{
  "_public_export": {
    "status": "RIEMANN HYPOTHESIS OPEN",
    "record_type": "SANITIZED_HISTORICAL_SOURCE_SNAPSHOT",
    "source_path": "research/local_to_global/experiments/results.json",
    "source_sha256": "2040c0f72e95247646cf1fb7f1308f0814f524ad581fbd1a3da5f490adc26425",
    "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": {}
  },
  "purpose": "normalization verification and explicit failed limiting path",
  "precision_decimal_digits": 65,
  "certified_interval_computation": false,
  "proof_location": "../notes/spectral_approximants_and_exact_gap.md",
  "mellin_checks": [
    {
      "s": {
        "real": "2.0",
        "imag": "0.0"
      },
      "mellin_abs_error": "1.4836825e-67",
      "zeta_times_mellin_divided_by_xi": {
        "real": "0.25",
        "imag": "0.0"
      }
    },
    {
      "s": {
        "real": "3.0",
        "imag": "0.0"
      },
      "mellin_abs_error": "0.0",
      "zeta_times_mellin_divided_by_xi": {
        "real": "0.25",
        "imag": "0.0"
      }
    },
    {
      "s": {
        "real": "2.0",
        "imag": "1.0"
      },
      "mellin_abs_error": "7.4184123e-68",
      "zeta_times_mellin_divided_by_xi": {
        "real": "0.25",
        "imag": "-1.80766026227674599691393881268e-67"
      }
    }
  ],
  "fourier_checks": [
    {
      "z": {
        "real": "0.0",
        "imag": "0.0"
      },
      "fourier_abs_error": "0.0"
    },
    {
      "z": {
        "real": "2.0",
        "imag": "0.0"
      },
      "fourier_abs_error": "4.2097469e-68"
    },
    {
      "z": {
        "real": "0.0",
        "imag": "0.25"
      },
      "fourier_abs_error": "2.9673649e-67"
    },
    {
      "z": {
        "real": "3.0",
        "imag": "0.3"
      },
      "fourier_abs_error": "2.7819046e-68"
    }
  ],
  "N_zero_tail_diagnostic": [
    {
      "log_lambda": 4,
      "N": 0,
      "normalized_value_at_0": "0.85091812823932154513",
      "normalized_value_at_i_over_4": "1",
      "normalized_value_at_0_4i": "1.2633836476515347854",
      "real_tail_spacing": "0.78539816339744830962"
    },
    {
      "log_lambda": 8,
      "N": 0,
      "normalized_value_at_0": "0.55144112954356641552",
      "normalized_value_at_i_over_4": "1",
      "normalized_value_at_0_4i": "2.1102762822892368333",
      "real_tail_spacing": "0.39269908169872415481"
    },
    {
      "log_lambda": 16,
      "N": 0,
      "normalized_value_at_0": "0.14657428130346242386",
      "normalized_value_at_i_over_4": "1",
      "normalized_value_at_0_4i": "6.8917781516087805776",
      "real_tail_spacing": "0.1963495408493620774"
    },
    {
      "log_lambda": 32,
      "N": 0,
      "normalized_value_at_0": "0.0053674026504617844795",
      "normalized_value_at_i_over_4": "1",
      "normalized_value_at_0_4i": "75.944019495003968212",
      "real_tail_spacing": "0.098174770424681038702"
    },
    {
      "log_lambda": 64,
      "N": 0,
      "normalized_value_at_0": "3.6011255910163372697e-6",
      "normalized_value_at_i_over_4": "1",
      "normalized_value_at_0_4i": "9227.9884784859122495",
      "real_tail_spacing": "0.049087385212340519351"
    }
  ],
  "rh_inference": "NONE",
  "all_diagnostic_assertions_passed": true
}
