{
  "same_actual_74_bins": true,
  "likelihood_and_atmospheric_priors_shared": true,
  "models": {
    "cloud": {
      "data_kind": "Actual measured author-released nirHiss NIRISS radius-ratio-squared spectrum",
      "selected_bins": 74,
      "model": "cloud",
      "conditional_scope": "Isothermal hydrogen/helium/water, gray opaque cloud, fixed stellar spectra; independent reported Gaussian errors. Missing absorbers and data covariance are not inferred.",
      "priors": {
        "temperature_kelvin": {
          "kind": "uniform",
          "minimum": 800,
          "maximum": 1600
        },
        "log10_water_fraction": {
          "kind": "uniform",
          "minimum": -7,
          "maximum": -2
        },
        "log10_cloud_pressure_bar": {
          "kind": "uniform",
          "minimum": -4,
          "maximum": 1
        },
        "reference_radius_ratio_at10bar": {
          "kind": "uniform",
          "minimum": 0.13,
          "maximum": 0.145
        },
        "spot_fraction": {
          "kind": "point mass",
          "minimum": 0,
          "maximum": 0
        },
        "fixed_spot_temperature_kelvin": 4500,
        "reference_pressure_bar": 10,
        "normalized_gaussian_reported_errors": true,
        "missing_data_covariance": "independence assumed",
        "radius_reparameterization": "radius = deterministic conditional anchor + 1e-5*z; original uniform physical radius prior, exact constant triangular Jacobian",
        "log_physical_prior_density": -5.703782474656199,
        "log_coordinate_jacobian": -1.6094379124341014
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      "seed": 20261028,
      "chains": 4,
      "warmup_per_chain": 6000,
      "retained_per_chain": 16000,
      "proposal": "Symmetric Gaussian random walk in reparameterized coordinates; hard support rejection. Covariance and scale adapt only during warmup, then freeze.",
      "diagnostics_passed": true,
      "diagnostic_target": {
        "maximum_rhat": 1.01,
        "minimum_bulk_and_tail_ess": 400
      },
      "parameters": {
        "temperature_kelvin": {
          "quantiles_025_16_50_84_975": [
            800.1224839234524,
            800.767915017447,
            803.0308185905193,
            807.9795503633318,
            816.3828445869781
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          "rank_folded_split_rhat": 1.0026241331525712,
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        },
        "log10_water_fraction": {
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            -2.383784452271877,
            -2.161400266236501,
            -2.0561843002448796,
            -2.0140423955869187,
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        "log10_cloud_pressure_bar": {
          "quantiles_025_16_50_84_975": [
            -3.4724652531741587,
            -3.4289343377896264,
            -3.378194384156237,
            -3.295738453451017,
            -3.1068131312693046
          ],
          "rank_folded_split_rhat": 1.0015623685374775,
          "bulk_ess": 2442.6271184379657,
          "tail_ess": 1926.9958844328528
        },
        "reference_radius_ratio_at10bar": {
          "quantiles_025_16_50_84_975": [
            0.1350624833537871,
            0.13521552683661653,
            0.1353143256661113,
            0.13540552417780366,
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          "bulk_ess": 2143.7158798629534,
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        "spot_fraction": {
          "quantiles_025_16_50_84_975": [
            0.0,
            0.0,
            0.0,
            0.0,
            0.0
          ],
          "rank_folded_split_rhat": 1.0,
          "bulk_ess": 64000.0,
          "tail_ess": 64000.0
        }
      },
      "joint_posterior": {
        "varying_parameter_order": [
          "temperature_kelvin",
          "log10_water_fraction",
          "log10_cloud_pressure_bar",
          "reference_radius_ratio_at10bar"
        ],
        "physical_draw_correlation": [
          [
            1.0,
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            -0.16801454479059502,
            -0.5965973224712845
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          [
            0.01062708560462449,
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            -0.6869160182138838
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          [
            -0.16801454479059502,
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            0.8611281055787452
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          [
            -0.5965973224712845,
            -0.6869160182138838,
            0.8611281055787452,
            1.0
          ]
        ],
        "scope": "Linear correlation summarizes one part of the sampled joint degeneracy; full physical chains retain nonlinear ridges."
      },
      "chi_square": {
        "minimum_retained": 331.95256159546193,
        "posterior_quantiles_025_50_975": [
          332.9892302569966,
          337.0770606397285,
          346.3027964749382
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      },
      "posterior_predictive": {
        "latent_draws": 1600,
        "observations_outside_95_percent_replicated_interval": 28,
        "median_curve_standardized_residual_rms": 2.130032673954872,
        "median_curve_maximum_absolute_standardized_residual": 4.454795119605101
      },
      "evidence_or_bayes_factor": "Not computed. The constrained models are compared by posterior ranges and predictive failures, not by a MAP score relabelled as evidence."
    },
    "spots4500": {
      "data_kind": "Actual measured author-released nirHiss NIRISS radius-ratio-squared spectrum",
      "selected_bins": 74,
      "model": "spots4500",
      "conditional_scope": "Isothermal hydrogen/helium/water, gray opaque cloud, fixed stellar spectra; independent reported Gaussian errors. Missing absorbers and data covariance are not inferred.",
      "priors": {
        "temperature_kelvin": {
          "kind": "uniform",
          "minimum": 800,
          "maximum": 1600
        },
        "log10_water_fraction": {
          "kind": "uniform",
          "minimum": -7,
          "maximum": -2
        },
        "log10_cloud_pressure_bar": {
          "kind": "uniform",
          "minimum": -4,
          "maximum": 1
        },
        "reference_radius_ratio_at10bar": {
          "kind": "uniform",
          "minimum": 0.13,
          "maximum": 0.145
        },
        "spot_fraction": {
          "kind": "uniform",
          "minimum": 0,
          "maximum": 0.05
        },
        "fixed_spot_temperature_kelvin": 4500,
        "reference_pressure_bar": 10,
        "normalized_gaussian_reported_errors": true,
        "missing_data_covariance": "independence assumed",
        "radius_reparameterization": "radius = deterministic conditional anchor + 1e-5*z; original uniform physical radius prior, exact constant triangular Jacobian",
        "log_physical_prior_density": -2.7080502011022083,
        "log_coordinate_jacobian": -4.605170185988092
      },
      "seed": 20261029,
      "chains": 4,
      "warmup_per_chain": 6000,
      "retained_per_chain": 16000,
      "proposal": "Symmetric Gaussian random walk in reparameterized coordinates; hard support rejection. Covariance and scale adapt only during warmup, then freeze.",
      "diagnostics_passed": true,
      "diagnostic_target": {
        "maximum_rhat": 1.01,
        "minimum_bulk_and_tail_ess": 400
      },
      "parameters": {
        "temperature_kelvin": {
          "quantiles_025_16_50_84_975": [
            800.3911059652725,
            802.8310800536949,
            810.5302846046959,
            827.7965859497153,
            854.54335416191
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          "rank_folded_split_rhat": 1.0016309807861583,
          "bulk_ess": 2246.360900288951,
          "tail_ess": 2148.374314717236
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        "log10_water_fraction": {
          "quantiles_025_16_50_84_975": [
            -2.5641868266026258,
            -2.2283873231167868,
            -2.077885877258618,
            -2.0184388633781776,
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          "rank_folded_split_rhat": 1.0024038354240594,
          "bulk_ess": 1379.2247812750622,
          "tail_ess": 918.1426027300644
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        "log10_cloud_pressure_bar": {
          "quantiles_025_16_50_84_975": [
            -3.445422411786543,
            -3.3550248660208646,
            -3.2809461749599933,
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          "rank_folded_split_rhat": 1.0034077161301724,
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          "tail_ess": 916.4211336668127
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        "reference_radius_ratio_at10bar": {
          "quantiles_025_16_50_84_975": [
            0.13399121726996172,
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          "rank_folded_split_rhat": 1.002967856956649,
          "bulk_ess": 1387.0911596741473,
          "tail_ess": 1057.8466584135956
        },
        "spot_fraction": {
          "quantiles_025_16_50_84_975": [
            0.017457063238408187,
            0.019879880402385593,
            0.022429707623018404,
            0.02490805011151053,
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          "rank_folded_split_rhat": 1.0009839928280009,
          "bulk_ess": 2066.9749469832764,
          "tail_ess": 3437.731833445119
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      },
      "joint_posterior": {
        "varying_parameter_order": [
          "temperature_kelvin",
          "log10_water_fraction",
          "log10_cloud_pressure_bar",
          "reference_radius_ratio_at10bar",
          "spot_fraction"
        ],
        "physical_draw_correlation": [
          [
            0.9999999999999999,
            0.01522999404745161,
            -0.32205157696619635,
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            0.2702483739779162
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            0.015229994047451609,
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          [
            -0.3220515769661964,
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            -0.8097698569477123,
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            0.2702483739779162,
            -0.02078926081804775,
            0.00786930836179892,
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            1.0
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        ],
        "scope": "Linear correlation summarizes one part of the sampled joint degeneracy; full physical chains retain nonlinear ridges."
      },
      "chi_square": {
        "minimum_retained": 257.11462260559955,
        "posterior_quantiles_025_50_975": [
          258.5836525811657,
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          273.21724210598484
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      },
      "posterior_predictive": {
        "latent_draws": 1600,
        "observations_outside_95_percent_replicated_interval": 23,
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        "median_curve_maximum_absolute_standardized_residual": 4.722299355486327
      },
      "evidence_or_bayes_factor": "Not computed. The constrained models are compared by posterior ranges and predictive failures, not by a MAP score relabelled as evidence."
    },
    "spots3500": {
      "data_kind": "Actual measured author-released nirHiss NIRISS radius-ratio-squared spectrum",
      "selected_bins": 74,
      "model": "spots3500",
      "conditional_scope": "Isothermal hydrogen/helium/water, gray opaque cloud, fixed stellar spectra; independent reported Gaussian errors. Missing absorbers and data covariance are not inferred.",
      "priors": {
        "temperature_kelvin": {
          "kind": "uniform",
          "minimum": 800,
          "maximum": 1600
        },
        "log10_water_fraction": {
          "kind": "uniform",
          "minimum": -7,
          "maximum": -2
        },
        "log10_cloud_pressure_bar": {
          "kind": "uniform",
          "minimum": -4,
          "maximum": 1
        },
        "reference_radius_ratio_at10bar": {
          "kind": "uniform",
          "minimum": 0.13,
          "maximum": 0.145
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        "spot_fraction": {
          "kind": "uniform",
          "minimum": 0,
          "maximum": 0.05
        },
        "fixed_spot_temperature_kelvin": 3500,
        "reference_pressure_bar": 10,
        "normalized_gaussian_reported_errors": true,
        "missing_data_covariance": "independence assumed",
        "radius_reparameterization": "radius = deterministic conditional anchor + 1e-5*z; original uniform physical radius prior, exact constant triangular Jacobian",
        "log_physical_prior_density": -2.7080502011022083,
        "log_coordinate_jacobian": -4.605170185988092
      },
      "seed": 20261030,
      "chains": 4,
      "warmup_per_chain": 6000,
      "retained_per_chain": 16000,
      "proposal": "Symmetric Gaussian random walk in reparameterized coordinates; hard support rejection. Covariance and scale adapt only during warmup, then freeze.",
      "diagnostics_passed": true,
      "diagnostic_target": {
        "maximum_rhat": 1.01,
        "minimum_bulk_and_tail_ess": 400
      },
      "parameters": {
        "temperature_kelvin": {
          "quantiles_025_16_50_84_975": [
            800.3355937398925,
            802.4312866636586,
            809.7288697000648,
            825.3711810015278,
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          ],
          "rank_folded_split_rhat": 1.0021545511749521,
          "bulk_ess": 2305.8572890871255,
          "tail_ess": 2572.265844290977
        },
        "log10_water_fraction": {
          "quantiles_025_16_50_84_975": [
            -2.5310872435311778,
            -2.24435331199075,
            -2.0801274086467254,
            -2.0191784086552165,
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          "rank_folded_split_rhat": 1.005364208490542,
          "bulk_ess": 1158.6997697481697,
          "tail_ess": 821.0612834899654
        },
        "log10_cloud_pressure_bar": {
          "quantiles_025_16_50_84_975": [
            -3.414681628980685,
            -3.3418943877670007,
            -3.2694116901141594,
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          "rank_folded_split_rhat": 1.0029119512867586,
          "bulk_ess": 1204.0266959599496,
          "tail_ess": 862.3813014089135
        },
        "reference_radius_ratio_at10bar": {
          "quantiles_025_16_50_84_975": [
            0.13290539378068497,
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          "rank_folded_split_rhat": 1.0026107290872917,
          "bulk_ess": 1461.039779787042,
          "tail_ess": 1238.670507198113
        },
        "spot_fraction": {
          "quantiles_025_16_50_84_975": [
            0.0297650735291585,
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          "rank_folded_split_rhat": 1.000733438624199,
          "bulk_ess": 2017.7007651655074,
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      },
      "joint_posterior": {
        "varying_parameter_order": [
          "temperature_kelvin",
          "log10_water_fraction",
          "log10_cloud_pressure_bar",
          "reference_radius_ratio_at10bar",
          "spot_fraction"
        ],
        "physical_draw_correlation": [
          [
            1.0,
            0.016604144430595626,
            -0.29710713507871955,
            -0.7338033423811131,
            0.190692128376705
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          [
            0.016604144430595623,
            1.0,
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          [
            -0.2971071350787195,
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            0.9999999999999998,
            0.6494816182152886,
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          [
            -0.7338033423811131,
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            1.0,
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          [
            0.190692128376705,
            -0.01804431844347429,
            0.05136274228396353,
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            1.0
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        ],
        "scope": "Linear correlation summarizes one part of the sampled joint degeneracy; full physical chains retain nonlinear ridges."
      },
      "chi_square": {
        "minimum_retained": 248.16906587335134,
        "posterior_quantiles_025_50_975": [
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      },
      "posterior_predictive": {
        "latent_draws": 1600,
        "observations_outside_95_percent_replicated_interval": 20,
        "median_curve_standardized_residual_rms": 1.8433032765411255,
        "median_curve_maximum_absolute_standardized_residual": 4.5806955651094174
      },
      "evidence_or_bayes_factor": "Not computed. The constrained models are compared by posterior ranges and predictive failures, not by a MAP score relabelled as evidence."
    },
    "spots4500-narrow": {
      "data_kind": "Actual measured author-released nirHiss NIRISS radius-ratio-squared spectrum",
      "selected_bins": 74,
      "model": "spots4500-narrow",
      "conditional_scope": "Isothermal hydrogen/helium/water, gray opaque cloud, fixed stellar spectra; independent reported Gaussian errors. Missing absorbers and data covariance are not inferred.",
      "priors": {
        "temperature_kelvin": {
          "kind": "uniform",
          "minimum": 800,
          "maximum": 1600
        },
        "log10_water_fraction": {
          "kind": "uniform",
          "minimum": -7,
          "maximum": -2
        },
        "log10_cloud_pressure_bar": {
          "kind": "uniform",
          "minimum": -4,
          "maximum": 1
        },
        "reference_radius_ratio_at10bar": {
          "kind": "uniform",
          "minimum": 0.13,
          "maximum": 0.145
        },
        "spot_fraction": {
          "kind": "uniform",
          "minimum": 0,
          "maximum": 0.01
        },
        "fixed_spot_temperature_kelvin": 4500,
        "reference_pressure_bar": 10,
        "normalized_gaussian_reported_errors": true,
        "missing_data_covariance": "independence assumed",
        "radius_reparameterization": "radius = deterministic conditional anchor + 1e-5*z; original uniform physical radius prior, exact constant triangular Jacobian",
        "log_physical_prior_density": -1.0986122886681082,
        "log_coordinate_jacobian": -6.214608098422192
      },
      "seed": 20261031,
      "chains": 4,
      "warmup_per_chain": 6000,
      "retained_per_chain": 16000,
      "proposal": "Symmetric Gaussian random walk in reparameterized coordinates; hard support rejection. Covariance and scale adapt only during warmup, then freeze.",
      "diagnostics_passed": true,
      "diagnostic_target": {
        "maximum_rhat": 1.01,
        "minimum_bulk_and_tail_ess": 400
      },
      "parameters": {
        "temperature_kelvin": {
          "quantiles_025_16_50_84_975": [
            800.1605964920664,
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          "rank_folded_split_rhat": 1.0040510360036203,
          "bulk_ess": 1302.643594927208,
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        "log10_water_fraction": {
          "quantiles_025_16_50_84_975": [
            -2.422891915390064,
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          "rank_folded_split_rhat": 1.0017279609717624,
          "bulk_ess": 1558.0246574567134,
          "tail_ess": 1307.0223662109865
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        "log10_cloud_pressure_bar": {
          "quantiles_025_16_50_84_975": [
            -3.4375437584041255,
            -3.384168317054239,
            -3.331052472741463,
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          "rank_folded_split_rhat": 1.0035582688455547,
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        },
        "reference_radius_ratio_at10bar": {
          "quantiles_025_16_50_84_975": [
            0.13478767736647937,
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          "rank_folded_split_rhat": 1.006525967351943,
          "bulk_ess": 1221.8299683087469,
          "tail_ess": 1219.009342092449
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        "spot_fraction": {
          "quantiles_025_16_50_84_975": [
            0.008165989483292113,
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          "rank_folded_split_rhat": 1.0036804440701985,
          "bulk_ess": 1434.1866040941977,
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      },
      "joint_posterior": {
        "varying_parameter_order": [
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          "log10_water_fraction",
          "log10_cloud_pressure_bar",
          "reference_radius_ratio_at10bar",
          "spot_fraction"
        ],
        "physical_draw_correlation": [
          [
            1.0,
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          [
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          [
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          [
            -0.6628228866874709,
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          [
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            0.0015419612791014576,
            0.02629664096472479,
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            1.0
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        ],
        "scope": "Linear correlation summarizes one part of the sampled joint degeneracy; full physical chains retain nonlinear ridges."
      },
      "chi_square": {
        "minimum_retained": 279.2669455216586,
        "posterior_quantiles_025_50_975": [
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        ]
      },
      "posterior_predictive": {
        "latent_draws": 1600,
        "observations_outside_95_percent_replicated_interval": 28,
        "median_curve_standardized_residual_rms": 1.9610464963485315,
        "median_curve_maximum_absolute_standardized_residual": 4.488731175354435
      },
      "evidence_or_bayes_factor": "Not computed. The constrained models are compared by posterior ranges and predictive failures, not by a MAP score relabelled as evidence."
    }
  },
  "interpretation": "Credible regions are conditional on each constrained model. A poor predictive fit invalidates a complete physical explanation even when Markov-chain diagnostics pass. Positive spot-fraction quantiles do not by themselves test the point-null model f=0."
}