Datasets:

PureOne
/

Evies-Pure-Form-RSI

{
  "gating": {
    "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.",
    "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
        },
        {
          "h_over_E": 1,
          "rank0_bits_per_E": 0.08930492672643701,
          "rank1_bits_per_E": 0.04962245281593508
        },
        {
          "h_over_E": 13.962056153108229,
          "rank0_bits_per_E": 0.006633106079557986,
          "rank1_bits_per_E": 0.006633106079557986
        },
        {
          "h_over_E": 27.924112306216458,
          "rank0_bits_per_E": 0.00332129705311074,
          "rank1_bits_per_E": 0.0034312169922857115
        },
        {
          "h_over_E": 100,
          "rank0_bits_per_E": 0.0009283998780037434,
          "rank1_bits_per_E": 0.0009826228280383185
        }
      ]
    },
    "checks_passed": true,
    "execution_status": "PASS"
  },
  "deficiency": {
    "status": "PASS",
    "scope": "Classical erased q-ary symmetric experiment theorem only",
    "tv_convention": "half_l1",
    "formula": "(q-1)/q * max(0,t2*u2-u1*min(t1,t2))",
    "seed": 20261017,
    "q_values": [
      2,
      3,
      5,
      7
    ],
    "checks_per_q": {
      "endpoint_grid": 81,
      "boundary": 8,
      "seeded_random": 50
    },
    "independent_lp": "Unrestricted full stochastic output kernel",
    "max_formula_lp_error": 1.887379141862766e-15,
    "max_formula_constructed_kernel_error": 1.8041124150158794e-16,
    "max_kernel_stochastic_error": 2.220446049250313e-16,
    "max_constructed_retention_error": 4.440892098500626e-16,
    "tolerance": 1e-07,
    "physical_photonic_measurements": false,
    "parameter_box_checks": {
      "interpretation": "POINTWISE PARAMETER-AWARE ONLY; not one common kernel",
      "quantifier_order": "sup_parameters inf_kernel; not inf_kernel sup_parameters",
      "seed": 20261018,
      "boxes": 200,
      "corner_checks": 3200,
      "sample_inclusion_checks": 4000,
      "max_corner_disagreement": 0.0,
      "max_inclusion_violation": 0.0,
      "status": "PASS"
    },
    "execution_status": "PASS"
  },
  "reliability": {
    "poisson_integral_checks": 24,
    "max_integral_relative_error": 7.7733332580952e-16,
    "generator_checks": 24,
    "max_generator_residual": 2.9103830456733704e-11,
    "coupled_paths": 10000,
    "real_dimension": 4,
    "steps": 400,
    "adapted_unitary_resets_per_path": 80,
    "max_coupled_radius_difference": 1.1102230246251565e-14,
    "mean_final_coordinate_difference": 1.4775447540126077,
    "sampled_grid_exit_fraction": 0.0037,
    "sampled_grid_exits": 37,
    "continuous_exit_upper_bound": 0.030198482266093618,
    "mc_caveat": "Grid exit count is a lower-resolution event, not continuum validation.",
    "no_update_count_factor": true,
    "execution_status": "PASS"
  },
  "robust": {
    "status": "PASS",
    "corner_theorem": "A fixed kernel has a multi-affine channel residual; row-TV is separately convex. Its box maximum occurs at parameter corners.",
    "quantifier_counterexample": {
      "pointwise_worst_deficiency": 0.0,
      "one_common_kernel_minimax_tv": 0.5,
      "q": 2,
      "source_box": [
        [
          1,
          1
        ],
        [
          1,
          1
        ]
      ],
      "target_box": [
        [
          0,
          1
        ],
        [
          0,
          0
        ]
      ]
    },
    "degenerate_box_checks": [
      {
        "q": 2,
        "robust_value": 0.0949999999999999,
        "formula": 0.09499999999999997
      },
      {
        "q": 3,
        "robust_value": 0.16000000000000003,
        "formula": 0.16000000000000003
      },
      {
        "q": 5,
        "robust_value": 0.128,
        "formula": 0.128
      }
    ],
    "interior_checks": 1000,
    "robust_q3_box_value": 0.1856432510622909,
    "max_sampled_interior_value": 0.1832311606098727,
    "kernel_stochasticity_residual": 1.1102230246251565e-16,
    "hardware_calibration_coverage_established": false,
    "execution_status": "PASS"
  },
  "purification": {
    "status": "PASS",
    "scope": "Exact finite classical-channel formula, floating-point verification; no hardware or general RSI performance claim",
    "seed": 20261019,
    "independent_lp_cases": 375,
    "max_formula_lp_error": 2.498001805406602e-16,
    "max_histogram_vs_sequence_frontier_error": 4.440892098500626e-16,
    "max_constructed_kernel_attainment_error": 3.3306690738754696e-16,
    "max_constructed_kernel_stochastic_error": 2.220446049250313e-16,
    "max_constructed_kernel_retention_error": 5.551115123125783e-16,
    "max_constructed_full_channel_symmetry_error": 3.3306690738754696e-16,
    "conditional_independence_required": true,
    "fixed_hidden_target_per_block": true,
    "information_caveat": "Purification selects and discards; it does not create information. Same-target block information <= log2(q), not repeats*one-read MI.",
    "unanimity_comparison": {
      "q": 5,
      "u": 0.6,
      "repeats": 4,
      "requested_retention": 0.5,
      "unanimity_natural_retention": 0.2139775999999999,
      "unanimity_natural_contrast": 0.9990428904707782,
      "confidence_optimal_contrast_at_requested_retention": 0.9864465134865138,
      "unanimity_then_uniform_fill_or_thin_contrast": 0.4275455999999998
    },
    "exact_rational_benchmark": {
      "q": 5,
      "input_contrast": "3/5",
      "accepted_reads": 4,
      "output_retention": "1/2",
      "histograms": 70,
      "exact_max_output_contrast": "3085728/3128125",
      "exact_accepted_error_probability": "169588/15640625",
      "arithmetic": "Python arbitrary-precision integers and Fraction; no numerical optimization",
      "proof_status": "Exact rational evaluation of the proved finite frontier formula"
    },
    "execution_status": "PASS"
  },
  "bootstrap": {
    "status": "PASS",
    "research": "Evie's Pure Form RSI",
    "scope": "mathematical verifier-strengthening component under explicit conditional-independent channels",
    "physical_measurements": false,
    "general_intelligence_gain_established": false,
    "prior_art_boundary": "binary hierarchy equals classical SPRT; neither consensus nor sequential testing is claimed as invention",
    "cost_contract": "h includes every nonreadout cost per primitive trial; E is acquisition cost; expected cost, unbounded retry tails",
    "independent_checks": {
      "status": "PASS",
      "cases": 21,
      "method": "full raw-symbol absorbing Markov chain on recursive pending stack",
      "max_relative_cost_error": 1.166553612248517e-15,
      "max_output_probability_error": 1.5543122344752192e-15,
      "max_linear_system_residual": 1.8207657603852567e-14,
      "binary_SPRT_identity_checks": 20,
      "max_binary_identity_error": 3.9968642269392163e-16,
      "records": [
        {
          "q": 2,
          "u": 0.2,
          "level": 1,
          "relative_expected_cost_error": 3.4638958368304885e-16,
          "max_output_probability_error": 3.3306690738754696e-16,
          "independent_absorbing_chain": {
            "expected_raw_signal_calls": 3.846153846153847,
            "output_probabilities_given_target_zero": [
              0.6923076923076926,
              0.30769230769230776
            ],
            "transient_states": 3,
            "linear_residual": 4.440892098500626e-16,
            "transition_row_sum_error": 0.0
          }
        },
        {
          "q": 2,
          "u": 0.2,
          "level": 2,
          "relative_expected_cost_error": 1.0603483902881494e-15,
          "max_output_probability_error": 1.3322676295501878e-15,
          "independent_absorbing_chain": {
            "expected_raw_signal_calls": 13.402061855670118,
            "output_probabilities_given_target_zero": [
              0.8350515463917538,
              0.16494845360824759
            ],
            "transient_states": 9,
            "linear_residual": 1.7763568394002505e-15,
            "transition_row_sum_error": 0.0
          }
        },
        {
          "q": 2,
          "u": 0.6,
          "level": 1,
          "relative_expected_cost_error": 3.0198066269804265e-16,
          "max_output_probability_error": 2.220446049250313e-16,
          "independent_absorbing_chain": {
            "expected_raw_signal_calls": 2.9411764705882355,
            "output_probabilities_given_target_zero": [
              0.9411764705882355,
              0.05882352941176471
            ],
            "transient_states": 3,
            "linear_residual": 2.220446049250313e-16,
            "transition_row_sum_error": 0.0
          }
        },
        {
          "q": 2,
          "u": 0.6,
          "level": 2,
          "relative_expected_cost_error": 4.028150362287039e-16,
          "max_output_probability_error": 5.551115123125783e-16,
          "independent_absorbing_chain": {
            "expected_raw_signal_calls": 6.6147859922179,
            "output_probabilities_given_target_zero": [
              0.996108949416343,
              0.0038910505836575893
            ],
            "transient_states": 9,
            "linear_residual": 1.7763568394002505e-15,
            "transition_row_sum_error": 0.0
          }
        },
        {
          "q": 2,
          "u": 0.9,
          "level": 1,
          "relative_expected_cost_error": 2.0095036745715332e-16,
          "max_output_probability_error": 1.1102230246251565e-16,
          "independent_absorbing_chain": {
            "expected_raw_signal_calls": 2.209944751381215,
            "output_probabilities_given_target_zero": [
              0.9972375690607733,
              0.002762430939226518
            ],
            "transient_states": 3,
            "linear_residual": 4.440892098500626e-16,
            "transition_row_sum_error": 0.0
          }
        },
        {
          "q": 2,
          "u": 0.9,
          "level": 2,
          "relative_expected_cost_error": 1.9984321134696091e-16,
          "max_output_probability_error": 3.3306690738754696e-16,
          "independent_absorbing_chain": {
            "expected_raw_signal_calls": 4.444376237319869,
            "output_probabilities_given_target_zero": [
              0.9999923266984849,
              7.673301514709712e-06
            ],
            "transient_states": 9,
            "linear_residual": 1.7763568394002505e-15,
            "transition_row_sum_error": 0.0
          }
        },
        {
          "q": 3,
          "u": 0.2,
          "level": 1,
          "relative_expected_cost_error": 3.1974423109204507e-16,
          "max_output_probability_error": 2.220446049250313e-16,
          "independent_absorbing_chain": {
            "expected_raw_signal_calls": 5.555555555555557,
            "output_probabilities_given_target_zero": [
              0.6049382716049384,
              0.1975308641975309,
              0.1975308641975309
            ],
            "transient_states": 4,
            "linear_residual": 8.881784197001252e-16,
            "transition_row_sum_error": 0.0
          }
        },
        {
          "q": 3,
          "u": 0.2,
          "level": 2,
          "relative_expected_cost_error": 7.098117247150795e-16,
          "max_output_probability_error": 7.771561172376096e-16,
          "independent_absorbing_chain": {
            "expected_raw_signal_calls": 25.025746652935137,
            "output_probabilities_given_target_zero": [
              0.8242361826295922,
              0.0878819086852043,
              0.08788190868520432
            ],
            "transient_states": 16,
            "linear_residual": 3.552713678800501e-15,
            "transition_row_sum_error": 0.0
          }
        },
        {
          "q": 3,
          "u": 0.6,
          "level": 1,
          "relative_expected_cost_error": 1.2730557349035131e-16,
          "max_output_probability_error": 4.440892098500626e-16,
          "independent_absorbing_chain": {
            "expected_raw_signal_calls": 3.4883720930232553,
            "output_probabilities_given_target_zero": [
              0.9379844961240306,
              0.031007751937984492,
              0.031007751937984492
            ],
            "transient_states": 4,
            "linear_residual": 8.881784197001252e-16,
            "transition_row_sum_error": 1.1102230246251565e-16
          }
        },
        {
          "q": 3,
          "u": 0.6,
          "level": 2,
          "relative_expected_cost_error": 0.0,
          "max_output_probability_error": 7.771561172376096e-16,
          "independent_absorbing_chain": {
            "expected_raw_signal_calls": 7.912492332856265,
            "output_probabilities_given_target_zero": [
              0.99781912356028,
              0.0010904382198596056,
              0.0010904382198596058
            ],
            "transient_states": 16,
            "linear_residual": 2.4424906541753444e-15,
            "transition_row_sum_error": 1.1102230246251565e-16
          }
        },
        {
          "q": 3,
          "u": 0.9,
          "level": 1,
          "relative_expected_cost_error": 0.0,
          "max_output_probability_error": 1.1102230246251565e-16,
          "independent_absorbing_chain": {
            "expected_raw_signal_calls": 2.290076335877863,
            "output_probabilities_given_target_zero": [
              0.9974554707379136,
              0.0012722646310432562,
              0.0012722646310432562
            ],
            "transient_states": 4,
            "linear_residual": 2.220446049250313e-16,
            "transition_row_sum_error": 0.0
          }
        },
        {
          "q": 3,
          "u": 0.9,
          "level": 2,
          "relative_expected_cost_error": 1.9293397338706517e-16,
          "max_output_probability_error": 1.1102230246251565e-16,
          "independent_absorbing_chain": {
            "expected_raw_signal_calls": 4.603535624688852,
            "output_probabilities_given_target_zero": [
              0.999996746158026,
              1.626920986955346e-06,
              1.6269209869553462e-06
            ],
            "transient_states": 16,
            "linear_residual": 1.7763568394002505e-15,
            "transition_row_sum_error": 0.0
          }
        },
        {
          "q": 5,
          "u": 0.2,
          "level": 1,
          "relative_expected_cost_error": 2.0605739337042904e-16,
          "max_output_probability_error": 2.7755575615628914e-17,
          "independent_absorbing_chain": {
            "expected_raw_signal_calls": 8.620689655172413,
            "output_probabilities_given_target_zero": [
              0.5586206896551724,
              0.11034482758620691,
              0.11034482758620692,
              0.11034482758620694,
              0.11034482758620692
            ],
            "transient_states": 6,
            "linear_residual": 1.7763568394002505e-15,
            "transition_row_sum_error": 0.0
          }
        },
        {
          "q": 5,
          "u": 0.2,
          "level": 2,
          "relative_expected_cost_error": 1.4867494208938923e-16,
          "max_output_probability_error": 3.3306690738754696e-16,
          "independent_absorbing_chain": {
            "expected_raw_signal_calls": 47.791694133157556,
            "output_probabilities_given_target_zero": [
              0.8649967040210945,
              0.03375082399472645,
              0.03375082399472646,
              0.03375082399472646,
              0.03375082399472647
            ],
            "transient_states": 36,
            "linear_residual": 1.4210854715202004e-14,
            "transition_row_sum_error": 0.0
          }
        },
        {
          "q": 5,
          "u": 0.6,
          "level": 1,
          "relative_expected_cost_error": 2.1671553440683053e-16,
          "max_output_probability_error": 1.1102230246251565e-16,
          "independent_absorbing_chain": {
            "expected_raw_signal_calls": 4.098360655737705,
            "output_probabilities_given_target_zero": [
              0.9475409836065573,
              0.013114754098360656,
              0.013114754098360657,
              0.013114754098360657,
              0.013114754098360654
            ],
            "transient_states": 6,
            "linear_residual": 4.440892098500626e-16,
            "transition_row_sum_error": 2.220446049250313e-16
          }
        },
        {
          "q": 5,
          "u": 0.6,
          "level": 2,
          "relative_expected_cost_error": 5.841709629689307e-16,
          "max_output_probability_error": 5.551115123125783e-16,
          "independent_absorbing_chain": {
            "expected_raw_signal_calls": 9.122450200394805,
            "output_probabilities_given_target_zero": [
              0.9992343123766221,
              0.00019142190584435007,
              0.00019142190584435002,
              0.00019142190584435002,
              0.00019142190584435005
            ],
            "transient_states": 36,
            "linear_residual": 5.329070518200751e-15,
            "transition_row_sum_error": 2.220446049250313e-16
          }
        },
        {
          "q": 5,
          "u": 0.9,
          "level": 1,
          "relative_expected_cost_error": 1.882938249764265e-16,
          "max_output_probability_error": 3.2526065174565133e-19,
          "independent_absorbing_chain": {
            "expected_raw_signal_calls": 2.358490566037736,
            "output_probabilities_given_target_zero": [
              0.9981132075471698,
              0.000471698113207547,
              0.00047169811320754707,
              0.0004716981132075469,
              0.00047169811320754696
            ],
            "transient_states": 6,
            "linear_residual": 4.440892098500626e-16,
            "transition_row_sum_error": 0.0
          }
        },
        {
          "q": 5,
          "u": 0.9,
          "level": 2,
          "relative_expected_cost_error": 1.8758412014483595e-16,
          "max_output_probability_error": 1.1102230246251565e-16,
          "independent_absorbing_chain": {
            "expected_raw_signal_calls": 4.734827335140905,
            "output_probabilities_given_target_zero": [
              0.9999991066363519,
              2.233409120349483e-07,
              2.2334091203494825e-07,
              2.2334091203494827e-07,
              2.2334091203494825e-07
            ],
            "transient_states": 36,
            "linear_residual": 3.552713678800501e-15,
            "transition_row_sum_error": 0.0
          }
        },
        {
          "q": 2,
          "u": 0.6,
          "level": 3,
          "relative_expected_cost_error": 5.329233151008205e-16,
          "max_output_probability_error": 9.992007221626409e-16,
          "independent_absorbing_chain": {
            "expected_raw_signal_calls": 13.332926438500394,
            "output_probabilities_given_target_zero": [
              0.9999847414437656,
              1.5258556235409017e-05
            ],
            "transient_states": 27,
            "linear_residual": 3.552713678800501e-15,
            "transition_row_sum_error": 0.0
          }
        },
        {
          "q": 3,
          "u": 0.6,
          "level": 3,
          "relative_expected_cost_error": 4.470453577865234e-16,
          "max_output_probability_error": 1.5543122344752192e-15,
          "independent_absorbing_chain": {
            "expected_raw_signal_calls": 15.894197834381803,
            "output_probabilities_given_target_zero": [
              0.9999976114879168,
              1.1942560408351217e-06,
              1.194256040835122e-06
            ],
            "transient_states": 64,
            "linear_residual": 1.8207657603852567e-14,
            "transition_row_sum_error": 1.1102230246251565e-16
          }
        },
        {
          "q": 5,
          "u": 0.6,
          "level": 3,
          "relative_expected_cost_error": 1.166553612248517e-15,
          "max_output_probability_error": 1.2212453270876722e-15,
          "independent_absorbing_chain": {
            "expected_raw_signal_calls": 18.27286962981163,
            "output_probabilities_given_target_zero": [
              0.9999998532059254,
              3.669851834527357e-08,
              3.669851834527354e-08,
              3.6698518345273574e-08,
              3.6698518345273554e-08
            ],
            "transient_states": 216,
            "linear_residual": 1.7763568394002505e-14,
            "transition_row_sum_error": 2.220446049250313e-16
          }
        }
      ]
    },
    "finite_mixture_LP_checks": {
      "status": "PASS",
      "cases": 27,
      "max_contrast_error": 3.774758283725532e-15,
      "scope": "all mixtures of supplied finite levels, not all sequential programs",
      "records": [
        {
          "q": 2,
          "u": 0.55,
          "budget": 0.35,
          "hull_contrast": 0.55,
          "unrestricted_mixture_LP_contrast": 0.55,
          "absolute_error": 0.0
        },
        {
          "q": 2,
          "u": 0.55,
          "budget": 0.9425494031047768,
          "hull_contrast": 0.7907697760000741,
          "unrestricted_mixture_LP_contrast": 0.7907697760000744,
          "absolute_error": 2.220446049250313e-16
        },
        {
          "q": 2,
          "u": 0.55,
          "budget": 1.5350988062095534,
          "hull_contrast": 0.8898781729319492,
          "unrestricted_mixture_LP_contrast": 0.88987817293195,
          "absolute_error": 8.881784197001252e-16
        },
        {
          "q": 2,
          "u": 0.55,
          "budget": 2.1276482093143305,
          "hull_contrast": 0.94826297109219,
          "unrestricted_mixture_LP_contrast": 0.9482629710921914,
          "absolute_error": 1.3322676295501878e-15
        },
        {
          "q": 2,
          "u": 0.55,
          "budget": 2.720197612419107,
          "hull_contrast": 0.9870348920710282,
          "unrestricted_mixture_LP_contrast": 0.9870348920710308,
          "absolute_error": 2.55351295663786e-15
        },
        {
          "q": 2,
          "u": 0.55,
          "budget": 3.312747015523884,
          "hull_contrast": 0.9902509345587192,
          "unrestricted_mixture_LP_contrast": 0.9902509345587225,
          "absolute_error": 3.3306690738754696e-15
        },
        {
          "q": 2,
          "u": 0.55,
          "budget": 3.905296418628661,
          "hull_contrast": 0.9934669770464102,
          "unrestricted_mixture_LP_contrast": 0.9934669770464126,
          "absolute_error": 2.4424906541753444e-15
        },
        {
          "q": 2,
          "u": 0.55,
          "budget": 4.497845821733437,
          "hull_contrast": 0.9966830195341011,
          "unrestricted_mixture_LP_contrast": 0.9966830195341012,
          "absolute_error": 1.1102230246251565e-16
        },
        {
          "q": 2,
          "u": 0.55,
          "budget": 5.090395224838214,
          "hull_contrast": 0.999899062021792,
          "unrestricted_mixture_LP_contrast": 0.999899062021791,
          "absolute_error": 9.992007221626409e-16
        },
        {
          "q": 3,
          "u": 0.4,
          "budget": 0.2111111111111111,
          "hull_contrast": 0.4,
          "unrestricted_mixture_LP_contrast": 0.4,
          "absolute_error": 0.0
        },
        {
          "q": 3,
          "u": 0.4,
          "budget": 0.9189308327831106,
          "hull_contrast": 0.7094920240509147,
          "unrestricted_mixture_LP_contrast": 0.7094920240509152,
          "absolute_error": 4.440892098500626e-16
        },
        {
          "q": 3,
          "u": 0.4,
          "budget": 1.62675055445511,
          "hull_contrast": 0.8131349273658215,
          "unrestricted_mixture_LP_contrast": 0.8131349273658227,
          "absolute_error": 1.2212453270876722e-15
        },
        {
          "q": 3,
          "u": 0.4,
          "budget": 2.33457027612711,
          "hull_contrast": 0.9042306929355248,
          "unrestricted_mixture_LP_contrast": 0.904230692935527,
          "absolute_error": 2.220446049250313e-15
        },
        {
          "q": 3,
          "u": 0.4,
          "budget": 3.042389997799109,
          "hull_contrast": 0.9666926329062546,
          "unrestricted_mixture_LP_contrast": 0.9666926329062581,
          "absolute_error": 3.4416913763379853e-15
        },
        {
          "q": 3,
          "u": 0.4,
          "budget": 3.7502097194711084,
          "hull_contrast": 0.9749051976722249,
          "unrestricted_mixture_LP_contrast": 0.9749051976722269,
          "absolute_error": 1.9984014443252818e-15
        },
        {
          "q": 3,
          "u": 0.4,
          "budget": 4.4580294411431085,
          "hull_contrast": 0.9831177624381952,
          "unrestricted_mixture_LP_contrast": 0.9831177624381989,
          "absolute_error": 3.774758283725532e-15
        },
        {
          "q": 3,
          "u": 0.4,
          "budget": 5.165849162815108,
          "hull_contrast": 0.9913303272041654,
          "unrestricted_mixture_LP_contrast": 0.9913303272041666,
          "absolute_error": 1.2212453270876722e-15
        },
        {
          "q": 3,
          "u": 0.4,
          "budget": 5.873668884487107,
          "hull_contrast": 0.9995428919701356,
          "unrestricted_mixture_LP_contrast": 0.9995428919701344,
          "absolute_error": 1.2212453270876722e-15
        },
        {
          "q": 5,
          "u": 0.6,
          "budget": 0.14,
          "hull_contrast": 0.6,
          "unrestricted_mixture_LP_contrast": 0.6,
          "absolute_error": 0.0
        },
        {
          "q": 5,
          "u": 0.6,
          "budget": 0.44227521852170393,
          "hull_contrast": 0.833046653735554,
          "unrestricted_mixture_LP_contrast": 0.8330466537355539,
          "absolute_error": 1.1102230246251565e-16
        },
        {
          "q": 5,
          "u": 0.6,
          "budget": 0.7445504370434078,
          "hull_contrast": 0.9501152552406944,
          "unrestricted_mixture_LP_contrast": 0.9501152552406944,
          "absolute_error": 0.0
        },
        {
          "q": 5,
          "u": 0.6,
          "budget": 1.0468256555651116,
          "hull_contrast": 0.9778843453116344,
          "unrestricted_mixture_LP_contrast": 0.9778843453116344,
          "absolute_error": 0.0
        },
        {
          "q": 5,
          "u": 0.6,
          "budget": 1.3491008740868158,
          "hull_contrast": 0.9990966415871994,
          "unrestricted_mixture_LP_contrast": 0.9990966415871994,
          "absolute_error": 0.0
        },
        {
          "q": 5,
          "u": 0.6,
          "budget": 1.6513760926085195,
          "hull_contrast": 0.9993224353172515,
          "unrestricted_mixture_LP_contrast": 0.9993224353172516,
          "absolute_error": 1.1102230246251565e-16
        },
        {
          "q": 5,
          "u": 0.6,
          "budget": 1.9536513111302236,
          "hull_contrast": 0.9995482290473038,
          "unrestricted_mixture_LP_contrast": 0.9995482290473038,
          "absolute_error": 0.0
        },
        {
          "q": 5,
          "u": 0.6,
          "budget": 2.2559265296519277,
          "hull_contrast": 0.999774022777356,
          "unrestricted_mixture_LP_contrast": 0.9997740227773559,
          "absolute_error": 1.1102230246251565e-16
        },
        {
          "q": 5,
          "u": 0.6,
          "budget": 2.5582017481736314,
          "hull_contrast": 0.9999998165074083,
          "unrestricted_mixture_LP_contrast": 0.9999998165074083,
          "absolute_error": 0.0
        }
      ]
    },
    "q5_example": {
      "q": 5,
      "base_retention": 0.04,
      "base_contrast": 0.6,
      "overhead_h_over_E": 0.1,
      "readout_E": 1.0,
      "ungated_expected_cost": 1.1,
      "gated_primitive_expected_cost": 0.14,
      "gate_saving_ratio": 7.857142857142857,
      "levels": [
        {
          "level": 0,
          "m": 2,
          "q": 5,
          "initial_contrast": 0.6,
          "contrast": 0.6,
          "contrast_recursion": 0.6,
          "accepted_signal_correct_probability": 0.6799999999999999,
          "accepted_signal_error_probability": 0.32,
          "log_accepted_signal_error_probability": -1.1394342831883648,
          "contrast_rounded_to_one": false,
          "expected_raw_signal_calls": 1.0,
          "node_acceptance_probabilities": [],
          "scope": "independent repeated signals of ONE fixed target",
          "outer_retention": 0.04,
          "expected_logical_cost": 0.14,
          "uniform_prior_full_call_MAP_error": 0.7808
        },
        {
          "level": 1,
          "m": 2,
          "q": 5,
          "initial_contrast": 0.6,
          "contrast": 0.9344262295081968,
          "contrast_recursion": 0.9344262295081966,
          "accepted_signal_correct_probability": 0.9475409836065574,
          "accepted_signal_error_probability": 0.05245901639344263,
          "log_accepted_signal_error_probability": -2.9477230543676303,
          "contrast_rounded_to_one": false,
          "expected_raw_signal_calls": 4.0983606557377055,
          "node_acceptance_probabilities": [
            0.48799999999999993
          ],
          "scope": "independent repeated signals of ONE fixed target",
          "outer_retention": 0.04,
          "expected_logical_cost": 0.5737704918032788,
          "uniform_prior_full_call_MAP_error": 0.7700983606557377
        },
        {
          "level": 2,
          "m": 2,
          "q": 5,
          "initial_contrast": 0.6,
          "contrast": 0.9990428904707782,
          "contrast_recursion": 0.9990428904707782,
          "accepted_signal_correct_probability": 0.9992343123766226,
          "accepted_signal_error_probability": 0.0007656876233774005,
          "log_accepted_signal_error_probability": -7.174736273777059,
          "contrast_rounded_to_one": false,
          "expected_raw_signal_calls": 9.12245020039481,
          "node_acceptance_probabilities": [
            0.48799999999999993,
            0.8985219027143241
          ],
          "scope": "independent repeated signals of ONE fixed target",
          "outer_retention": 0.04,
          "expected_logical_cost": 1.2771430280552736,
          "uniform_prior_full_call_MAP_error": 0.7680306275049351
        },
        {
          "level": 3,
          "m": 2,
          "q": 5,
          "initial_contrast": 0.6,
          "contrast": 0.9999998165074083,
          "contrast_recursion": 0.9999998165074082,
          "accepted_signal_correct_probability": 0.9999998532059267,
          "accepted_signal_error_probability": 1.4679407338109432e-07,
          "log_accepted_signal_error_probability": -15.73423509364436,
          "contrast_rounded_to_one": false,
          "expected_raw_signal_calls": 18.27286962981165,
          "node_acceptance_probabilities": [
            0.48799999999999993,
            0.8985219027143241,
            0.9984693576001659
          ],
          "scope": "independent repeated signals of ONE fixed target",
          "outer_retention": 0.04,
          "expected_logical_cost": 2.5582017481736314,
          "uniform_prior_full_call_MAP_error": 0.768000005871763
        }
      ],
      "fixed_budget_mixture": {
        "family": "finite-level recursive unanimous signal verifiers",
        "hull_levels": [
          0,
          1,
          2,
          3
        ],
        "left_level": 1,
        "right_level": 2,
        "right_probability": 0.7481519124997381,
        "budget": 1.1,
        "expected_logical_cost": 1.1,
        "unused_budget": 0.0,
        "contrast": 0.9827693079866993,
        "outer_retention": 0.04,
        "accepted_signal_error_probability": 0.013784553610640593,
        "accepted_error_relative_reduction": 0.9569232699667483,
        "original_uniform_prior_full_call_MAP_error": 0.7808,
        "uniform_prior_full_call_MAP_error": 0.7685513821444256,
        "old_to_new_deficiency": 0.012248617855574377,
        "new_to_old_deficiency": 0.0,
        "claims": "same outer retention and expected cost; not constant latency; not hardware evidence",
        "full_call_MAP_error_absolute_reduction": 0.012248617855574406,
        "full_call_MAP_error_relative_reduction": 0.0156872667207664
      }
    },
    "execution_status": "PASS"
  },
  "gaussian_pure_form": {
    "seed": 42817,
    "scope": "real Gaussian coherent-quadrature model; no hardware",
    "energy": {
      "old_budget": 2.0,
      "new_budget": 2.0,
      "old_photons": 1.0,
      "new_photons": 1.55,
      "gamma": 1.55,
      "routing_overhead": 0.15,
      "fixed": 0.2,
      "per_detector": 0.05,
      "old_detectors": 16,
      "new_detectors": 2,
      "resource_units": "abstract common resource units"
    },
    "old_binary_bayes_error": 0.15865525393145707,
    "channels": {
      "oracle": {
        "information_min_margin": 0.5499999999999999,
        "dominates": true,
        "retained_rank": 2,
        "mean_leakage_operator": 3.2001034903066126e-16,
        "min_principal_angle_cos_squared": 1.0000000000000002,
        "gamma_times_min_cos_squared": 1.5500000000000003,
        "reverse_kernel_available": true,
        "reverse_added_cov_min_eigenvalue": 0.3548387096774195,
        "reverse_mean_error": 1.2412670766236368e-16,
        "reverse_covariance_error": 1.0204274098687891e-16,
        "old_ols_mse": 2.0,
        "new_ols_mse": 1.290322580645161,
        "binary_bayes_error": 0.1065677204369842
      },
      "learned": {
        "information_min_margin": 0.5373823304659676,
        "dominates": true,
        "retained_rank": 2,
        "mean_leakage_operator": 0.09022434237743285,
        "min_principal_angle_cos_squared": 0.99185956804256,
        "gamma_times_min_cos_squared": 1.537382330465968,
        "reverse_kernel_available": true,
        "reverse_added_cov_min_eigenvalue": 0.3495437145443786,
        "reverse_mean_error": 1.4148301363828725e-16,
        "reverse_covariance_error": 8.352669508610183e-17,
        "old_ols_mse": 2.0,
        "new_ols_mse": 1.2971464295595228,
        "binary_bayes_error": 0.10750270861308736
      },
      "random": {
        "information_min_margin": -0.9953880532783431,
        "dominates": false,
        "retained_rank": 2,
        "mean_leakage_operator": 0.9985111669391368,
        "min_principal_angle_cos_squared": 0.002975449497843108,
        "gamma_times_min_cos_squared": 0.004611946721656817,
        "reverse_kernel_available": false,
        "reverse_added_cov_min_eigenvalue": -215.82817698309293,
        "reverse_mean_error": 4.024424951800077e-16,
        "reverse_covariance_error": 2.0489764566520145e-14,
        "old_ols_mse": 2.0,
        "new_ols_mse": 229.94552856530296,
        "binary_bayes_error": 0.3912387072868743
      }
    },
    "calibration": {
      "pilot_noise_std": 0.02,
      "alpha": 0.001,
      "operator_error_bound": 0.18262271502445868,
      "actual_operator_error": 0.09024658323436077,
      "h_min_singular_lower_bound": 0.8023009629081197,
      "pointwise_information_gain_lower_bound": 1.4696905481843314,
      "energy_consistency": "Pilot precision and amortized overhead are independent declared inputs; their consistency requires measured pilot energy and stable lifetime.",
      "scope": "Ordering on calibration event; exact reverse kernel still requires true H. This is not one robust common kernel over unknown H."
    },
    "common_kernel": {
      "added_cov_min_eigenvalue": 0.3548387096774188,
      "covariance_error": 0.0,
      "true_operator_leakage": 0.09022434237743285,
      "actual_uniform_tv_bound": 0.07189105920717642,
      "calibrated_uniform_tv_bound": 0.14490593994082324,
      "calibration_failure_probability": 0.001,
      "parameter_radius": 2.0,
      "scope": "One fixed implementable Q-only kernel. TV bound holds for ||theta||<=B; calibrated bound holds on the declared independent calibration event."
    },
    "likelihood_training": {
      "steps": 120,
      "batch_size": 32,
      "learning_rate": 0.2,
      "max_coupled_gradient_difference": 3.885780586188048e-16,
      "max_coupled_parameter_difference": 2.220446049250313e-16,
      "interpretation": "Learning 2 modal coefficients in a linear Gaussian model, not a neural benchmark."
    },
    "holdout": {
      "basis": "oracle",
      "independent_replicates": 100000,
      "old_mse": 1.996303670221155,
      "new_mse": 1.2909284374715835,
      "empirical_ratio": 0.6466593518452889,
      "analytic_ratio": 0.6451612903225806
    },
    "approximation": {
      "learned_projection_leakage_operator": 0.09022434237743285,
      "bounded_parameter_radius": 2.0,
      "no_reinvestment_reconstruction_tv_upper_bound": 0.07189105920717642,
      "scope": "Fixed Q-fill reverse kernel at unchanged noise; a valid bound, not necessarily optimal deficiency."
    },
    "execution_status": "PASS"
  },
  "orbit_audit": {
    "status": "PASS",
    "seed": 8751,
    "scope": "Independent finite-orbit LP checks and explicit hypothesis-boundary examples; no hardware or general-RSI claim",
    "arbitrary_orbit_lp_cases": 96,
    "max_formula_lp_error": 5.551115123125783e-16,
    "missing_symmetry_counterexample": {
      "source": [
        [
          1.0,
          0.0
        ],
        [
          0.5,
          0.5
        ]
      ],
      "target": "perfect binary experiment",
      "outside_hypotheses_frontier_prediction": 0.25,
      "actual_worst_state_deficiency_lp": 0.3333333333333334,
      "exact_worst_state_deficiency": "1/3",
      "proof": "At outcome 0 choose label 0 with probability a; at outcome 1 choose label 1. Worst-state error is max(1-a,a/2), minimized at a=2/3. Erasure cannot improve approximation to a target that always gives the correct label."
    },
    "unknown_H_common_kernel_counterexample": {
      "Q": [
        [
          1.0
        ],
        [
          0.0
        ]
      ],
      "sigma0": 1.0,
      "sigma1": 0.5,
      "theta": 1.0,
      "cases": [
        {
          "name": "plus",
          "H": [
            [
              1.0
            ],
            [
              1.0
            ]
          ],
          "old_information": 2.0,
          "new_information": 4.0,
          "known_H_reverse_linear": [
            [
              1.0
            ],
            [
              1.0
            ]
          ],
          "known_H_added_covariance": [
            [
              0.75,
              -0.25
            ],
            [
              -0.25,
              0.75
            ]
          ],
          "added_covariance_min_eigenvalue": 0.5
        },
        {
          "name": "minus",
          "H": [
            [
              1.0
            ],
            [
              -1.0
            ]
          ],
          "old_information": 2.0,
          "new_information": 4.0,
          "known_H_reverse_linear": [
            [
              1.0
            ],
            [
              -1.0
            ]
          ],
          "known_H_added_covariance": [
            [
              0.75,
              0.25
            ],
            [
              0.25,
              0.75
            ]
          ],
          "added_covariance_min_eigenvalue": 0.5
        }
      ],
      "common_new_law": "N(theta, 0.25)",
      "distinct_old_laws": "N((theta,theta),I_2) and N((theta,-theta),I_2)",
      "old_pair_total_variation_at_theta_1": 0.6826894921370859,
      "any_common_kernel_worst_error_lower_bound_at_theta_1": 0.3413447460685429,
      "lower_bound_as_abs_theta_goes_to_infinity": 0.5,
      "conclusion": "For each known H there exists a reverse kernel, but no single H-blind kernel reproduces both old laws. The triangle inequality gives the displayed lower bound."
    },
    "principal_angle_rank_counterexample": {
      "H": [
        [
          1.0,
          0.0
        ],
        [
          0.0,
          1.0
        ]
      ],
      "Q": [
        [
          1.0
        ],
        [
          0.0
        ]
      ],
      "sigma0": 1.0,
      "sigma1": 0.1,
      "gamma": 100.0,
      "conventional_list_of_principal_angle_cosines": [
        1.0
      ],
      "information_margin_eigenvalues": [
        -1.0,
        98.99999999999999
      ],
      "extended_maximum_angle_degrees": 90.0,
      "dominates": false,
      "conclusion": "Require r>=p and full retained signal rank, or define the maximum angle using inf_{v in range(H), ||v||=1} ||Q^T v||."
    },
    "restricted_parameter_space_counterexample": {
      "H": [
        [
          1.0,
          0.0
        ],
        [
          0.0,
          1.0
        ]
      ],
      "Q": [
        [
          1.0
        ],
        [
          0.0
        ]
      ],
      "sigma0": 1.0,
      "sigma1": 1.0,
      "parameter_space": [
        [
          -1.0,
          0.0
        ],
        [
          1.0,
          0.0
        ]
      ],
      "information_margin_eigenvalues": [
        -1.0,
        0.0
      ],
      "nevertheless_exact_dominance": true,
      "reverse_kernel": "Output (T,Z) with independent Z~N(0,1).",
      "conclusion": "The global matrix inequality is sufficient for arbitrary parameter sets. Its necessity as stated uses theta in all R^p; a nonempty open parameter set also suffices."
    },
    "execution_status": "PASS"
  },
  "learning_check": {
    "status": "PASS",
    "paths": 20000,
    "seed": 71037,
    "steps": 120,
    "moment_checks": 12,
    "gamma": 1.55,
    "old_asymptotic_mse": 0.006944444444444445,
    "new_asymptotic_mse": 0.004480286738351254,
    "scope": "Linear Gaussian modal coefficient SGD; no neural benchmark or hardware",
    "execution_status": "PASS"
  },
  "catalogue": {
    "status": "PASS",
    "seed": 864112,
    "theorem_scope": "Fully S_q-equivariant finite source to visible nonnegative symmetric reliability catalogue",
    "tv_convention": "half_l1",
    "formula": "(q-1)/q * max_a (E_target[(V-a)+]-E_source[(R-a)+])_+",
    "randomized_comparisons": 220,
    "visible_mixture_comparisons": 160,
    "arbitrary_posterior_orbit_comparisons": 60,
    "independent_solver": "Full unrestricted stochastic-kernel minimax TV LP",
    "compiler": "Explicit uniform-tie MAP collapse, scalar weak transport, label mixing",
    "max_formula_full_lp_error": 2.848277169675839e-13,
    "max_formula_kernel_tv_error": 3.625572064791527e-16,
    "max_kernel_stochastic_error": 2.1094237467877974e-15,
    "max_MAP_collapse_identity_error": 2.220446049250313e-16,
    "tolerance": 1e-07,
    "exact_rational_witness": {
      "q": 5,
      "source_values": [
        "0",
        "1/2",
        "9/10"
      ],
      "source_masses": [
        "1/5",
        "1/2",
        "3/10"
      ],
      "target_values": [
        "1/5",
        "7/10",
        "1"
      ],
      "target_masses": [
        "2/5",
        "2/5",
        "1/5"
      ],
      "exact_stoploss_gap": "3/50",
      "exact_deficiency": "6/125",
      "exact_witness_threshold": "1/2",
      "formula": 0.04799999999999999,
      "constructed_kernel_tv": 0.048000000000000084,
      "unrestricted_full_lp": 0.048,
      "coupling": [
        [
          0.20000000000000004,
          0.0,
          0.0
        ],
        [
          0.19999999999999998,
          0.30000000000000004,
          0.0
        ],
        [
          0.0,
          0.09999999999999998,
          0.20000000000000007
        ]
      ],
      "threshold_audit": {
        "gap": 0.059999999999999984,
        "witness_threshold": 0.5000000000000001,
        "thresholds": [
          0.0,
          0.2,
          0.5000000000000001,
          0.7,
          0.8999999999999999,
          1.0
        ],
        "source_stoploss": [
          0.52,
          0.36000000000000004,
          0.11999999999999995,
          0.06,
          0.0,
          0.0
        ],
        "target_stoploss": [
          0.56,
          0.36,
          0.17999999999999994,
          0.06000000000000001,
          0.020000000000000018,
          0.0
        ],
        "differences": [
          0.040000000000000036,
          -5.551115123125783e-17,
          0.059999999999999984,
          1.3877787807814457e-17,
          0.020000000000000018,
          0.0
        ]
      },
      "exact_fraction_check_passed": true
    },
    "equal_mean_obstruction": {
      "q": 5,
      "source_values": [
        0.5
      ],
      "source_masses": [
        1
      ],
      "target_values": [
        0,
        1
      ],
      "target_masses": [
        0.5,
        0.5
      ],
      "source_mean": 0.5,
      "target_mean": 0.5,
      "stoploss_gap": 0.25,
      "exact_deficiency": 0.2,
      "interpretation": "Mean confidence alone misses coverage/purity constraints"
    },
    "same_profile_blackwell_counterexample": {
      "q": 3,
      "A": [
        [
          0.5,
          0.25,
          0.25
        ],
        [
          0.25,
          0.5,
          0.25
        ],
        [
          0.25,
          0.25,
          0.5
        ]
      ],
      "B": [
        [
          0.0,
          0.5,
          0.5
        ],
        [
          0.5,
          0.0,
          0.5
        ],
        [
          0.5,
          0.5,
          0.0
        ]
      ],
      "confidence_A": 0.25,
      "confidence_B": 0.25,
      "deficiency_A_to_B": 0.25,
      "deficiency_B_to_A": 0.0,
      "interpretation": "Same MAP-confidence profile is not complete Blackwell order for q>=3"
    },
    "physical_photonic_measurements": false,
    "world_first_priority_established": false,
    "execution_status": "PASS"
  },
  "uncertainty_closure": {
    "seed": 1072026,
    "status": "PASS",
    "scope": "Fixed-Q, equal-Gaussian coherent-mode surrogate, unknown H, common-null bounded theta family.",
    "theorem": "One H-independent exact reverse kernel iff gamma U.T Q Q.T U >= I on the full mutation closure.",
    "novelty_status": "Present synthesis and proof; independent priority unverified.",
    "hardware_experiments": 0,
    "neural_benchmarks": 0,
    "counterexample": {
      "uncertainty_angle": 0.01,
      "theta": 2.0,
      "gamma": 1.0001000066670445,
      "known_H_information_margin": 0.0,
      "compressed_mean_difference": 0.0,
      "full_mean_difference": 0.03999933333666666,
      "exact_mutation_closure_dimension": 2,
      "receiver_coordinates": 1,
      "common_kernel_exists": false,
      "any_common_kernel_max_TV_error_lower_bound": 0.007978180763399623,
      "derivation": "Half the TV of two target laws sharing one source law."
    },
    "exact_structured_example": {
      "physical_modes": 32,
      "pointwise_H_rank": 2,
      "exact_mutation_closure_dimension": 6,
      "bounded_nuisance_coordinates": [
        -0.1,
        0.1
      ],
      "resource": {
        "resource_units": "abstract common convertible resource units",
        "exposure_units": "coefficient P in variance sigma^2=1/P",
        "conversion_status": "declared model only; no measured physical conversion",
        "bounded_parameter_norm": 2.0,
        "transfer_operator_norm_bound": 1.0099504938362078,
        "maximum_signal_norm": 2.0199009876724157,
        "photon_resource_per_exposure": 4.08,
        "old_worst_case_photon_resource": 4.08,
        "new_worst_case_photon_resource": 8.68,
        "old_fixed_resource": 0.8,
        "new_fixed_resource": 1.4,
        "per_receiver_resource": 0.2,
        "old_receiver_coordinates": 32,
        "new_receiver_coordinates": 6,
        "old_exposure": 1.0,
        "new_exposure": 2.127450980392157,
        "gamma": 2.127450980392157,
        "old_budget": 11.280000000000001,
        "new_budget": 11.28,
        "receiver_coordinate_reduction_fraction": 0.8125,
        "minimum_exact_receiver_count": 6,
        "note": "The specified H(z1,z2) family has exact closure dimension six."
      },
      "common_kernel": {
        "closure_dimension": 6,
        "receiver_coordinates": 6,
        "gamma": 2.127450980392157,
        "minimum_retained_cos_squared": 0.9999999999999992,
        "universal_information_margin": 1.127450980392155,
        "common_kernel_exists": true,
        "candidate_available": true,
        "candidate_covariance_min_eigenvalue": 0.5299539170506903,
        "common_mean_operator_error": 3.8453742011065983e-16,
        "common_covariance_identity_error": 2.681517473081736e-17
      },
      "independent_holdout": {
        "replications": 100000,
        "unknown_H_coefficients": [
          -0.06446286983254929,
          0.08115451815611968
        ],
        "theta": [
          1.1,
          -0.7
        ],
        "maximum_empirical_mean_coordinate_error": 0.004621841779348393,
        "maximum_empirical_covariance_entry_error": 0.010264230353982594,
        "interpretation": "Monte Carlo implementation check, not hardware."
      }
    },
    "rotation_orbit": {
      "physical_modes": 32,
      "pointwise_H_rank": 1,
      "drift_parameter_interval": [
        -0.2,
        0.2
      ],
      "exact_mutation_closure_dimension": 32,
      "exact_dimension_valid_for_every_positive_drift_radius": true,
      "proof": "Even and odd derivatives each form a 16-by-16 Vandermonde system in distinct j^2.",
      "positive_integer_vandermonde_determinant": "14355973656491146827638004051975967715503775251095756038091878465144346560214586188455148959995319764939603245797057978391666871809628140938011931649692860847934073804758712320000000000000000000000000000000000000000000000",
      "maximum_generator_operator_norm": 1,
      "seed_signal_norm": 1,
      "bounded_parameter_absolute_value": 2.0,
      "selected_derivative_order": 2,
      "selected_receivers": 3,
      "selected_rigorous_uniform_leakage": 0.0013333333333333337,
      "selected_rigorous_uniform_TV_upper_bound": 0.0010638457658569411,
      "selected_grid_leakage": 0.00022260840884392346,
      "selected_resource": {
        "resource_units": "abstract common convertible resource units",
        "exposure_units": "coefficient P in variance sigma^2=1/P",
        "conversion_status": "declared model only; no measured physical conversion",
        "bounded_parameter_norm": 2.0,
        "transfer_operator_norm_bound": 1.0,
        "maximum_signal_norm": 2.0,
        "photon_resource_per_exposure": 4.0,
        "old_worst_case_photon_resource": 4.0,
        "new_worst_case_photon_resource": 9.2,
        "old_fixed_resource": 0.8,
        "new_fixed_resource": 1.4,
        "per_receiver_resource": 0.2,
        "old_receiver_coordinates": 32,
        "new_receiver_coordinates": 3,
        "old_exposure": 1.0,
        "new_exposure": 2.3,
        "gamma": 2.3,
        "old_budget": 11.2,
        "new_budget": 11.2,
        "receiver_coordinate_reduction_fraction": 0.90625,
        "minimum_exact_receiver_count": 32,
        "note": "The last count applies to the full 32-mode orbit class only."
      },
      "selected_common_kernel_added_covariance_min_eigenvalue": 0.5652173913043473,
      "selected_common_kernel_covariance_identity_error": 0.0,
      "krylov_orders": [
        {
          "derivative_order": 0,
          "receiver_coordinates": 1,
          "exact_full_class_dimension": 32,
          "rigorous_uniform_operator_leakage": 0.2,
          "rigorous_uniform_common_kernel_TV_upper_bound": 0.15851941887820598,
          "grid_maximum_operator_leakage": 0.12052081551261949,
          "grid_maximum_common_kernel_TV": 0.0959294085675193,
          "grid_points": 1001,
          "grid_status": "Sanity check only; the Taylor theorem supplies the uniform certificate.",
          "resource": {
            "resource_units": "abstract common convertible resource units",
            "exposure_units": "coefficient P in variance sigma^2=1/P",
            "conversion_status": "declared model only; no measured physical conversion",
            "bounded_parameter_norm": 2.0,
            "transfer_operator_norm_bound": 1.0,
            "maximum_signal_norm": 2.0,
            "photon_resource_per_exposure": 4.0,
            "old_worst_case_photon_resource": 4.0,
            "new_worst_case_photon_resource": 9.6,
            "old_fixed_resource": 0.8,
            "new_fixed_resource": 1.4,
            "per_receiver_resource": 0.2,
            "old_receiver_coordinates": 32,
            "new_receiver_coordinates": 1,
            "old_exposure": 1.0,
            "new_exposure": 2.4,
            "gamma": 2.4,
            "old_budget": 11.2,
            "new_budget": 11.2,
            "receiver_coordinate_reduction_fraction": 0.96875,
            "minimum_exact_receiver_count": 32,
            "note": "The last count applies to the full 32-mode orbit class only."
          }
        },
        {
          "derivative_order": 1,
          "receiver_coordinates": 2,
          "exact_full_class_dimension": 32,
          "rigorous_uniform_operator_leakage": 0.020000000000000004,
          "rigorous_uniform_common_kernel_TV_upper_bound": 0.015956627433803883,
          "grid_maximum_operator_leakage": 0.0062824669579412,
          "grid_maximum_common_kernel_TV": 0.005012650415097131,
          "grid_points": 1001,
          "grid_status": "Sanity check only; the Taylor theorem supplies the uniform certificate.",
          "resource": {
            "resource_units": "abstract common convertible resource units",
            "exposure_units": "coefficient P in variance sigma^2=1/P",
            "conversion_status": "declared model only; no measured physical conversion",
            "bounded_parameter_norm": 2.0,
            "transfer_operator_norm_bound": 1.0,
            "maximum_signal_norm": 2.0,
            "photon_resource_per_exposure": 4.0,
            "old_worst_case_photon_resource": 4.0,
            "new_worst_case_photon_resource": 9.399999999999999,
            "old_fixed_resource": 0.8,
            "new_fixed_resource": 1.4,
            "per_receiver_resource": 0.2,
            "old_receiver_coordinates": 32,
            "new_receiver_coordinates": 2,
            "old_exposure": 1.0,
            "new_exposure": 2.3499999999999996,
            "gamma": 2.3499999999999996,
            "old_budget": 11.2,
            "new_budget": 11.2,
            "receiver_coordinate_reduction_fraction": 0.9375,
            "minimum_exact_receiver_count": 32,
            "note": "The last count applies to the full 32-mode orbit class only."
          }
        },
        {
          "derivative_order": 2,
          "receiver_coordinates": 3,
          "exact_full_class_dimension": 32,
          "rigorous_uniform_operator_leakage": 0.0013333333333333337,
          "rigorous_uniform_common_kernel_TV_upper_bound": 0.0010638457658569411,
          "grid_maximum_operator_leakage": 0.00022260840884392346,
          "grid_maximum_common_kernel_TV": 0.00017761581105446567,
          "grid_points": 1001,
          "grid_status": "Sanity check only; the Taylor theorem supplies the uniform certificate.",
          "resource": {
            "resource_units": "abstract common convertible resource units",
            "exposure_units": "coefficient P in variance sigma^2=1/P",
            "conversion_status": "declared model only; no measured physical conversion",
            "bounded_parameter_norm": 2.0,
            "transfer_operator_norm_bound": 1.0,
            "maximum_signal_norm": 2.0,
            "photon_resource_per_exposure": 4.0,
            "old_worst_case_photon_resource": 4.0,
            "new_worst_case_photon_resource": 9.2,
            "old_fixed_resource": 0.8,
            "new_fixed_resource": 1.4,
            "per_receiver_resource": 0.2,
            "old_receiver_coordinates": 32,
            "new_receiver_coordinates": 3,
            "old_exposure": 1.0,
            "new_exposure": 2.3,
            "gamma": 2.3,
            "old_budget": 11.2,
            "new_budget": 11.2,
            "receiver_coordinate_reduction_fraction": 0.90625,
            "minimum_exact_receiver_count": 32,
            "note": "The last count applies to the full 32-mode orbit class only."
          }
        },
        {
          "derivative_order": 3,
          "receiver_coordinates": 4,
          "exact_full_class_dimension": 32,
          "rigorous_uniform_operator_leakage": 6.666666666666668e-05,
          "rigorous_uniform_common_kernel_TV_upper_bound": 5.319230401412689e-05,
          "grid_maximum_operator_leakage": 5.623087164267221e-06,
          "grid_maximum_common_kernel_TV": 4.48657443241629e-06,
          "grid_points": 1001,
          "grid_status": "Sanity check only; the Taylor theorem supplies the uniform certificate.",
          "resource": {
            "resource_units": "abstract common convertible resource units",
            "exposure_units": "coefficient P in variance sigma^2=1/P",
            "conversion_status": "declared model only; no measured physical conversion",
            "bounded_parameter_norm": 2.0,
            "transfer_operator_norm_bound": 1.0,
            "maximum_signal_norm": 2.0,
            "photon_resource_per_exposure": 4.0,
            "old_worst_case_photon_resource": 4.0,
            "new_worst_case_photon_resource": 8.999999999999998,
            "old_fixed_resource": 0.8,
            "new_fixed_resource": 1.4,
            "per_receiver_resource": 0.2,
            "old_receiver_coordinates": 32,
            "new_receiver_coordinates": 4,
            "old_exposure": 1.0,
            "new_exposure": 2.2499999999999996,
            "gamma": 2.2499999999999996,
            "old_budget": 11.2,
            "new_budget": 11.2,
            "receiver_coordinate_reduction_fraction": 0.875,
            "minimum_exact_receiver_count": 32,
            "note": "The last count applies to the full 32-mode orbit class only."
          }
        },
        {
          "derivative_order": 4,
          "receiver_coordinates": 5,
          "exact_full_class_dimension": 32,
          "rigorous_uniform_operator_leakage": 2.6666666666666673e-06,
          "rigorous_uniform_common_kernel_TV_upper_bound": 2.127692162234851e-06,
          "grid_maximum_operator_leakage": 1.1771295222400346e-07,
          "grid_maximum_common_kernel_TV": 9.392134714403255e-08,
          "grid_points": 1001,
          "grid_status": "Sanity check only; the Taylor theorem supplies the uniform certificate.",
          "resource": {
            "resource_units": "abstract common convertible resource units",
            "exposure_units": "coefficient P in variance sigma^2=1/P",
            "conversion_status": "declared model only; no measured physical conversion",
            "bounded_parameter_norm": 2.0,
            "transfer_operator_norm_bound": 1.0,
            "maximum_signal_norm": 2.0,
            "photon_resource_per_exposure": 4.0,
            "old_worst_case_photon_resource": 4.0,
            "new_worst_case_photon_resource": 8.799999999999999,
            "old_fixed_resource": 0.8,
            "new_fixed_resource": 1.4,
            "per_receiver_resource": 0.2,
            "old_receiver_coordinates": 32,
            "new_receiver_coordinates": 5,
            "old_exposure": 1.0,
            "new_exposure": 2.1999999999999997,
            "gamma": 2.1999999999999997,
            "old_budget": 11.2,
            "new_budget": 11.2,
            "receiver_coordinate_reduction_fraction": 0.84375,
            "minimum_exact_receiver_count": 32,
            "note": "The last count applies to the full 32-mode orbit class only."
          }
        },
        {
          "derivative_order": 5,
          "receiver_coordinates": 6,
          "exact_full_class_dimension": 32,
          "rigorous_uniform_operator_leakage": 8.888888888888892e-08,
          "rigorous_uniform_common_kernel_TV_upper_bound": 7.092307208189652e-08,
          "grid_maximum_operator_leakage": 1.952424282607876e-09,
          "grid_maximum_common_kernel_TV": 1.5578092149581835e-09,
          "grid_points": 1001,
          "grid_status": "Sanity check only; the Taylor theorem supplies the uniform certificate.",
          "resource": {
            "resource_units": "abstract common convertible resource units",
            "exposure_units": "coefficient P in variance sigma^2=1/P",
            "conversion_status": "declared model only; no measured physical conversion",
            "bounded_parameter_norm": 2.0,
            "transfer_operator_norm_bound": 1.0,
            "maximum_signal_norm": 2.0,
            "photon_resource_per_exposure": 4.0,
            "old_worst_case_photon_resource": 4.0,
            "new_worst_case_photon_resource": 8.599999999999998,
            "old_fixed_resource": 0.8,
            "new_fixed_resource": 1.4,
            "per_receiver_resource": 0.2,
            "old_receiver_coordinates": 32,
            "new_receiver_coordinates": 6,
            "old_exposure": 1.0,
            "new_exposure": 2.1499999999999995,
            "gamma": 2.1499999999999995,
            "old_budget": 11.2,
            "new_budget": 11.199999999999998,
            "receiver_coordinate_reduction_fraction": 0.8125,
            "minimum_exact_receiver_count": 32,
            "note": "The last count applies to the full 32-mode orbit class only."
          }
        },
        {
          "derivative_order": 6,
          "receiver_coordinates": 7,
          "exact_full_class_dimension": 32,
          "rigorous_uniform_operator_leakage": 2.5396825396825407e-09,
          "rigorous_uniform_common_kernel_TV_upper_bound": 2.0263735134307126e-09,
          "grid_maximum_operator_leakage": 2.8825222547854315e-11,
          "grid_maximum_common_kernel_TV": 2.2999158133529818e-11,
          "grid_points": 1001,
          "grid_status": "Sanity check only; the Taylor theorem supplies the uniform certificate.",
          "resource": {
            "resource_units": "abstract common convertible resource units",
            "exposure_units": "coefficient P in variance sigma^2=1/P",
            "conversion_status": "declared model only; no measured physical conversion",
            "bounded_parameter_norm": 2.0,
            "transfer_operator_norm_bound": 1.0,
            "maximum_signal_norm": 2.0,
            "photon_resource_per_exposure": 4.0,
            "old_worst_case_photon_resource": 4.0,
            "new_worst_case_photon_resource": 8.399999999999999,
            "old_fixed_resource": 0.8,
            "new_fixed_resource": 1.4,
            "per_receiver_resource": 0.2,
            "old_receiver_coordinates": 32,
            "new_receiver_coordinates": 7,
            "old_exposure": 1.0,
            "new_exposure": 2.0999999999999996,
            "gamma": 2.0999999999999996,
            "old_budget": 11.2,
            "new_budget": 11.2,
            "receiver_coordinate_reduction_fraction": 0.78125,
            "minimum_exact_receiver_count": 32,
            "note": "The last count applies to the full 32-mode orbit class only."
          }
        }
      ]
    },
    "execution_status": "PASS"
  },
  "reference_gluing": {
    "status": "PASS",
    "seed": 731,
    "known_context_cases": 128,
    "rank_increment_identity_checks": 128,
    "required_reference_deletion_checks": 128,
    "future_interface_cases": 90,
    "strict_naive_future_contract_losses": 90,
    "max_known_context_relative_information_error": 2.0841237094270004e-15,
    "max_future_contract_relative_information_error": 2.908787601858244e-13,
    "future_interface_theorem": "For known Y=H theta+epsilon with epsilon~N(0,I), Q.T Y preserves the full joint experiment with every Z=D theta+B epsilon+eta whose B rows lie in E iff im(H)+E is contained in im(Q).",
    "exact_minimum_retained_modes": "dim(im(H)+E)",
    "exact_known_context_reference_minimum": "rank(G.T S^-1 C)=rank(J_full-J_T), conditional on keeping T fixed",
    "reference_counterexample": {
      "rho": 0.99,
      "current_marginal_information_before": 1.0,
      "current_marginal_information_after": 1.0,
      "future_joint_information_full": 51.25125628140696,
      "future_joint_information_naive": 2.0,
      "lost_information": 49.25125628140696,
      "full_unbiased_variance": 0.01951171683498385,
      "naive_unbiased_variance": 0.5,
      "conclusion": "Marginally sufficient local compression is not sufficient after correlated extension.",
      "unbounded_penalty_limit": "The information loss diverges as rho increases to one."
    },
    "coordination_cost_oracle": {
      "local_reference_modules": 16,
      "full_physical_modes": 17,
      "fixed_semantic_modes": 1,
      "centralized_reference_modes": 1,
      "separate_local_reference_exports": 16,
      "coherent_to_local_reference_count_ratio": 16,
      "full_information": 24.999999999999996,
      "naive_information": 1.0,
      "repaired_information": 25.00000000000019,
      "unrestricted_global_oracle_information": 24.99999999999987,
      "unrestricted_global_oracle_total_modes": 1,
      "completed_total_modes": 2,
      "fixed_cost": 0.2,
      "per_detector_cost": 0.05,
      "source_cost": 1.0,
      "extra_mixer_cost": 0.15,
      "full_cost": 2.05,
      "repaired_cost": 1.45,
      "unrestricted_global_oracle_cost": 1.4,
      "completed_cost_reduction_fraction": 0.2926829268292683,
      "completed_physical_mode_reduction_fraction": 0.8823529411764706,
      "resource_units": "abstract common units, unchanged exposure, known covariance",
      "oracle_scope": "Global score oracle is stronger and uses fewer total modes; two-mode repair is minimal only while keeping the original semantic output fixed.",
      "hardware_scope": "Passive real-mode mixing and noiseless linear readout are model assumptions; actual insertion loss, source, detector, reference and calibration costs must be measured."
    },
    "proof_scope": "All Gaussian means and covariances are known; linear optical mode exports; unconstrained theta; all allowed future D and positive definite independent eta covariance. No generic statistical-priority claim.",
    "physical_validation_percent": 0,
    "neural_benchmarks": 0,
    "execution_status": "PASS"
  },
  "bilinear_gluing": {
    "experiment": "exact_prime_field_shared_bilinear_gluing",
    "seed": 20261017,
    "case_count": 91,
    "affine_random_cases": 60,
    "centered_no_compression_cases": 24,
    "curated_cases": 4,
    "direct_uniformizer_source_cases": 3,
    "direct_uniformizer_mixture_checks": [
      "uniformized_seed_k1_L1",
      "uniformized_seed_k1_L2",
      "uniformized_seed_k2_L1"
    ],
    "seed_oracle_simulator_mixture_identity_exact_checked": true,
    "uniformizer_family_curve": [
      {
        "blocks": 1,
        "target_dimension": 3,
        "uniformizer_dimension": 1,
        "exact_minimum_sufficient_alphabet": 8,
        "minimum_expected_binary_queries_to_sufficiently_encode_Y": 3,
        "query_lower_bound_scope": "Prefix-free q-ary queries of one realized Y; no cheap hidden-uniformizer flag or separate seed-channel oracle.",
        "alternative_seed_oracle_expected_binary_readouts_exact": "3/2",
        "alternative_seed_oracle_expected_binary_readouts": 1.5,
        "alternative_seed_oracle_contract": "If a separately available seed channel can be acquired, Bernoulli(2^-L) seed-oracle use and otherwise uniform output exactly simulates the unflagged experiment; this is outside the encoding lower bound.",
        "cheap_uniformizer_flag_contract": "If A0 is cheap observable metadata, acquire only when A0=0; this can also attain expected 3k*2^-L readouts and is excluded from the hidden-nuisance query contract.",
        "all_singleton_information_exactly_zero": true,
        "uniform_target_information_bits": 0.043252437039192335,
        "information_upper_bound_bits": 0.0874628412503394,
        "chi2_exact": "1/16",
        "chi2": 0.0625,
        "zero_readout_deficiency_exact": "3/32",
        "zero_readout_deficiency": 0.09375,
        "zero_readout_deficiency_upper_bound": 0.5
      },
      {
        "blocks": 2,
        "target_dimension": 6,
        "uniformizer_dimension": 2,
        "exact_minimum_sufficient_alphabet": 64,
        "minimum_expected_binary_queries_to_sufficiently_encode_Y": 6,
        "query_lower_bound_scope": "Prefix-free q-ary queries of one realized Y; no cheap hidden-uniformizer flag or separate seed-channel oracle.",
        "alternative_seed_oracle_expected_binary_readouts_exact": "3/2",
        "alternative_seed_oracle_expected_binary_readouts": 1.5,
        "alternative_seed_oracle_contract": "If a separately available seed channel can be acquired, Bernoulli(2^-L) seed-oracle use and otherwise uniform output exactly simulates the unflagged experiment; this is outside the encoding lower bound.",
        "cheap_uniformizer_flag_contract": "If A0 is cheap observable metadata, acquire only when A0=0; this can also attain expected 3k*2^-L readouts and is excluded from the hidden-nuisance query contract.",
        "all_singleton_information_exactly_zero": true,
        "uniform_target_information_bits": 0.023370230721314722,
        "information_upper_bound_bits": 0.04984854945056153,
        "chi2_exact": "9/256",
        "chi2": 0.03515625,
        "zero_readout_deficiency_exact": "69/1024",
        "zero_readout_deficiency": 0.0673828125,
        "zero_readout_deficiency_upper_bound": 0.25
      },
      {
        "blocks": 3,
        "target_dimension": 9,
        "uniformizer_dimension": 3,
        "exact_minimum_sufficient_alphabet": 512,
        "minimum_expected_binary_queries_to_sufficiently_encode_Y": 9,
        "query_lower_bound_scope": "Prefix-free q-ary queries of one realized Y; no cheap hidden-uniformizer flag or separate seed-channel oracle.",
        "alternative_seed_oracle_expected_binary_readouts_exact": "9/8",
        "alternative_seed_oracle_expected_binary_readouts": 1.125,
        "alternative_seed_oracle_contract": "If a separately available seed channel can be acquired, Bernoulli(2^-L) seed-oracle use and otherwise uniform output exactly simulates the unflagged experiment; this is outside the encoding lower bound.",
        "cheap_uniformizer_flag_contract": "If A0 is cheap observable metadata, acquire only when A0=0; this can also attain expected 3k*2^-L readouts and is excluded from the hidden-nuisance query contract.",
        "all_singleton_information_exactly_zero": true,
        "uniform_target_information_bits": 0.00985924915041796,
        "information_upper_bound_bits": 0.021327032624372442,
        "chi2_exact": "61/4096",
        "chi2": 0.014892578125,
        "zero_readout_deficiency_exact": "675/16384",
        "zero_readout_deficiency": 0.04119873046875,
        "zero_readout_deficiency_upper_bound": 0.125
      },
      {
        "blocks": 4,
        "target_dimension": 12,
        "uniformizer_dimension": 4,
        "exact_minimum_sufficient_alphabet": 4096,
        "minimum_expected_binary_queries_to_sufficiently_encode_Y": 12,
        "query_lower_bound_scope": "Prefix-free q-ary queries of one realized Y; no cheap hidden-uniformizer flag or separate seed-channel oracle.",
        "alternative_seed_oracle_expected_binary_readouts_exact": "3/4",
        "alternative_seed_oracle_expected_binary_readouts": 0.75,
        "alternative_seed_oracle_contract": "If a separately available seed channel can be acquired, Bernoulli(2^-L) seed-oracle use and otherwise uniform output exactly simulates the unflagged experiment; this is outside the encoding lower bound.",
        "cheap_uniformizer_flag_contract": "If A0 is cheap observable metadata, acquire only when A0=0; this can also attain expected 3k*2^-L readouts and is excluded from the hidden-nuisance query contract.",
        "all_singleton_information_exactly_zero": true,
        "uniform_target_information_bits": 0.00376410755660513,
        "information_upper_bound_bits": 0.008100301559194709,
        "chi2_exact": "369/65536",
        "chi2": 0.0056304931640625,
        "zero_readout_deficiency_exact": "24813/1048576",
        "zero_readout_deficiency": 0.02366352081298828,
        "zero_readout_deficiency_upper_bound": 0.0625
      },
      {
        "blocks": 5,
        "target_dimension": 15,
        "uniformizer_dimension": 5,
        "exact_minimum_sufficient_alphabet": 32768,
        "minimum_expected_binary_queries_to_sufficiently_encode_Y": 15,
        "query_lower_bound_scope": "Prefix-free q-ary queries of one realized Y; no cheap hidden-uniformizer flag or separate seed-channel oracle.",
        "alternative_seed_oracle_expected_binary_readouts_exact": "15/32",
        "alternative_seed_oracle_expected_binary_readouts": 0.46875,
        "alternative_seed_oracle_contract": "If a separately available seed channel can be acquired, Bernoulli(2^-L) seed-oracle use and otherwise uniform output exactly simulates the unflagged experiment; this is outside the encoding lower bound.",
        "cheap_uniformizer_flag_contract": "If A0 is cheap observable metadata, acquire only when A0=0; this can also attain expected 3k*2^-L readouts and is excluded from the hidden-nuisance query contract.",
        "all_singleton_information_exactly_zero": true,
        "uniform_target_information_bits": 0.001357904787553977,
        "information_upper_bound_bits": 0.002887792269877051,
        "chi2_exact": "2101/1048576",
        "chi2": 0.0020036697387695312,
        "zero_readout_deficiency_exact": "110097/8388608",
        "zero_readout_deficiency": 0.013124585151672363,
        "zero_readout_deficiency_upper_bound": 0.03125
      },
      {
        "blocks": 6,
        "target_dimension": 18,
        "uniformizer_dimension": 6,
        "exact_minimum_sufficient_alphabet": 262144,
        "minimum_expected_binary_queries_to_sufficiently_encode_Y": 18,
        "query_lower_bound_scope": "Prefix-free q-ary queries of one realized Y; no cheap hidden-uniformizer flag or separate seed-channel oracle.",
        "alternative_seed_oracle_expected_binary_readouts_exact": "9/32",
        "alternative_seed_oracle_expected_binary_readouts": 0.28125,
        "alternative_seed_oracle_contract": "If a separately available seed channel can be acquired, Bernoulli(2^-L) seed-oracle use and otherwise uniform output exactly simulates the unflagged experiment; this is outside the encoding lower bound.",
        "cheap_uniformizer_flag_contract": "If A0 is cheap observable metadata, acquire only when A0=0; this can also attain expected 3k*2^-L readouts and is excluded from the hidden-nuisance query contract.",
        "all_singleton_information_exactly_zero": true,
        "uniform_target_information_bits": 0.00047194835374961085,
        "information_upper_bound_bits": 0.0009910535128422298,
        "chi2_exact": "11529/16777216",
        "chi2": 0.0006871819496154785,
        "zero_readout_deficiency_exact": "3825333/536870912",
        "zero_readout_deficiency": 0.0071252379566431046,
        "zero_readout_deficiency_upper_bound": 0.015625
      },
      {
        "blocks": 7,
        "target_dimension": 21,
        "uniformizer_dimension": 7,
        "exact_minimum_sufficient_alphabet": 2097152,
        "minimum_expected_binary_queries_to_sufficiently_encode_Y": 21,
        "query_lower_bound_scope": "Prefix-free q-ary queries of one realized Y; no cheap hidden-uniformizer flag or separate seed-channel oracle.",
        "alternative_seed_oracle_expected_binary_readouts_exact": "21/128",
        "alternative_seed_oracle_expected_binary_readouts": 0.1640625,
        "alternative_seed_oracle_contract": "If a separately available seed channel can be acquired, Bernoulli(2^-L) seed-oracle use and otherwise uniform output exactly simulates the unflagged experiment; this is outside the encoding lower bound.",
        "cheap_uniformizer_flag_contract": "If A0 is cheap observable metadata, acquire only when A0=0; this can also attain expected 3k*2^-L readouts and is excluded from the hidden-nuisance query contract.",
        "all_singleton_information_exactly_zero": true,
        "uniform_target_information_bits": 0.0001597785793852491,
        "information_upper_bound_bits": 0.0003317862469880793,
        "chi2_exact": "61741/268435456",
        "chi2": 0.00023000314831733704,
        "zero_readout_deficiency_exact": "130994307/34359738368",
        "zero_readout_deficiency": 0.003812436101725325,
        "zero_readout_deficiency_upper_bound": 0.0078125
      },
      {
        "blocks": 8,
        "target_dimension": 24,
        "uniformizer_dimension": 8,
        "exact_minimum_sufficient_alphabet": 16777216,
        "minimum_expected_binary_queries_to_sufficiently_encode_Y": 24,
        "query_lower_bound_scope": "Prefix-free q-ary queries of one realized Y; no cheap hidden-uniformizer flag or separate seed-channel oracle.",
        "alternative_seed_oracle_expected_binary_readouts_exact": "3/32",
        "alternative_seed_oracle_expected_binary_readouts": 0.09375,
        "alternative_seed_oracle_contract": "If a separately available seed channel can be acquired, Bernoulli(2^-L) seed-oracle use and otherwise uniform output exactly simulates the unflagged experiment; this is outside the encoding lower bound.",
        "cheap_uniformizer_flag_contract": "If A0 is cheap observable metadata, acquire only when A0=0; this can also attain expected 3k*2^-L readouts and is excluded from the hidden-nuisance query contract.",
        "all_singleton_information_exactly_zero": true,
        "uniform_target_information_bits": 5.3067413347554113e-05,
        "information_upper_bound_bits": 0.0001091944378372626,
        "chi2_exact": "325089/4294967296",
        "chi2": 7.569068111479282e-05,
        "zero_readout_deficiency_exact": "2219440149/1099511627776",
        "zero_readout_deficiency": 0.0020185690564176184,
        "zero_readout_deficiency_upper_bound": 0.00390625
      },
      {
        "blocks": 9,
        "target_dimension": 27,
        "uniformizer_dimension": 9,
        "exact_minimum_sufficient_alphabet": 134217728,
        "minimum_expected_binary_queries_to_sufficiently_encode_Y": 27,
        "query_lower_bound_scope": "Prefix-free q-ary queries of one realized Y; no cheap hidden-uniformizer flag or separate seed-channel oracle.",
        "alternative_seed_oracle_expected_binary_readouts_exact": "27/512",
        "alternative_seed_oracle_expected_binary_readouts": 0.052734375,
        "alternative_seed_oracle_contract": "If a separately available seed channel can be acquired, Bernoulli(2^-L) seed-oracle use and otherwise uniform output exactly simulates the unflagged experiment; this is outside the encoding lower bound.",
        "cheap_uniformizer_flag_contract": "If A0 is cheap observable metadata, acquire only when A0=0; this can also attain expected 3k*2^-L readouts and is excluded from the hidden-nuisance query contract.",
        "all_singleton_information_exactly_zero": true,
        "uniform_target_information_bits": 1.7376309845441023e-05,
        "information_upper_bound_bits": 3.549997764882141e-05,
        "chi2_exact": "1690981/68719476736",
        "chi2": 2.4607012164779007e-05,
        "zero_readout_deficiency_exact": "4663345203/4398046511104",
        "zero_readout_deficiency": 0.0010603219386666751,
        "zero_readout_deficiency_upper_bound": 0.001953125
      },
      {
        "blocks": 10,
        "target_dimension": 30,
        "uniformizer_dimension": 10,
        "exact_minimum_sufficient_alphabet": 1073741824,
        "minimum_expected_binary_queries_to_sufficiently_encode_Y": 30,
        "query_lower_bound_scope": "Prefix-free q-ary queries of one realized Y; no cheap hidden-uniformizer flag or separate seed-channel oracle.",
        "alternative_seed_oracle_expected_binary_readouts_exact": "15/512",
        "alternative_seed_oracle_expected_binary_readouts": 0.029296875,
        "alternative_seed_oracle_contract": "If a separately available seed channel can be acquired, Bernoulli(2^-L) seed-oracle use and otherwise uniform output exactly simulates the unflagged experiment; this is outside the encoding lower bound.",
        "cheap_uniformizer_flag_contract": "If A0 is cheap observable metadata, acquire only when A0=0; this can also attain expected 3k*2^-L readouts and is excluded from the hidden-nuisance query contract.",
        "all_singleton_information_exactly_zero": true,
        "uniform_target_information_bits": 5.629109118957922e-06,
        "information_upper_bound_bits": 1.1437799468351623e-05,
        "chi2_exact": "8717049/1099511627776",
        "chi2": 7.928109880595002e-06,
        "zero_readout_deficiency_exact": "155803303251/281474976710656",
        "zero_readout_deficiency": 0.0005535245266621303,
        "zero_readout_deficiency_upper_bound": 0.0009765625
      },
      {
        "blocks": 11,
        "target_dimension": 33,
        "uniformizer_dimension": 11,
        "exact_minimum_sufficient_alphabet": 8589934592,
        "minimum_expected_binary_queries_to_sufficiently_encode_Y": 33,
        "query_lower_bound_scope": "Prefix-free q-ary queries of one realized Y; no cheap hidden-uniformizer flag or separate seed-channel oracle.",
        "alternative_seed_oracle_expected_binary_readouts_exact": "33/2048",
        "alternative_seed_oracle_expected_binary_readouts": 0.01611328125,
        "alternative_seed_oracle_contract": "If a separately available seed channel can be acquired, Bernoulli(2^-L) seed-oracle use and otherwise uniform output exactly simulates the unflagged experiment; this is outside the encoding lower bound.",
        "cheap_uniformizer_flag_contract": "If A0 is cheap observable metadata, acquire only when A0=0; this can also attain expected 3k*2^-L readouts and is excluded from the hidden-nuisance query contract.",
        "all_singleton_information_exactly_zero": true,
        "uniform_target_information_bits": 1.808826355650987e-06,
        "information_upper_bound_bits": 3.660313184683359e-06,
        "chi2_exact": "44633821/17592186044416",
        "chi2": 2.537138982461329e-06,
        "zero_readout_deficiency_exact": "5179548661767/18014398509481984",
        "zero_readout_deficiency": 0.00028752270907300703,
        "zero_readout_deficiency_upper_bound": 0.00048828125
      },
      {
        "blocks": 12,
        "target_dimension": 36,
        "uniformizer_dimension": 12,
        "exact_minimum_sufficient_alphabet": 68719476736,
        "minimum_expected_binary_queries_to_sufficiently_encode_Y": 36,
        "query_lower_bound_scope": "Prefix-free q-ary queries of one realized Y; no cheap hidden-uniformizer flag or separate seed-channel oracle.",
        "alternative_seed_oracle_expected_binary_readouts_exact": "9/1024",
        "alternative_seed_oracle_expected_binary_readouts": 0.0087890625,
        "alternative_seed_oracle_contract": "If a separately available seed channel can be acquired, Bernoulli(2^-L) seed-oracle use and otherwise uniform output exactly simulates the unflagged experiment; this is outside the encoding lower bound.",
        "cheap_uniformizer_flag_contract": "If A0 is cheap observable metadata, acquire only when A0=0; this can also attain expected 3k*2^-L readouts and is excluded from the hidden-nuisance query contract.",
        "all_singleton_information_exactly_zero": true,
        "uniform_target_information_bits": 5.776469617391241e-07,
        "information_upper_bound_bits": 1.165346681962837e-06,
        "chi2_exact": "227363409/281474976710656",
        "chi2": 8.077570932130129e-07,
        "zero_readout_deficiency_exact": "85743757826397/576460752303423488",
        "zero_readout_deficiency": 0.00014874170961992096,
        "zero_readout_deficiency_upper_bound": 0.000244140625
      },
      {
        "blocks": 13,
        "target_dimension": 39,
        "uniformizer_dimension": 13,
        "exact_minimum_sufficient_alphabet": 549755813888,
        "minimum_expected_binary_queries_to_sufficiently_encode_Y": 39,
        "query_lower_bound_scope": "Prefix-free q-ary queries of one realized Y; no cheap hidden-uniformizer flag or separate seed-channel oracle.",
        "alternative_seed_oracle_expected_binary_readouts_exact": "39/8192",
        "alternative_seed_oracle_expected_binary_readouts": 0.0047607421875,
        "alternative_seed_oracle_contract": "If a separately available seed channel can be acquired, Bernoulli(2^-L) seed-oracle use and otherwise uniform output exactly simulates the unflagged experiment; this is outside the encoding lower bound.",
        "cheap_uniformizer_flag_contract": "If A0 is cheap observable metadata, acquire only when A0=0; this can also attain expected 3k*2^-L readouts and is excluded from the hidden-nuisance query contract.",
        "all_singleton_information_exactly_zero": true,
        "uniform_target_information_bits": 1.835950499457662e-07,
        "information_upper_bound_bits": 3.6954539570420805e-07,
        "chi2_exact": "1153594261/4503599627370496",
        "chi2": 2.5614938192752845e-07,
        "zero_readout_deficiency_exact": "2829190226733315/36893488147419103232",
        "zero_readout_deficiency": 7.668535475497542e-05,
        "zero_readout_deficiency_upper_bound": 0.0001220703125
      },
      {
        "blocks": 14,
        "target_dimension": 42,
        "uniformizer_dimension": 14,
        "exact_minimum_sufficient_alphabet": 4398046511104,
        "minimum_expected_binary_queries_to_sufficiently_encode_Y": 42,
        "query_lower_bound_scope": "Prefix-free q-ary queries of one realized Y; no cheap hidden-uniformizer flag or separate seed-channel oracle.",
        "alternative_seed_oracle_expected_binary_readouts_exact": "21/8192",
        "alternative_seed_oracle_expected_binary_readouts": 0.0025634765625,
        "alternative_seed_oracle_contract": "If a separately available seed channel can be acquired, Bernoulli(2^-L) seed-oracle use and otherwise uniform output exactly simulates the unflagged experiment; this is outside the encoding lower bound.",
        "cheap_uniformizer_flag_contract": "If A0 is cheap observable metadata, acquire only when A0=0; this can also attain expected 3k*2^-L readouts and is excluded from the hidden-nuisance query contract.",
        "all_singleton_information_exactly_zero": true,
        "uniform_target_information_bits": 5.8138505843225554e-08,
        "information_upper_bound_bits": 1.1682656067768062e-07,
        "chi2_exact": "5835080169/72057594037927936",
        "chi2": 8.097800442696812e-08,
        "zero_readout_deficiency_exact": "46541247274219725/1180591620717411303424",
        "zero_readout_deficiency": 3.942196984757351e-05,
        "zero_readout_deficiency_upper_bound": 6.103515625e-05
      },
      {
        "blocks": 15,
        "target_dimension": 45,
        "uniformizer_dimension": 15,
        "exact_minimum_sufficient_alphabet": 35184372088832,
        "minimum_expected_binary_queries_to_sufficiently_encode_Y": 45,
        "query_lower_bound_scope": "Prefix-free q-ary queries of one realized Y; no cheap hidden-uniformizer flag or separate seed-channel oracle.",
        "alternative_seed_oracle_expected_binary_readouts_exact": "45/32768",
        "alternative_seed_oracle_expected_binary_readouts": 0.001373291015625,
        "alternative_seed_oracle_contract": "If a separately available seed channel can be acquired, Bernoulli(2^-L) seed-oracle use and otherwise uniform output exactly simulates the unflagged experiment; this is outside the encoding lower bound.",
        "cheap_uniformizer_flag_contract": "If A0 is cheap observable metadata, acquire only when A0=0; this can also attain expected 3k*2^-L readouts and is excluded from the hidden-nuisance query contract.",
        "all_singleton_information_exactly_zero": true,
        "uniform_target_information_bits": 1.8358183403894668e-08,
        "information_upper_bound_bits": 3.684420483445418e-08,
        "chi2_exact": "29443836301/1152921504606846976",
        "chi2": 2.5538457027081407e-08,
        "zero_readout_deficiency_exact": "381864694850077185/18889465931478580854784",
        "zero_readout_deficiency": 2.0215748620701558e-05,
        "zero_readout_deficiency_upper_bound": 3.0517578125e-05
      },
      {
        "blocks": 16,
        "target_dimension": 48,
        "uniformizer_dimension": 16,
        "exact_minimum_sufficient_alphabet": 281474976710656,
        "minimum_expected_binary_queries_to_sufficiently_encode_Y": 48,
        "query_lower_bound_scope": "Prefix-free q-ary queries of one realized Y; no cheap hidden-uniformizer flag or separate seed-channel oracle.",
        "alternative_seed_oracle_expected_binary_readouts_exact": "3/4096",
        "alternative_seed_oracle_expected_binary_readouts": 0.000732421875,
        "alternative_seed_oracle_contract": "If a separately available seed channel can be acquired, Bernoulli(2^-L) seed-oracle use and otherwise uniform output exactly simulates the unflagged experiment; this is outside the encoding lower bound.",
        "cheap_uniformizer_flag_contract": "If A0 is cheap observable metadata, acquire only when A0=0; this can also attain expected 3k*2^-L readouts and is excluded from the hidden-nuisance query contract.",
        "all_singleton_information_exactly_zero": true,
        "uniform_target_information_bits": 5.784058730987646e-09,
        "information_upper_bound_bits": 1.1597790014913883e-08,
        "chi2_exact": "148292923329/18446744073709551616",
        "chi2": 8.038975481876407e-09,
        "zero_readout_deficiency_exact": "12505779216837064773/1208925819614629174706176",
        "zero_readout_deficiency": 1.0344538113036206e-05,
        "zero_readout_deficiency_upper_bound": 1.52587890625e-05
      },
      {
        "blocks": 17,
        "target_dimension": 51,
        "uniformizer_dimension": 17,
        "exact_minimum_sufficient_alphabet": 2251799813685248,
        "minimum_expected_binary_queries_to_sufficiently_encode_Y": 51,
        "query_lower_bound_scope": "Prefix-free q-ary queries of one realized Y; no cheap hidden-uniformizer flag or separate seed-channel oracle.",
        "alternative_seed_oracle_expected_binary_readouts_exact": "51/131072",
        "alternative_seed_oracle_expected_binary_readouts": 0.00038909912109375,
        "alternative_seed_oracle_contract": "If a separately available seed channel can be acquired, Bernoulli(2^-L) seed-oracle use and otherwise uniform output exactly simulates the unflagged experiment; this is outside the encoding lower bound.",
        "cheap_uniformizer_flag_contract": "If A0 is cheap observable metadata, acquire only when A0=0; this can also attain expected 3k*2^-L readouts and is excluded from the hidden-nuisance query contract.",
        "all_singleton_information_exactly_zero": true,
        "uniform_target_information_bits": 1.8192136512073742e-09,
        "information_upper_bound_bits": 3.645303365558505e-09,
        "chi2_exact": "745759583941/295147905179352825856",
        "chi2": 2.526731753314744e-09,
        "zero_readout_deficiency_exact": "25549322106933038781/4835703278458516698824704",
        "zero_readout_deficiency": 5.283475977681871e-06,
        "zero_readout_deficiency_upper_bound": 7.62939453125e-06
      },
      {
        "blocks": 18,
        "target_dimension": 54,
        "uniformizer_dimension": 18,
        "exact_minimum_sufficient_alphabet": 18014398509481984,
        "minimum_expected_binary_queries_to_sufficiently_encode_Y": 54,
        "query_lower_bound_scope": "Prefix-free q-ary queries of one realized Y; no cheap hidden-uniformizer flag or separate seed-channel oracle.",
        "alternative_seed_oracle_expected_binary_readouts_exact": "27/131072",
        "alternative_seed_oracle_expected_binary_readouts": 0.00020599365234375,
        "alternative_seed_oracle_contract": "If a separately available seed channel can be acquired, Bernoulli(2^-L) seed-oracle use and otherwise uniform output exactly simulates the unflagged experiment; this is outside the encoding lower bound.",
        "cheap_uniformizer_flag_contract": "If A0 is cheap observable metadata, acquire only when A0=0; this can also attain expected 3k*2^-L readouts and is excluded from the hidden-nuisance query contract.",
        "all_singleton_information_exactly_zero": true,
        "uniform_target_information_bits": 5.714071714262822e-10,
        "information_upper_bound_bits": 1.1444057967061605e-09,
        "chi2_exact": "3745977788889/4722366482869645213696",
        "chi2": 7.932416517179492e-10,
        "zero_readout_deficiency_exact": "416891007338622809751/154742504910672534362390528",
        "zero_readout_deficiency": 2.6940949907672717e-06,
        "zero_readout_deficiency_upper_bound": 3.814697265625e-06
      },
      {
        "blocks": 19,
        "target_dimension": 57,
        "uniformizer_dimension": 19,
        "exact_minimum_sufficient_alphabet": 144115188075855872,
        "minimum_expected_binary_queries_to_sufficiently_encode_Y": 57,
        "query_lower_bound_scope": "Prefix-free q-ary queries of one realized Y; no cheap hidden-uniformizer flag or separate seed-channel oracle.",
        "alternative_seed_oracle_expected_binary_readouts_exact": "57/524288",
        "alternative_seed_oracle_expected_binary_readouts": 0.0001087188720703125,
        "alternative_seed_oracle_contract": "If a separately available seed channel can be acquired, Bernoulli(2^-L) seed-oracle use and otherwise uniform output exactly simulates the unflagged experiment; this is outside the encoding lower bound.",
        "cheap_uniformizer_flag_contract": "If A0 is cheap observable metadata, acquire only when A0=0; this can also attain expected 3k*2^-L readouts and is excluded from the hidden-nuisance query contract.",
        "all_singleton_information_exactly_zero": true,
        "uniform_target_information_bits": 1.7928546763373366e-10,
        "information_upper_bound_bits": 3.589389350638284e-10,
        "chi2_exact": "18798608421181/75557863725914323419136",
        "chi2": 2.4879751086363206e-10,
        "zero_readout_deficiency_exact": "3396263946349773448035/2475880078570760549798248448",
        "zero_readout_deficiency": 1.3717400837565276e-06,
        "zero_readout_deficiency_upper_bound": 1.9073486328125e-06
      },
      {
        "blocks": 20,
        "target_dimension": 60,
        "uniformizer_dimension": 20,
        "exact_minimum_sufficient_alphabet": 1152921504606846976,
        "minimum_expected_binary_queries_to_sufficiently_encode_Y": 60,
        "query_lower_bound_scope": "Prefix-free q-ary queries of one realized Y; no cheap hidden-uniformizer flag or separate seed-channel oracle.",
        "alternative_seed_oracle_expected_binary_readouts_exact": "15/262144",
        "alternative_seed_oracle_expected_binary_readouts": 5.7220458984375e-05,
        "alternative_seed_oracle_contract": "If a separately available seed channel can be acquired, Bernoulli(2^-L) seed-oracle use and otherwise uniform output exactly simulates the unflagged experiment; this is outside the encoding lower bound.",
        "cheap_uniformizer_flag_contract": "If A0 is cheap observable metadata, acquire only when A0=0; this can also attain expected 3k*2^-L readouts and is excluded from the hidden-nuisance query contract.",
        "all_singleton_information_exactly_zero": true,
        "uniform_target_information_bits": 5.620570673846415e-11,
        "information_upper_bound_bits": 1.124964480910046e-10,
        "chi2_exact": "94267920012849/1208925819614629174706176",
        "chi2": 7.797659582032825e-11,
        "zero_readout_deficiency_exact": "221057196795688744395387/316912650057057350374175801344",
        "zero_readout_deficiency": 6.975335214794655e-07,
        "zero_readout_deficiency_upper_bound": 9.5367431640625e-07
      },
      {
        "blocks": 21,
        "target_dimension": 63,
        "uniformizer_dimension": 21,
        "exact_minimum_sufficient_alphabet": 9223372036854775808,
        "minimum_expected_binary_queries_to_sufficiently_encode_Y": 63,
        "query_lower_bound_scope": "Prefix-free q-ary queries of one realized Y; no cheap hidden-uniformizer flag or separate seed-channel oracle.",
        "alternative_seed_oracle_expected_binary_readouts_exact": "63/2097152",
        "alternative_seed_oracle_expected_binary_readouts": 3.0040740966796875e-05,
        "alternative_seed_oracle_contract": "If a separately available seed channel can be acquired, Bernoulli(2^-L) seed-oracle use and otherwise uniform output exactly simulates the unflagged experiment; this is outside the encoding lower bound.",
        "cheap_uniformizer_flag_contract": "If A0 is cheap observable metadata, acquire only when A0=0; this can also attain expected 3k*2^-L readouts and is excluded from the hidden-nuisance query contract.",
        "all_singleton_information_exactly_zero": true,
        "uniform_target_information_bits": 1.760875460756701e-11,
        "information_upper_bound_bits": 3.5237147747876914e-11,
        "chi2_exact": "472439111692021/19342813113834066795298816",
        "chi2": 2.4424529612713387e-11,
        "zero_readout_deficiency_exact": "1796431366517053636999467/5070602400912917605986812821504",
        "zero_readout_deficiency": 3.5428361848951555e-07,
        "zero_readout_deficiency_upper_bound": 4.76837158203125e-07
      },
      {
        "blocks": 22,
        "target_dimension": 66,
        "uniformizer_dimension": 22,
        "exact_minimum_sufficient_alphabet": 73786976294838206464,
        "minimum_expected_binary_queries_to_sufficiently_encode_Y": 66,
        "query_lower_bound_scope": "Prefix-free q-ary queries of one realized Y; no cheap hidden-uniformizer flag or separate seed-channel oracle.",
        "alternative_seed_oracle_expected_binary_readouts_exact": "33/2097152",
        "alternative_seed_oracle_expected_binary_readouts": 1.5735626220703125e-05,
        "alternative_seed_oracle_contract": "If a separately available seed channel can be acquired, Bernoulli(2^-L) seed-oracle use and otherwise uniform output exactly simulates the unflagged experiment; this is outside the encoding lower bound.",
        "cheap_uniformizer_flag_contract": "If A0 is cheap observable metadata, acquire only when A0=0; this can also attain expected 3k*2^-L readouts and is excluded from the hidden-nuisance query contract.",
        "all_singleton_information_exactly_zero": true,
        "uniform_target_information_bits": 5.513788516663325e-12,
        "information_upper_bound_bits": 1.1032110600928247e-11,
        "chi2_exact": "2366593604971209/309485009821345068724781056",
        "chi2": 7.646876358688135e-12,
        "zero_readout_deficiency_exact": "116667385105619650393173969/649037107316853453566312041152512",
        "zero_readout_deficiency": 1.797545684066162e-07,
        "zero_readout_deficiency_upper_bound": 2.384185791015625e-07
      },
      {
        "blocks": 23,
        "target_dimension": 69,
        "uniformizer_dimension": 23,
        "exact_minimum_sufficient_alphabet": 590295810358705651712,
        "minimum_expected_binary_queries_to_sufficiently_encode_Y": 69,
        "query_lower_bound_scope": "Prefix-free q-ary queries of one realized Y; no cheap hidden-uniformizer flag or separate seed-channel oracle.",
        "alternative_seed_oracle_expected_binary_readouts_exact": "69/8388608",
        "alternative_seed_oracle_expected_binary_readouts": 8.225440979003906e-06,
        "alternative_seed_oracle_contract": "If a separately available seed channel can be acquired, Bernoulli(2^-L) seed-oracle use and otherwise uniform output exactly simulates the unflagged experiment; this is outside the encoding lower bound.",
        "cheap_uniformizer_flag_contract": "If A0 is cheap observable metadata, acquire only when A0=0; this can also attain expected 3k*2^-L readouts and is excluded from the hidden-nuisance query contract.",
        "all_singleton_information_exactly_zero": true,
        "uniform_target_information_bits": 1.725806905850529e-12,
        "information_upper_bound_bits": 3.452660045205231e-12,
        "chi2_exact": "11850560210900461/4951760157141521099596496896",
        "chi2": 2.3932015757688426e-12,
        "zero_readout_deficiency_exact": "1892406978409974216532522173/20769187434139310514121985316880384",
        "zero_readout_deficiency": 9.111608166717847e-08,
        "zero_readout_deficiency_upper_bound": 1.1920928955078125e-07
      },
      {
        "blocks": 24,
        "target_dimension": 72,
        "uniformizer_dimension": 24,
        "exact_minimum_sufficient_alphabet": 4722366482869645213696,
        "minimum_expected_binary_queries_to_sufficiently_encode_Y": 72,
        "query_lower_bound_scope": "Prefix-free q-ary queries of one realized Y; no cheap hidden-uniformizer flag or separate seed-channel oracle.",
        "alternative_seed_oracle_expected_binary_readouts_exact": "9/2097152",
        "alternative_seed_oracle_expected_binary_readouts": 4.291534423828125e-06,
        "alternative_seed_oracle_contract": "If a separately available seed channel can be acquired, Bernoulli(2^-L) seed-oracle use and otherwise uniform output exactly simulates the unflagged experiment; this is outside the encoding lower bound.",
        "cheap_uniformizer_flag_contract": "If A0 is cheap observable metadata, acquire only when A0=0; this can also attain expected 3k*2^-L readouts and is excluded from the hidden-nuisance query contract.",
        "all_singleton_information_exactly_zero": true,
        "uniform_target_information_bits": 5.399981263724517e-13,
        "information_upper_bound_bits": 1.0802376347290472e-12,
        "chi2_exact": "59323169798679969/79228162514264337593543950336",
        "chi2": 7.487636708474635e-13,
        "zero_readout_deficiency_exact": "30669280291515173907620210949/664613997892457936451903530140172288",
        "zero_readout_deficiency": 4.61460041298706e-08,
        "zero_readout_deficiency_upper_bound": 5.960464477539063e-08
      }
    ],
    "exact_reconstruction_pass_count": 91,
    "exact_minimal_profile_pass_count": 91,
    "fourier_max_abs_error": 2.2084876237282098e-16,
    "curated_results": [
      {
        "name": "shared_linear_parity_q2",
        "q": 2,
        "m": 3,
        "source_dimensions": [
          1,
          1
        ],
        "balanced_frequency_count": 2,
        "minimal_readout_rank": 1,
        "minimum_sufficient_alphabet": 2,
        "quotient_rows": [
          [
            1,
            1,
            1
          ]
        ],
        "local_informative": [
          false,
          false,
          false
        ],
        "uniform_target_information_bits": 1.0,
        "fourier_max_abs_error": 6.123233995736766e-17,
        "exact_integer_reconstruction": true,
        "exact_profile_minimality": true,
        "noise_numerators": [
          {
            "point": [
              0,
              0,
              0
            ],
            "count": 1
          },
          {
            "point": [
              0,
              0,
              1
            ],
            "count": 0
          },
          {
            "point": [
              0,
              1,
              0
            ],
            "count": 0
          },
          {
            "point": [
              0,
              1,
              1
            ],
            "count": 1
          },
          {
            "point": [
              1,
              0,
              0
            ],
            "count": 0
          },
          {
            "point": [
              1,
              0,
              1
            ],
            "count": 1
          },
          {
            "point": [
              1,
              1,
              0
            ],
            "count": 1
          },
          {
            "point": [
              1,
              1,
              1
            ],
            "count": 0
          }
        ],
        "noise_denominator": 4
      },
      {
        "name": "shared_linear_parity_q3",
        "q": 3,
        "m": 3,
        "source_dimensions": [
          1,
          1
        ],
        "balanced_frequency_count": 3,
        "minimal_readout_rank": 1,
        "minimum_sufficient_alphabet": 3,
        "quotient_rows": [
          [
            1,
            1,
            1
          ]
        ],
        "local_informative": [
          false,
          false,
          false
        ],
        "uniform_target_information_bits": 1.584962500721156,
        "fourier_max_abs_error": 1.5797546573185213e-16,
        "exact_integer_reconstruction": true,
        "exact_profile_minimality": true,
        "noise_numerators": [
          {
            "point": [
              0,
              0,
              0
            ],
            "count": 1
          },
          {
            "point": [
              0,
              0,
              1
            ],
            "count": 0
          },
          {
            "point": [
              0,
              0,
              2
            ],
            "count": 0
          },
          {
            "point": [
              0,
              1,
              0
            ],
            "count": 0
          },
          {
            "point": [
              0,
              1,
              1
            ],
            "count": 0
          },
          {
            "point": [
              0,
              1,
              2
            ],
            "count": 1
          },
          {
            "point": [
              0,
              2,
              0
            ],
            "count": 0
          },
          {
            "point": [
              0,
              2,
              1
            ],
            "count": 1
          },
          {
            "point": [
              0,
              2,
              2
            ],
            "count": 0
          },
          {
            "point": [
              1,
              0,
              0
            ],
            "count": 0
          },
          {
            "point": [
              1,
              0,
              1
            ],
            "count": 0
          },
          {
            "point": [
              1,
              0,
              2
            ],
            "count": 1
          },
          {
            "point": [
              1,
              1,
              0
            ],
            "count": 0
          },
          {
            "point": [
              1,
              1,
              1
            ],
            "count": 1
          },
          {
            "point": [
              1,
              1,
              2
            ],
            "count": 0
          },
          {
            "point": [
              1,
              2,
              0
            ],
            "count": 1
          },
          {
            "point": [
              1,
              2,
              1
            ],
            "count": 0
          },
          {
            "point": [
              1,
              2,
              2
            ],
            "count": 0
          },
          {
            "point": [
              2,
              0,
              0
            ],
            "count": 0
          },
          {
            "point": [
              2,
              0,
              1
            ],
            "count": 1
          },
          {
            "point": [
              2,
              0,
              2
            ],
            "count": 0
          },
          {
            "point": [
              2,
              1,
              0
            ],
            "count": 1
          },
          {
            "point": [
              2,
              1,
              1
            ],
            "count": 0
          },
          {
            "point": [
              2,
              1,
              2
            ],
            "count": 0
          },
          {
            "point": [
              2,
              2,
              0
            ],
            "count": 0
          },
          {
            "point": [
              2,
              2,
              1
            ],
            "count": 0
          },
          {
            "point": [
              2,
              2,
              2
            ],
            "count": 1
          }
        ],
        "noise_denominator": 9
      },
      {
        "name": "shared_common_mask",
        "q": 2,
        "m": 3,
        "source_dimensions": [
          1,
          1
        ],
        "balanced_frequency_count": 4,
        "minimal_readout_rank": 2,
        "minimum_sufficient_alphabet": 4,
        "quotient_rows": [
          [
            1,
            0,
            1
          ],
          [
            0,
            1,
            1
          ]
        ],
        "local_informative": [
          false,
          false,
          false
        ],
        "uniform_target_information_bits": 2.0,
        "fourier_max_abs_error": 6.123233995736766e-17,
        "exact_integer_reconstruction": true,
        "exact_profile_minimality": true,
        "noise_numerators": [
          {
            "point": [
              0,
              0,
              0
            ],
            "count": 2
          },
          {
            "point": [
              0,
              0,
              1
            ],
            "count": 0
          },
          {
            "point": [
              0,
              1,
              0
            ],
            "count": 0
          },
          {
            "point": [
              0,
              1,
              1
            ],
            "count": 0
          },
          {
            "point": [
              1,
              0,
              0
            ],
            "count": 0
          },
          {
            "point": [
              1,
              0,
              1
            ],
            "count": 0
          },
          {
            "point": [
              1,
              1,
              0
            ],
            "count": 0
          },
          {
            "point": [
              1,
              1,
              1
            ],
            "count": 2
          }
        ],
        "noise_denominator": 4
      },
      {
        "name": "hidden_joint_interactions_full_rank",
        "q": 2,
        "m": 3,
        "source_dimensions": [
          2,
          2
        ],
        "balanced_frequency_count": 5,
        "minimal_readout_rank": 3,
        "minimum_sufficient_alphabet": 8,
        "quotient_rows": [
          [
            1,
            0,
            0
          ],
          [
            0,
            1,
            0
          ],
          [
            0,
            0,
            1
          ]
        ],
        "local_informative": [
          false,
          false,
          false
        ],
        "uniform_target_information_bits": 0.17218046888521688,
        "fourier_max_abs_error": 6.123233995736765e-17,
        "exact_integer_reconstruction": true,
        "exact_profile_minimality": true,
        "noise_numerators": [
          {
            "point": [
              0,
              0,
              0
            ],
            "count": 4
          },
          {
            "point": [
              0,
              0,
              1
            ],
            "count": 1
          },
          {
            "point": [
              0,
              1,
              0
            ],
            "count": 1
          },
          {
            "point": [
              0,
              1,
              1
            ],
            "count": 2
          },
          {
            "point": [
              1,
              0,
              0
            ],
            "count": 1
          },
          {
            "point": [
              1,
              0,
              1
            ],
            "count": 2
          },
          {
            "point": [
              1,
              1,
              0
            ],
            "count": 2
          },
          {
            "point": [
              1,
              1,
              1
            ],
            "count": 3
          }
        ],
        "noise_denominator": 16
      }
    ],
    "scope": "Finite-field simulator theorem checks; no measured photonic or neural RSI result.",
    "execution_status": "PASS"
  },
  "contract_audit": {
    "status": "PASS",
    "seed": 461107,
    "random_contracts": 60,
    "sufficient_joint_models": 180,
    "missing_mean_rejections": 60,
    "missing_interface_rejections": 60,
    "maximum_reverse_mean_operator_error": 1.9433363136495265e-15,
    "maximum_reverse_joint_covariance_error": 2.460481661111946e-15,
    "maximum_necessity_information_identity_error": 7.160936003957117e-15,
    "approximate_joint_KL_checks": 60,
    "maximum_approximate_joint_KL_identity_error": 2.1316282072803006e-14,
    "minimum_missing_mean_pairwise_KL_loss": 0.4999999999999991,
    "minimum_missing_interface_pairwise_KL_loss": 0.08571822689509778,
    "theorem_scope": "Fixed equal noise, fixed Q, unknown H with mean closure S, all future linear noise couplings in E; one common reverse kernel. Exact real linear local mode minimum dim(S+E).",
    "excluded_claims": "No unequal-exposure composition, arbitrary receiver encodings, hardware savings, general RSI, or certified priority.",
    "approximate_records": [
      {
        "case": 0,
        "full_matrix_KL": 4.2878853729491215,
        "ledger_KL": 4.287885372949123,
        "mean_leak_squared": 7.1102079554257305,
        "covariance_logdet_leak": 1.4655627904725164,
        "Pinsker_TV_upper_bound": 1.0
      },
      {
        "case": 1,
        "full_matrix_KL": 7.179455920946927,
        "ledger_KL": 7.179455920946925,
        "mean_leak_squared": 8.500672275013253,
        "covariance_logdet_leak": 5.858239566880597,
        "Pinsker_TV_upper_bound": 1.0
      },
      {
        "case": 2,
        "full_matrix_KL": 8.019569666187554,
        "ledger_KL": 8.019569666187554,
        "mean_leak_squared": 12.117572037810216,
        "covariance_logdet_leak": 3.9215672945648907,
        "Pinsker_TV_upper_bound": 1.0
      },
      {
        "case": 3,
        "full_matrix_KL": 4.4519222913752845,
        "ledger_KL": 4.45192229137528,
        "mean_leak_squared": 2.127013518490728,
        "covariance_logdet_leak": 6.776831064259832,
        "Pinsker_TV_upper_bound": 1.0
      },
      {
        "case": 4,
        "full_matrix_KL": 13.772067968270536,
        "ledger_KL": 13.772067968270537,
        "mean_leak_squared": 24.8801552671631,
        "covariance_logdet_leak": 2.6639806693779735,
        "Pinsker_TV_upper_bound": 1.0
      },
      {
        "case": 5,
        "full_matrix_KL": 1.8786437751183291,
        "ledger_KL": 1.8786437751183287,
        "mean_leak_squared": 2.0242527395215197,
        "covariance_logdet_leak": 1.7330348107151377,
        "Pinsker_TV_upper_bound": 0.9691861986012618
      },
      {
        "case": 6,
        "full_matrix_KL": 7.816942895033902,
        "ledger_KL": 7.8169428950338995,
        "mean_leak_squared": 13.226684509497918,
        "covariance_logdet_leak": 2.4072012805698813,
        "Pinsker_TV_upper_bound": 1.0
      },
      {
        "case": 7,
        "full_matrix_KL": 10.282212813604692,
        "ledger_KL": 10.282212813604696,
        "mean_leak_squared": 16.260249756756387,
        "covariance_logdet_leak": 4.304175870453005,
        "Pinsker_TV_upper_bound": 1.0
      },
      {
        "case": 8,
        "full_matrix_KL": 2.011042959146211,
        "ledger_KL": 2.0110429591462116,
        "mean_leak_squared": 0.4814755675077865,
        "covariance_logdet_leak": 3.5406103507846365,
        "Pinsker_TV_upper_bound": 1.0
      },
      {
        "case": 9,
        "full_matrix_KL": 55.89274672667102,
        "ledger_KL": 55.89274672667104,
        "mean_leak_squared": 108.70168200746177,
        "covariance_logdet_leak": 3.0838114458803196,
        "Pinsker_TV_upper_bound": 1.0
      },
      {
        "case": 10,
        "full_matrix_KL": 5.592490606673724,
        "ledger_KL": 5.592490606673726,
        "mean_leak_squared": 3.0505802357354437,
        "covariance_logdet_leak": 8.134400977612009,
        "Pinsker_TV_upper_bound": 1.0
      },
      {
        "case": 11,
        "full_matrix_KL": 1.3533864224836254,
        "ledger_KL": 1.3533864224836263,
        "mean_leak_squared": 0.605323367600933,
        "covariance_logdet_leak": 2.1014494773663195,
        "Pinsker_TV_upper_bound": 0.8226136463989722
      },
      {
        "case": 12,
        "full_matrix_KL": 1.2217788330227557,
        "ledger_KL": 1.221778833022756,
        "mean_leak_squared": 0.005735567279034414,
        "covariance_logdet_leak": 2.4378220987664774,
        "Pinsker_TV_upper_bound": 0.7815941507658422
      },
      {
        "case": 13,
        "full_matrix_KL": 1.8626994422891379,
        "ledger_KL": 1.8626994422891374,
        "mean_leak_squared": 2.760569498059373,
        "covariance_logdet_leak": 0.9648293865189019,
        "Pinsker_TV_upper_bound": 0.9650646201910879
      },
      {
        "case": 14,
        "full_matrix_KL": 2.9464326073390255,
        "ledger_KL": 2.946432607339025,
        "mean_leak_squared": 4.133721812529003,
        "covariance_logdet_leak": 1.7591434021490473,
        "Pinsker_TV_upper_bound": 1.0
      },
      {
        "case": 15,
        "full_matrix_KL": 9.355082412385897,
        "ledger_KL": 9.355082412385894,
        "mean_leak_squared": 15.994407141639593,
        "covariance_logdet_leak": 2.7157576831321957,
        "Pinsker_TV_upper_bound": 1.0
      },
      {
        "case": 16,
        "full_matrix_KL": 24.120939897458015,
        "ledger_KL": 24.12093989745801,
        "mean_leak_squared": 42.004428809879904,
        "covariance_logdet_leak": 6.237450985036116,
        "Pinsker_TV_upper_bound": 1.0
      },
      {
        "case": 17,
        "full_matrix_KL": 3.5986276947659257,
        "ledger_KL": 3.598627694765931,
        "mean_leak_squared": 0.21358896505535416,
        "covariance_logdet_leak": 6.983666424476508,
        "Pinsker_TV_upper_bound": 1.0
      },
      {
        "case": 18,
        "full_matrix_KL": 0.8761066238363955,
        "ledger_KL": 0.8761066238363966,
        "mean_leak_squared": 0.43538157501612423,
        "covariance_logdet_leak": 1.316831672656669,
        "Pinsker_TV_upper_bound": 0.6618559600987199
      },
      {
        "case": 19,
        "full_matrix_KL": 12.515771236802268,
        "ledger_KL": 12.515771236802262,
        "mean_leak_squared": 22.921972426768527,
        "covariance_logdet_leak": 2.109570046835998,
        "Pinsker_TV_upper_bound": 1.0
      },
      {
        "case": 20,
        "full_matrix_KL": 2.9887318622423438,
        "ledger_KL": 2.9887318622423416,
        "mean_leak_squared": 4.087735394114065,
        "covariance_logdet_leak": 1.8897283303706178,
        "Pinsker_TV_upper_bound": 1.0
      },
      {
        "case": 21,
        "full_matrix_KL": 0.940507294625669,
        "ledger_KL": 0.9405072946256675,
        "mean_leak_squared": 1.0801387159680051,
        "covariance_logdet_leak": 0.8008758732833299,
        "Pinsker_TV_upper_bound": 0.6857504264036836
      },
      {
        "case": 22,
        "full_matrix_KL": 22.602747270419993,
        "ledger_KL": 22.602747270419993,
        "mean_leak_squared": 41.80283353894626,
        "covariance_logdet_leak": 3.4026610018937236,
        "Pinsker_TV_upper_bound": 1.0
      },
      {
        "case": 23,
        "full_matrix_KL": 29.025133724485595,
        "ledger_KL": 29.025133724485606,
        "mean_leak_squared": 54.201722401332944,
        "covariance_logdet_leak": 3.8485450476382663,
        "Pinsker_TV_upper_bound": 1.0
      },
      {
        "case": 24,
        "full_matrix_KL": 1.7057747181111604,
        "ledger_KL": 1.7057747181111627,
        "mean_leak_squared": 0.5362448465802269,
        "covariance_logdet_leak": 2.8753045896420986,
        "Pinsker_TV_upper_bound": 0.9235190084971621
      },
      {
        "case": 25,
        "full_matrix_KL": 9.544758414310722,
        "ledger_KL": 9.54475841431072,
        "mean_leak_squared": 16.194703868717145,
        "covariance_logdet_leak": 2.8948129599042964,
        "Pinsker_TV_upper_bound": 1.0
      },
      {
        "case": 26,
        "full_matrix_KL": 1.0633915753097876,
        "ledger_KL": 1.0633915753097878,
        "mean_leak_squared": 0.2409932581654589,
        "covariance_logdet_leak": 1.8857898924541168,
        "Pinsker_TV_upper_bound": 0.7291747305378141
      },
      {
        "case": 27,
        "full_matrix_KL": 2.9661940433837457,
        "ledger_KL": 2.9661940433837426,
        "mean_leak_squared": 1.3531939184531456,
        "covariance_logdet_leak": 4.57919416831434,
        "Pinsker_TV_upper_bound": 1.0
      },
      {
        "case": 28,
        "full_matrix_KL": 0.9966660885108969,
        "ledger_KL": 0.9966660885108947,
        "mean_leak_squared": 8.310417128322325e-05,
        "covariance_logdet_leak": 1.9932490728505061,
        "Pinsker_TV_upper_bound": 0.7059270814010802
      },
      {
        "case": 29,
        "full_matrix_KL": 9.493432761646195,
        "ledger_KL": 9.493432761646195,
        "mean_leak_squared": 15.69592539857002,
        "covariance_logdet_leak": 3.290940124722371,
        "Pinsker_TV_upper_bound": 1.0
      },
      {
        "case": 30,
        "full_matrix_KL": 4.499779389062658,
        "ledger_KL": 4.499779389062659,
        "mean_leak_squared": 6.919331280712931,
        "covariance_logdet_leak": 2.080227497412386,
        "Pinsker_TV_upper_bound": 1.0
      },
      {
        "case": 31,
        "full_matrix_KL": 1.8892143402484787,
        "ledger_KL": 1.8892143402484805,
        "mean_leak_squared": 0.7816028669978567,
        "covariance_logdet_leak": 2.996825813499104,
        "Pinsker_TV_upper_bound": 0.9719090338731502
      },
      {
        "case": 32,
        "full_matrix_KL": 2.750847580078675,
        "ledger_KL": 2.750847580078674,
        "mean_leak_squared": 1.891138961593078,
        "covariance_logdet_leak": 3.61055619856427,
        "Pinsker_TV_upper_bound": 1.0
      },
      {
        "case": 33,
        "full_matrix_KL": 1.871529037915383,
        "ledger_KL": 1.8715290379153835,
        "mean_leak_squared": 1.1221468573276752,
        "covariance_logdet_leak": 2.620911218503092,
        "Pinsker_TV_upper_bound": 0.9673492228547516
      },
      {
        "case": 34,
        "full_matrix_KL": 1.9294257502747727,
        "ledger_KL": 1.9294257502747758,
        "mean_leak_squared": 0.8546133588263226,
        "covariance_logdet_leak": 3.004238141723229,
        "Pinsker_TV_upper_bound": 0.9821979816398463
      },
      {
        "case": 35,
        "full_matrix_KL": 3.342613301972069,
        "ledger_KL": 3.342613301972069,
        "mean_leak_squared": 3.763415916691696,
        "covariance_logdet_leak": 2.9218106872524423,
        "Pinsker_TV_upper_bound": 1.0
      },
      {
        "case": 36,
        "full_matrix_KL": 19.52854782659991,
        "ledger_KL": 19.52854782659991,
        "mean_leak_squared": 31.10984794967743,
        "covariance_logdet_leak": 7.947247703522392,
        "Pinsker_TV_upper_bound": 1.0
      },
      {
        "case": 37,
        "full_matrix_KL": 22.608394172290275,
        "ledger_KL": 22.608394172290268,
        "mean_leak_squared": 37.62756419740103,
        "covariance_logdet_leak": 7.589224147179506,
        "Pinsker_TV_upper_bound": 1.0
      },
      {
        "case": 38,
        "full_matrix_KL": 0.6583007855645588,
        "ledger_KL": 0.6583007855645565,
        "mean_leak_squared": 0.051778261166127326,
        "covariance_logdet_leak": 1.2648233099629858,
        "Pinsker_TV_upper_bound": 0.5737162999098755
      },
      {
        "case": 39,
        "full_matrix_KL": 8.609400633703734,
        "ledger_KL": 8.609400633703732,
        "mean_leak_squared": 11.50214908185438,
        "covariance_logdet_leak": 5.716652185553082,
        "Pinsker_TV_upper_bound": 1.0
      },
      {
        "case": 40,
        "full_matrix_KL": 4.297441008459913,
        "ledger_KL": 4.297441008459915,
        "mean_leak_squared": 7.397355209308862,
        "covariance_logdet_leak": 1.1975268076109682,
        "Pinsker_TV_upper_bound": 1.0
      },
      {
        "case": 41,
        "full_matrix_KL": 0.13048811633908192,
        "ledger_KL": 0.13048811633908364,
        "mean_leak_squared": 0.003771566841358147,
        "covariance_logdet_leak": 0.2572046658368091,
        "Pinsker_TV_upper_bound": 0.2554291646808207
      },
      {
        "case": 42,
        "full_matrix_KL": 0.6267111567984132,
        "ledger_KL": 0.6267111567984132,
        "mean_leak_squared": 0.17308894295419125,
        "covariance_logdet_leak": 1.080333370642635,
        "Pinsker_TV_upper_bound": 0.5597817238881657
      },
      {
        "case": 43,
        "full_matrix_KL": 3.4014792029321113,
        "ledger_KL": 3.401479202932115,
        "mean_leak_squared": 4.422451538156333,
        "covariance_logdet_leak": 2.380506867707896,
        "Pinsker_TV_upper_bound": 1.0
      },
      {
        "case": 44,
        "full_matrix_KL": 6.068066594586573,
        "ledger_KL": 6.0680665945865755,
        "mean_leak_squared": 7.080402767180813,
        "covariance_logdet_leak": 5.055730421992337,
        "Pinsker_TV_upper_bound": 1.0
      },
      {
        "case": 45,
        "full_matrix_KL": 6.395394742361862,
        "ledger_KL": 6.39539474236186,
        "mean_leak_squared": 11.82976215857799,
        "covariance_logdet_leak": 0.9610273261457288,
        "Pinsker_TV_upper_bound": 1.0
      },
      {
        "case": 46,
        "full_matrix_KL": 6.215088892125706,
        "ledger_KL": 6.215088892125709,
        "mean_leak_squared": 6.636796204662799,
        "covariance_logdet_leak": 5.793381579588619,
        "Pinsker_TV_upper_bound": 1.0
      },
      {
        "case": 47,
        "full_matrix_KL": 3.9756758335465165,
        "ledger_KL": 3.9756758335465125,
        "mean_leak_squared": 5.219633825086238,
        "covariance_logdet_leak": 2.731717842006787,
        "Pinsker_TV_upper_bound": 1.0
      },
      {
        "case": 48,
        "full_matrix_KL": 18.469244290677157,
        "ledger_KL": 18.469244290677153,
        "mean_leak_squared": 32.59102415814516,
        "covariance_logdet_leak": 4.347464423209146,
        "Pinsker_TV_upper_bound": 1.0
      },
      {
        "case": 49,
        "full_matrix_KL": 6.351419792778639,
        "ledger_KL": 6.351419792778643,
        "mean_leak_squared": 3.4051379982989642,
        "covariance_logdet_leak": 9.29770158725832,
        "Pinsker_TV_upper_bound": 1.0
      },
      {
        "case": 50,
        "full_matrix_KL": 1.65098825282946,
        "ledger_KL": 1.6509882528294555,
        "mean_leak_squared": 1.4930617413348397,
        "covariance_logdet_leak": 1.8089147643240713,
        "Pinsker_TV_upper_bound": 0.9085670731513044
      },
      {
        "case": 51,
        "full_matrix_KL": 2.813809134699336,
        "ledger_KL": 2.8138091346993344,
        "mean_leak_squared": 0.6628748357112891,
        "covariance_logdet_leak": 4.96474343368738,
        "Pinsker_TV_upper_bound": 1.0
      },
      {
        "case": 52,
        "full_matrix_KL": 1.0097320078262988,
        "ledger_KL": 1.0097320078262975,
        "mean_leak_squared": 0.03333940372377951,
        "covariance_logdet_leak": 1.9861246119288154,
        "Pinsker_TV_upper_bound": 0.710539234605063
      },
      {
        "case": 53,
        "full_matrix_KL": 3.571032835677952,
        "ledger_KL": 3.571032835677956,
        "mean_leak_squared": 3.707176356392421,
        "covariance_logdet_leak": 3.434889314963491,
        "Pinsker_TV_upper_bound": 1.0
      },
      {
        "case": 54,
        "full_matrix_KL": 38.47149415704551,
        "ledger_KL": 38.4714941570455,
        "mean_leak_squared": 71.87592123843123,
        "covariance_logdet_leak": 5.06706707565977,
        "Pinsker_TV_upper_bound": 1.0
      },
      {
        "case": 55,
        "full_matrix_KL": 1.4777877522809593,
        "ledger_KL": 1.4777877522809586,
        "mean_leak_squared": 0.3172765586865926,
        "covariance_logdet_leak": 2.6382989458753245,
        "Pinsker_TV_upper_bound": 0.8595893648367686
      },
      {
        "case": 56,
        "full_matrix_KL": 6.915603845041634,
        "ledger_KL": 6.915603845041634,
        "mean_leak_squared": 11.547050807687373,
        "covariance_logdet_leak": 2.284156882395894,
        "Pinsker_TV_upper_bound": 1.0
      },
      {
        "case": 57,
        "full_matrix_KL": 4.942514431531146,
        "ledger_KL": 4.942514431531145,
        "mean_leak_squared": 7.0896824921557915,
        "covariance_logdet_leak": 2.7953463709064987,
        "Pinsker_TV_upper_bound": 1.0
      },
      {
        "case": 58,
        "full_matrix_KL": 0.835206631559221,
        "ledger_KL": 0.8352066315592199,
        "mean_leak_squared": 0.6091345472290265,
        "covariance_logdet_leak": 1.0612787158894135,
        "Pinsker_TV_upper_bound": 0.6462223423711145
      },
      {
        "case": 59,
        "full_matrix_KL": 1.345341320739272,
        "ledger_KL": 1.3453413207392675,
        "mean_leak_squared": 2.158730443813523e-06,
        "covariance_logdet_leak": 2.6906804827480912,
        "Pinsker_TV_upper_bound": 0.8201650202060764
      }
    ],
    "execution_status": "PASS"
  },
  "runtime": {
    "python": "3.12.14",
    "numpy": "2.3.5",
    "scipy": "1.17.0",
    "seconds": 7.2540833489983925,
    "hardware_experiments": 0,
    "neural_benchmarks": 0,
    "scope": "CPU mathematical and Gaussian-surrogate checks only"
  },
  "verification_totals": {
    "baseline_channel_lp_cases": 556,
    "new_repeated_channel_lp_cases": 375,
    "new_arbitrary_orbit_lp_cases": 96,
    "visible_catalogue_lp_cases": 220,
    "total_channel_lp_cases": 1247
  }
}