{
  "_public_export": {
    "status": "RIEMANN HYPOTHESIS OPEN",
    "record_type": "SANITIZED_HISTORICAL_SOURCE_SNAPSHOT",
    "source_path": "experiments/results/internal-kernel-checks.json",
    "source_sha256": "90f97232f4649ce1cc22106b35f99835f8ef57b4cd56db88fb2c31536f70bce4",
    "exported_on": "2026-09-30",
    "public_credit": "@ykbballer91",
    "license": "CC-BY-4.0",
    "ai_assisted": true,
    "original_fields_are_historical": true,
    "checks_rerun_in_public_export": false,
    "scope": "Historical claims and verification records retain their original scope. Priority 1 cyclicity is even L2 only; full-ground capture and RH remain open.",
    "references": {}
  },
  "status": "EXACT_TOY_COUNTEREXAMPLE_VERIFIED",
  "source_sha256": "3c9b0f626383a1844013bd793b7828e60abdf9549494974a0bd2b2480be0d9ce",
  "proves_RH": false,
  "refutes_RH": false,
  "actual_Riemann_kernel_counterexample": false,
  "arithmetic": "Python Fraction exact rational arithmetic",
  "coefficient_matrix": [
    [
      "23473/160000",
      "0",
      "683/32000",
      "0",
      "1/800"
    ],
    [
      "0",
      "29/40000",
      "0",
      "3/16000",
      "0"
    ],
    [
      "683/32000",
      "0",
      "243/80000",
      "0",
      "3/16000"
    ],
    [
      "0",
      "3/16000",
      "0",
      "1/40000",
      "0"
    ],
    [
      "1/800",
      "0",
      "3/16000",
      "0",
      "1/80000"
    ]
  ],
  "nodes": [
    1,
    2,
    3,
    4,
    5
  ],
  "weights_after_Gaussian_cancellation": [
    "-49/24",
    "19/12",
    "3",
    "-43/12",
    "25/24"
  ],
  "feature_moments": [
    "0",
    "1",
    "0",
    "-15/2",
    "0"
  ],
  "negative_Gram_value": "-109/160000",
  "odd_block_determinant": "-109/6400000000",
  "negative_log_derivative_witness": "-76543/172850",
  "Fourier_quadratic_discriminant": "-109/160000",
  "numerical_cross_check": {
    "method": "mpmath original integral, non-certified",
    "decimal_precision": 70,
    "value": "-0.000681250000000000000000000000000000000000000000000000000206292",
    "absolute_error_against_exact": "2.0629199e-58"
  },
  "order_one_extension": "analytic existence by dominated convergence; no numerical epsilon claimed",
  "actual_theta_factor_cone_obstruction": {
    "arithmetic": "Arb 192 bits plus analytic relative tail bound",
    "u_nodes": [
      4,
      5,
      6,
      7
    ],
    "n_equals_one_log_third_difference": "[-13.21852414420906655704151623540814446386896569033748031 +/- 8.67e-54]",
    "absolute_omitted_tail_bound": "[2.63587851387495105595128930358637107104511909091550938498e-128 +/- 1.44e-185]",
    "negative_certified": true,
    "scope": "excludes the Gaussian real-linear-factor cone, not RH"
  }
}