{
  "model": "Exact prime-field d=2, M=I, separate fixed masks; noiseless metadata and Y",
  "status": "Exact source enumeration and reverse-kernel integer checks; no physical photonic experiment",
  "cost_model": "h per original trial plus E only for an accepted optical Y readout; all source, gate, control and waiting costs must be included in h or reported separately",
  "information_rate_caveat": "I/(h+tE) is for independent fresh C tasks, or one-shot expected information divided by expected energy. Information is not additive across repeated observations of one fixed C.",
  "geometries": [
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      "q": 2,
      "residual_rank": 0,
      "kernel_U": [
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      "kernel_V": [
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      ],
      "metadata": "(A2,B1)",
      "source_pairs_per_c": 16,
      "joint_integer_samples": 32,
      "kept_source_pairs_per_c": 4,
      "gate_duty_fraction": [
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      ],
      "gate_duty": 0.25,
      "accepted_noise_contrast": 1,
      "full_mutual_information_bits": 0.25,
      "gated_mutual_information_bits": 0.25,
      "rank_formula_mutual_information_bits": 0.25,
      "information_per_accepted_readout_bits": 1.0,
      "exact_reconstruction": true,
      "checks": {
        "uniform_discarded_fibers": 6,
        "exact_reconstruction_entries": 16,
        "accepted_conditional_laws": 2
      }
    },
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      "kernel_V": [
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      "metadata": "(A2,B2)",
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      "joint_integer_samples": 32,
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      "gate_duty_fraction": [
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      "gate_duty": 1.0,
      "accepted_noise_contrast": 0.5,
      "full_mutual_information_bits": 0.18872187554086717,
      "gated_mutual_information_bits": 0.18872187554086717,
      "rank_formula_mutual_information_bits": 0.18872187554086717,
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      "exact_reconstruction": true,
      "checks": {
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        "accepted_conditional_laws": 2
      }
    },
    {
      "q": 3,
      "residual_rank": 0,
      "kernel_U": [
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      ],
      "kernel_V": [
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      ],
      "metadata": "(A2,B1)",
      "source_pairs_per_c": 81,
      "joint_integer_samples": 243,
      "kept_source_pairs_per_c": 9,
      "gate_duty_fraction": [
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      ],
      "gate_duty": 0.1111111111111111,
      "accepted_noise_contrast": 1,
      "full_mutual_information_bits": 0.17610694452457287,
      "gated_mutual_information_bits": 0.17610694452457287,
      "rank_formula_mutual_information_bits": 0.1761069445245729,
      "information_per_accepted_readout_bits": 1.584962500721156,
      "exact_reconstruction": true,
      "checks": {
        "uniform_discarded_fibers": 24,
        "exact_reconstruction_entries": 81,
        "accepted_conditional_laws": 3
      }
    },
    {
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      "metadata": "(A2,B2)",
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      "joint_integer_samples": 243,
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      "gate_duty": 1.0,
      "accepted_noise_contrast": 0.3333333333333333,
      "full_mutual_information_bits": 0.14944199643848954,
      "gated_mutual_information_bits": 0.14944199643848954,
      "rank_formula_mutual_information_bits": 0.14944199643848943,
      "information_per_accepted_readout_bits": 0.14944199643848943,
      "exact_reconstruction": true,
      "checks": {
        "exact_reconstruction_entries": 81,
        "accepted_conditional_laws": 3
      }
    },
    {
      "q": 5,
      "residual_rank": 0,
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      ],
      "kernel_V": [
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      ],
      "metadata": "(A2,B1)",
      "source_pairs_per_c": 625,
      "joint_integer_samples": 3125,
      "kept_source_pairs_per_c": 25,
      "gate_duty_fraction": [
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      "gate_duty": 0.04,
      "accepted_noise_contrast": 1,
      "full_mutual_information_bits": 0.0928771237954945,
      "gated_mutual_information_bits": 0.0928771237954945,
      "rank_formula_mutual_information_bits": 0.0928771237954945,
      "information_per_accepted_readout_bits": 2.321928094887362,
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        "accepted_conditional_laws": 5
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      "metadata": "(A2,B2)",
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      "joint_integer_samples": 3125,
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      "gate_duty_fraction": [
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      "gate_duty": 1.0,
      "accepted_noise_contrast": 0.2,
      "full_mutual_information_bits": 0.09924490563187016,
      "gated_mutual_information_bits": 0.09924490563187012,
      "rank_formula_mutual_information_bits": 0.09924490563187008,
      "information_per_accepted_readout_bits": 0.09924490563187008,
      "exact_reconstruction": true,
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        "accepted_conditional_laws": 5
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    },
    {
      "q": 7,
      "residual_rank": 0,
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      "kernel_V": [
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      "metadata": "(A2,B1)",
      "source_pairs_per_c": 2401,
      "joint_integer_samples": 16807,
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      "gate_duty": 0.02040816326530612,
      "accepted_noise_contrast": 1,
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      "rank_formula_mutual_information_bits": 0.057292957593012325,
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      "checks": {
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        "accepted_conditional_laws": 7
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    },
    {
      "q": 7,
      "residual_rank": 1,
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      "metadata": "(A2,B2)",
      "source_pairs_per_c": 2401,
      "joint_integer_samples": 16807,
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      "gate_duty": 1.0,
      "accepted_noise_contrast": 0.14285714285714285,
      "full_mutual_information_bits": 0.07355051389741259,
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      "rank_formula_mutual_information_bits": 0.07355051389741274,
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      "exact_reconstruction": true,
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        "accepted_conditional_laws": 7
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    }
  ],
  "q5_energy_crossover": {
    "h_over_E": 13.962056153108229,
    "photon_only_information_ratio_r0_over_r1": 23.39594239224841,
    "rank0_rate_below_threshold": true,
    "rank1_rate_above_threshold": true,
    "equal_rate_at_threshold_bits_per_E": 0.006633106079557986,
    "example_rates": [
      {
        "h_over_E": 0,
        "rank0_bits_per_E": 2.321928094887362,
        "rank1_bits_per_E": 0.09924490563187016
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      {
        "h_over_E": 1,
        "rank0_bits_per_E": 0.08930492672643701,
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      {
        "h_over_E": 13.962056153108229,
        "rank0_bits_per_E": 0.006633106079557986,
        "rank1_bits_per_E": 0.006633106079557986
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      {
        "h_over_E": 27.924112306216458,
        "rank0_bits_per_E": 0.00332129705311074,
        "rank1_bits_per_E": 0.0034312169922857115
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      {
        "h_over_E": 100,
        "rank0_bits_per_E": 0.0009283998780037434,
        "rank1_bits_per_E": 0.0009826228280383185
      }
    ]
  },
  "checks_passed": true
}