{
  "release": "0.8.0",
  "experiment": "Bubble hidden-variable inverse",
  "model_class": "small-amplitude spherical Rayleigh-Plesset stiffness with fixed effective polytropic exponent; vapor pressure and surface tension included; compact airborne source; no free-surface, thermal-transfer, viscous, radiation, shape, or multibubble correction",
  "reference_inputs": {
    "temperature_k": 298.15,
    "water_vapor_pressure_pa": 3169.824486,
    "liquid_pressure_at_bubble_pa": 101364.1107638502,
    "surface_tension_n_m": 0.07197,
    "density_kg_m3": 997.047,
    "thermal_response_source": "Prosperetti 1977",
    "near_surface_source": "Oguz and Prosperetti 1990",
    "rain_noise_source": "Oguz and Prosperetti 1991"
  },
  "checks": {
    "release_07_ideal_frequency_hz": 4110.920533578131,
    "corrected_frequency_kappa_1_hz": 3421.6939460925273,
    "corrected_frequency_kappa_1_4_hz": 4048.9556866427374,
    "ideal_to_corrected_kappa_1_4_difference_hz": 61.964846935393325,
    "ideal_to_corrected_kappa_1_4_relative_percent": 1.507322908075271,
    "equivalent_family_size": 401,
    "radius_min_mm": 0.6659557704299047,
    "radius_max_mm": 0.7879498163010304,
    "radius_span_relative_to_min_percent": 18.318640859943752,
    "fractional_amplitude_min": 0.03,
    "fractional_amplitude_max": 0.04969134722042918,
    "frequency_family_max_error_hz": 9.094947017729282e-13,
    "volume_scale_family_max_error_m3": 3.877409121342317e-26,
    "endpoint_waveform_max_error_pa": 3.666771747345976e-16,
    "pressure_samples_per_endpoint": 3840,
    "jacobian_shape": [
      3,
      4
    ],
    "jacobian_rank": 3,
    "local_nullity": 1,
    "jacobian_singular_values": [
      3.3062241931480996,
      1.000000000139778,
      0.566143719072358
    ]
  },
  "counterexample": {
    "first": {
      "kappa": 1.0,
      "radius_mm": 0.6659557704299047,
      "fractional_volume_amplitude": 0.04969134722042918
    },
    "second": {
      "kappa": 1.4,
      "radius_mm": 0.7879498163010304,
      "fractional_volume_amplitude": 0.03
    },
    "shared": {
      "frequency_hz": 4110.920533578131,
      "decay_time_s": 0.018,
      "arrival_time_s": 0.006,
      "microphone_distance_m": 0.75
    },
    "meaning": "distinct radius, thermodynamic exponent, and fractional amplitude produce the same complete pressure trace inside the declared model"
  },
  "evidence_types": {
    "written_mathematics": [
      "small-amplitude stiffness relation",
      "bisection inverse on its monotone radius branch",
      "three-observable/four-parameter rank ceiling"
    ],
    "finite_computation": [
      "401-member exact equivalence family",
      "two 3840-sample endpoint waveform comparison",
      "finite-difference log-Jacobian rank check"
    ],
    "measured_evidence": [],
    "hypothesis": [
      "a real drop trace may be explained by some member only after independent calibration"
    ],
    "theological_interpretation": []
  },
  "claim_ceiling": {
    "supported": "the v0.7 ideal pitch is not a unique radius inverse; explicit ordinary nuisance variables generate an exact waveform-equivalence family",
    "not_supported": "which family member describes a real bubble, whether the effective kappa lies at either endpoint, or whether any residual requires extra dimensions"
  }
}