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              "normalized_real_tail_dm": "5.15290278938718369001858859165742646077804733073364879847922633557973854092061009908484e-5503",
              "normalized_real_tail_m": "3.00264229128806926924628035856384470722885347827778030396718357868962627409916784353851e-5505",
              "phi_derivative_lattice_tail": "2.50737769139390461140604289970947978026552167247759295861848898094712595491288661077877e-1475",
              "phi_lattice_tail": "3.66206913211656288971503605391217719671652972626284724188803303355780628449293648275906e-1479",
              "quadrature_error": "NOT bounded: fixed Gauss-Legendre approximation and replay only",
              "roundoff_error": "NOT bounded: ordinary mpmath arithmetic",
              "status": "analytic majorants evaluated as floating numbers; NOT interval bounds"
            },
            "normalization": "B=exp(2*pi*exp(2*z)-9*z)/(4*pi^4), analytic and nonzero",
            "positive_half_segments": [
              "0.0",
              "0.125",
              "0.25",
              "0.5",
              "1.0",
              "2.0",
              "4.0",
              "4.5"
            ]
          },
          "normalization_value": "58417232439200460039231931.8347789539905511669307676195690061100312871326549141848373898",
          "t": "5/4"
        }
      ],
      "values": [
        "0.0245800929637464618043383771928444881616179431064594026027673084760404560524574132678482",
        "0.0206063267010398088542540226123220083946488005266014681741249194108703699404068023138748",
        "0.013808304775488998264780821514286298828009526413359583348925798358294218473192472239144",
        "0.00864445808575824252123765712131380406810683373314303725894932289286327955562528806689437",
        "0.0053113335521013316287134897984026565153206357121369366744318554789341371207039799791677",
        "0.00324144114637190287945711965585082806560437351539981730357728822585539733837888781022554"
      ]
    }
  ],
  "finished_utc": "2026-10-06T15:12:39.229178+00:00",
  "name": "original_theta_quotient",
  "normalization_cancellation": "k=(B*C)/(B*M)=C/M; identical nonzero B in both factors",
  "precisions_bits": [
    128,
    256
  ],
  "preregistered_pr": "https://github.com/AlexanderEastwood/riemann/pull/81",
  "replay_error_status": "Observed discrepancies only; NOT error bounds",
  "replay_observed_relative_differences": [
    "3.2426301543348193754707535513342879260358149760906532241526994053404616887719389931313e-39",
    "1.877654327230453173412900609997711297298081196146677725575942760830540565837654512213e-39",
    "8.5685368453367333373564999903175658246022506803059046046210251425372966851584194776148e-39",
    "6.2245464855236238015644999013414816743833234955571453787706520597459956115502082102866e-39",
    "6.5010060746939729945302534325122510913625178000313866323071654804886468662530246571901e-39",
    "5.9476138017794412481082095692048356016059796358269265853739114922802996539440342786226e-39"
  ],
  "source_evaluator_sha256": "d4dd2964ff76b3e9fd2bd1f94b02ce40f5f02af39ba5adbdf34a4d6da729fb3d",
  "started_utc": "2026-10-06T15:12:36.138990+00:00",
  "status": "complete",
  "stencil": [
    "0",
    "1/4",
    "1/2",
    "3/4",
    "1",
    "5/4"
  ],
  "unbounded_errors": [
    "quadrature",
    "floating roundoff",
    "ratio error"
  ],
  "wrapper_sha256": "2b9dea9f86acb4c54e787453ce285c010e1896e92354ab666281d4da1e888046"
}