity field, not a unique physical rotation model. Split means two oppositely moving angular compartments, not a dynamical merger simulation.",
    "Split level A/sqrt(2) matches continuous uniform-sine RMS only; finite/warped mean RMS is explicitly reported for each case.",
    "Amplitude flags use strict greater-than the974th ordered amplitude from1024 calibration draws separately for each geometry/N/method. Calibration-threshold uncertainty is not included.",
    "Wilson95% intervals describe pointwise Monte Carlo fractions conditional on the estimated threshold and toy model. They are not physical-membership probabilities or multiplicity-adjusted claims.",
    "Evaluation draws are shared across all25 cases within each geometry/N and between methods. Cases and methods are correlated; no independence claim or combined p-value.",
    "Directed sine error uses the receding direction modulo360degrees; success requires an amplitude flag AND error<=30degrees. Zero amplitude has no defined direction.",
    "Any unexpected refusal/nonfinite fit is a mechanical failure with retained noise and partial coefficients, not a stochastic goodness-of-randomness test.",
    "No observed refits, classifications, new catalogue data, population H, native probability model, or population-parity detection-power calculation."
  ],
  "calibration_trials": 8192,
  "evaluation_case_trials": 51200,
  "unique_evaluation_noise_draws": 2048,
  "source_sha256": "8fc03c9d7385c89aa02e59790e9ca2b5fef49a4fbb47a0fea8ef302d2488cf84",
  "scope": "Saved synthetic aggregate summaries only, copied without new fitting or RNG. No observational or population parity calibration.",
  "methods": [
    "regression",
    "half_plane"
  ],
  "threshold_order": "Each thresholds row: regression then half_plane; geometry order N=12,24,48,96, each uniform then skewed.",
  "interpretation": "Flag intervals are Wilson 95% pointwise intervals conditional on estimated thresholds and toy model. Sine direction success is flag AND nonzero amplitude AND directed-angle error <=30 degrees. Angle quantiles use all defined sine fits. Threshold-estimation uncertainty is omitted."
}