{
  "schema": "sandboxphysics-ac16-conditional-real-data-v1",
  "record": "HD48682 / 56 Aur; six published photometry detections and one restored SMA map",
  "data_class": "Measured inputs; conditional synthetic radiative predictions; no dynamical planet fit",
  "stellar_model": {
    "mass_solar": 1.17,
    "luminosity_solar": 1.752,
    "temperature_kelvin": 6086.0,
    "distance_pc": 16.65,
    "blackbody_radius_solar_using_695700000m": 1.190573785
  },
  "input_audit": {
    "finite_pixels": 11585,
    "nan_pixels": 4799,
    "sampled_finite_pixels_within_15arcsec": 441,
    "continuum_reference_frequency_hz_CRVAL3": 229483098100.0,
    "rest_frequency_hz_RESTFRQ": 230538000000.0,
    "continuum_wavelength_micrometres": 1306.381431,
    "beam_major_arcsec": 7.210853577,
    "beam_minor_arcsec": 6.844987392,
    "beam_PA_degrees_east_of_north": 84.94906616,
    "RA_increment_arcsec": -0.6236127589,
    "Dec_increment_arcsec": 0.6236127589,
    "beam_solid_angle_sr": 1.314539024e-09,
    "pixel_solid_angle_sr": 9.140705522e-12,
    "pixels_per_beam": 143.8115495,
    "outer_annulus_median_jy_per_beam": 1.43769339e-05,
    "outer_annulus_MAD_sigma_jy_per_beam": 0.0002905551573,
    "image_score_weight_per_sample": 329464.8207
  },
  "fit_grid": {
    "radii_au": [
      25,
      40,
      60,
      80,
      100,
      120,
      160
    ],
    "minimum_grain_micrometres": [
      0.2,
      1,
      5,
      15
    ],
    "maximum_grain_micrometres": 1000,
    "grain_bins": 24,
    "dNds_exponent": -3.5,
    "opacity_exponents": [
      1,
      2
    ],
    "geometries": [
      [
        0,
        0,
        0,
        0
      ],
      [
        0,
        0,
        -1,
        3
      ],
      [
        0,
        110,
        0,
        0
      ],
      [
        0,
        110,
        -1,
        3
      ],
      [
        60,
        0,
        0,
        0
      ],
      [
        60,
        0,
        -1,
        3
      ],
      [
        60,
        110,
        0,
        0
      ],
      [
        60,
        110,
        -1,
        3
      ]
    ],
    "radial_annuli_factors": [
      0.9,
      1,
      1.1
    ],
    "radial_mass_fractions": [
      0.25,
      0.5,
      0.25
    ],
    "models": 448,
    "amplitude_solution": "One nonnegative dust mass, analytic weighted least squares at each discrete family"
  },
  "best_conditional_grid_model": {
    "radius_au": 40,
    "minimum_grain_micrometres": 5,
    "opacity_exponent": 2,
    "inclination_degrees": 0,
    "position_angle_degrees_east_of_north": 0,
    "east_offset_arcsec": -1,
    "north_offset_arcsec": 3,
    "dust_mass_kg": 9.172972758e+21,
    "sed_standardized_residual_square_sum": 5.056064509,
    "image_beam_area_weighted_score": 9.26271359,
    "combined_conditional_score": 14.3187781,
    "continuum_dust_flux_jy": 0.001467047944
  },
  "distinct_optical_radius_alternatives": [
    {
      "radius_au": 40,
      "minimum_grain_micrometres": 5,
      "opacity_exponent": 2,
      "inclination_degrees": 0,
      "position_angle_degrees_east_of_north": 0,
      "east_offset_arcsec": -1,
      "north_offset_arcsec": 3,
      "dust_mass_kg": 9.172972758e+21,
      "sed_standardized_residual_square_sum": 5.056064509,
      "image_beam_area_weighted_score": 9.26271359,
      "combined_conditional_score": 14.3187781,
      "continuum_dust_flux_jy": 0.001467047944
    },
    {
      "radius_au": 25,
      "minimum_grain_micrometres": 15,
      "opacity_exponent": 2,
      "inclination_degrees": 0,
      "position_angle_degrees_east_of_north": 0,
      "east_offset_arcsec": -1,
      "north_offset_arcsec": 3,
      "dust_mass_kg": 6.327129122e+21,
      "sed_standardized_residual_square_sum": 4.19126231,
      "image_beam_area_weighted_score": 10.13351974,
      "combined_conditional_score": 14.32478205,
      "continuum_dust_flux_jy": 0.001378297402
    },
    {
      "radius_au": 40,
      "minimum_grain_micrometres": 1,
      "opacity_exponent": 1,
      "inclination_degrees": 0,
      "position_angle_degrees_east_of_north": 0,
      "east_offset_arcsec": -1,
      "north_offset_arcsec": 3,
      "dust_mass_kg": 5.588929586e+21,
      "sed_standardized_residual_square_sum": 6.842646927,
      "image_beam_area_weighted_score": 9.27361976,
      "combined_conditional_score": 16.11626669,
      "continuum_dust_flux_jy": 0.001496358851
    },
    {
      "radius_au": 60,
      "minimum_grain_micrometres": 0.2,
      "opacity_exponent": 1,
      "inclination_degrees": 60,
      "position_angle_degrees_east_of_north": 110,
      "east_offset_arcsec": -1,
      "north_offset_arcsec": 3,
      "dust_mass_kg": 7.094387301e+21,
      "sed_standardized_residual_square_sum": 8.03204287,
      "image_beam_area_weighted_score": 8.136869359,
      "combined_conditional_score": 16.16891223,
      "continuum_dust_flux_jy": 0.001576904386
    },
    {
      "radius_au": 40,
      "minimum_grain_micrometres": 1,
      "opacity_exponent": 2,
      "inclination_degrees": 0,
      "position_angle_degrees_east_of_north": 0,
      "east_offset_arcsec": -1,
      "north_offset_arcsec": 3,
      "dust_mass_kg": 8.468324045e+21,
      "sed_standardized_residual_square_sum": 7.459361645,
      "image_beam_area_weighted_score": 9.328130653,
      "combined_conditional_score": 16.7874923,
      "continuum_dust_flux_jy": 0.001313244281
    },
    {
      "radius_au": 25,
      "minimum_grain_micrometres": 5,
      "opacity_exponent": 1,
      "inclination_degrees": 0,
      "position_angle_degrees_east_of_north": 0,
      "east_offset_arcsec": -1,
      "north_offset_arcsec": 3,
      "dust_mass_kg": 4.414061453e+21,
      "sed_standardized_residual_square_sum": 7.106331273,
      "image_beam_area_weighted_score": 10.26832019,
      "combined_conditional_score": 17.37465147,
      "continuum_dust_flux_jy": 0.001458782548
    },
    {
      "radius_au": 60,
      "minimum_grain_micrometres": 0.2,
      "opacity_exponent": 2,
      "inclination_degrees": 0,
      "position_angle_degrees_east_of_north": 0,
      "east_offset_arcsec": -1,
      "north_offset_arcsec": 3,
      "dust_mass_kg": 1.431128708e+22,
      "sed_standardized_residual_square_sum": 9.673330611,
      "image_beam_area_weighted_score": 8.050435009,
      "combined_conditional_score": 17.72376562,
      "continuum_dust_flux_jy": 0.001740324824
    },
    {
      "radius_au": 60,
      "minimum_grain_micrometres": 1,
      "opacity_exponent": 2,
      "inclination_degrees": 0,
      "position_angle_degrees_east_of_north": 0,
      "east_offset_arcsec": -1,
      "north_offset_arcsec": 3,
      "dust_mass_kg": 1.45747557e+22,
      "sed_standardized_residual_square_sum": 10.00836131,
      "image_beam_area_weighted_score": 8.046376319,
      "combined_conditional_score": 18.05473763,
      "continuum_dust_flux_jy": 0.001800849396
    }
  ],
  "insufficient_blackbody_SED_best": {
    "radius_au": 6.715,
    "sed_score": 28.73026517,
    "dust_mass_kg": 4.206190792e+21
  },
  "blackbody_search": "Positive amplitude profiled analytically; 64 golden-section iterations in log radius over 0.5–160 au, radius rounded to 0.001 au before final evaluation; SED only",
  "numerical_checks": {
    "peak_one_beam_finite_integral_relative_error_below": 1e-09,
    "blackbody_Stefan_Boltzmann_relative_error_below": 5e-08,
    "24_to_48_size_bins_and_fourfold_quadrature_maximum_fractional_band_change": 0.002342558543,
    "128_to_512_quadrature_maximum_fractional_band_change": 7.308879858e-05
  },
  "interpretation": [
    "A coarse grid minimum can sit on a boundary. Distinct alternatives are examples ordered by this grid score, not a credible set or posterior probability.",
    "Combined score is a conditional ranking only. Image correlations are reduced to an approximate beam-area weight; no CLEAN covariance or calibrated confidence probability is claimed.",
    "Photometry weights use reported errors and no inter-band covariance. Monochromatic predictions omit filter passbands and their calibration/color-correction conventions.",
    "Radius, minimum size, absorption exponent, mass, centering and inclination are conditional grid choices. Geometry is weak in this SMA image; offsets are not unique dynamical eccentricities.",
    "The FITS header does not identify a primary-beam correction or provide its response map. This exercise uses the delivered central restored map without an invented correction; the image score is conditional on that delivered response.",
    "The 2020 paper and 2025 REASONS reprocessing describe the same system; this exercise does not independently recalibrate the SMA measurement set.",
    "No hidden planet is detected or fitted. The live gas-poor dynamical Lab is a separate synthetic system."
  ]
}