{
  "slug": "2026-09-09-slow-fast-frictional-ruptures",
  "slip_example": {
    "slip_m": 0.0001,
    "slow_duration_s": 10.0,
    "fast_duration_s": 0.0001,
    "same_moment_if_same_area_and_modulus": true,
    "not_computed": "Radiated energy or shaking; those are not determined by final slip or moment alone."
  },
  "published_data": {
    "published_rows": 64,
    "positive_log_plot_rows": 47,
    "other_rows_preserved": 17,
    "all_zero_rows": 10,
    "negative_Vmin_rows": 7,
    "source_model_curve_points": 1000,
    "reference_max_relative_difference": 1.1869681375137606e-05,
    "recomputed_parameters": {
      "a_over_b": 0.55,
      "V0_m_s": 1e-06,
      "L_m": [
        3e-08,
        1e-07,
        3e-07
      ],
      "C0": 0.64174,
      "C1": 1.33245,
      "V1": 0.01332,
      "alpha": 2.1568,
      "Veff_over_Vmin": 2
    },
    "limits": "47-row selection is solely for logarithmic display; no absolute-value correction or new classification of the other rows. The supplied table does not identify every zero/negative row's physical meaning or experimental block. Repeated events are not independent faults. Vmin is fit-derived and the source EoM interpolation is not a universal inverse-time law. Small formula/table differences retained; no unverified attribution to a particular cause."
  },
  "toy_model": {
    "background": 0.6,
    "K0": 1.0,
    "rate_toughness_eta": 0.05,
    "reference_speed": 0.001,
    "initial_half_length": 0.01,
    "final_half_length": 3.0,
    "equations": [
      "Kdrive=q*sqrt(length)+I/sqrt(length)",
      "Kdrive*sqrt(1-u)=K0+eta*log(1+u/u0)",
      "dlength/dtime=u"
    ],
    "paths": [
      {
        "impulse": 0.2,
        "min_driving_K": 0.6928203230275509,
        "min_driving_at_length": 0.33333333333333337,
        "minimum_front_speed_after_initial_burst": null,
        "arrest_length": 0.05401353459333629,
        "time_to_display_endpoint": 89.06857557960187,
        "endpoint": "within one part per million of the analytic arrest length; finite display cutoff",
        "energy_balance_residual": 1.2589929099249275e-13,
        "integration_cross_check": 1.4325239377480095e-06
      },
      {
        "impulse": 0.45,
        "min_driving_K": 1.0392304845413265,
        "min_driving_at_length": 0.75,
        "minimum_front_speed_after_initial_burst": 0.0011651667801746313,
        "arrest_length": null,
        "time_to_display_endpoint": 649.575865616959,
        "endpoint": "length=3",
        "energy_balance_residual": 5.88418203051333e-14,
        "integration_cross_check": 1.9174644707674024e-07
      },
      {
        "impulse": 1.0,
        "min_driving_K": 1.5491933384829668,
        "min_driving_at_length": 1.6666666666666667,
        "minimum_front_speed_after_initial_burst": 0.30987833689877886,
        "arrest_length": null,
        "time_to_display_endpoint": 8.130545214466133,
        "endpoint": "length=3",
        "energy_balance_residual": 3.952393967665557e-14,
        "integration_cross_check": 5.5791081937011956e-08
      }
    ],
    "limits": "Structure inspired by increasing background/decreasing impulse SIF in Fryer et al.; chosen toughness law and units are not their full RSF EoM. Residual friction, healing, spatial heterogeneity, cohesive-zone formation and supershear branches are not resolved. The second high-length branch beyond an arrest barrier is not dynamically reached. Arrest display cutoff is not a measured finite arrest time."
  }
}