{
  "comparison_note": "Positive MSE difference favors the prespecified break baseline on this held-out sample. No p-value, universal law, or formal model-selection verdict is inferred.",
  "conditional_standard_error_of_mse_difference": 0.011270251,
  "dataset_kind": [
    "synthetic_demo"
  ],
  "held_out_log_mse_difference_power_minus_break": 0.036199583,
  "held_out_observations": 9,
  "interpretation": "Synthetic scale-break demonstration; no measured universal scaling finding.",
  "power_law": {
    "amplitude": 1.31905216,
    "exponent": 0.797268799,
    "held_out_log_rmse": 0.191434356,
    "parameter_count": 2,
    "training_log_rmse": 0.211525618
  },
  "prespecified_break_x_ratio": 20.0,
  "project": "cross-scale-relationships",
  "scale_break_baseline": {
    "amplitude_below_break": 1.731423165,
    "exponent_above_break": 1.167141234,
    "exponent_below_break": 0.590332879,
    "held_out_log_rmse": 0.021154893,
    "parameter_count": 3,
    "training_log_rmse": 0.057158822
  },
  "synthetic_demo": true,
  "training_observations": 28,
  "uncertainty_assumption": "Positive dimensionless ratios; independent log-scale observation noise with supplied sigma; x treated as exact; standard error is conditional on trained fits and independent test rows."
}