{
  "table": "T646",
  "skill_manifest": "agents/runs/20261101T082247Z-build-skills/manifest.json",
  "skill_local_sha256": "a2b28d9953264d7b0ca62663785c2952190c5be6d6d3597fd695d9a54d606278",
  "skill_live_sha256": "a2b28d9953264d7b0ca62663785c2952190c5be6d6d3597fd695d9a54d606278",
  "entries": 1,
  "parameters": [],
  "value_100_digits": "0.7825279853253842345766884742837840768058009796525991599926472087826073767199003522927165598264149835",
  "primary": {
    "terms": 400,
    "working_bits": 413,
    "relative_accuracy_bits": 398,
    "ball": "[0.782527985325384234576688474283784076805800979652599159992647208782607376719900352292716559826414983450222022596295028615 +/- 6.34e-121]",
    "tail_bound_exact": "1/2582249878086908589655919172003011874329705792829223512830659356540647622016841194629645353280137831435903171972747493376"
  },
  "independent": {
    "method": "Möbius kernel; exact Bernoulli recurrence; Machin pi enclosure",
    "working_bits": 700,
    "split": 16,
    "geometric_terms": 60,
    "atan_terms": [
      162,
      48
    ],
    "relative_accuracy_bits": 550,
    "ball": "[0.782527985325384234576688474283784076805800979652599159992647208782607376719900352292716559826414983450222022596295028615157626894029295387391746315611442777239406181 +/- 5.24e-166]",
    "tail_bound_exact": "289/4020488504238365975791147097486236101641032239468606893736901783206920503932688238618425133845956454062541161186566762685658003343314502673760096056095528254386441551872"
  },
  "higher_precision_relative_accuracy_bits": 503,
  "primary_independent_and_130_digit_balls_inside_written_interval": true,
  "controls": [
    "Bernoulli B0..B4 and B12",
    "Machin exact angle identity and pi enclosure",
    "Mobius known values and divisor convolution through 10000",
    "zeta(2), zeta(4), zeta(6)",
    "ten-last-place perturbation rejected",
    "radius-one ball rejected"
  ],
  "direct_mobius_terms": 10000,
  "direct_mobius_tail_bound": "1/10000",
  "partial_sum_checks": {
    "0": {
      "absolute_error_bound": "1/5000",
      "passed": true
    },
    "1": {
      "absolute_error_bound": "1/5000",
      "passed": true
    },
    "8": {
      "absolute_error_bound": "1/5000",
      "passed": true
    },
    "32": {
      "absolute_error_bound": "1/5000",
      "passed": true
    },
    "256": {
      "absolute_error_bound": "1/5000",
      "passed": true
    }
  },
  "oeis_prefix_digits": 87,
  "stored_checks": {
    "tid": "T646",
    "entries": 1,
    "stored_text": "0.7825279853253842345766884742837840768058009796525991599926472087826073767199003522927165598264149835",
    "independent_enclosure_contained": true,
    "verify": "<VerifyReport T646: 1/1 matched, 0 differing, 0 missing, 0 extra>",
    "T644_coefficients_checked": 257,
    "stored_partial_sum_checks": {
      "0": {
        "absolute_error_bound": "1/5000",
        "passed": true
      },
      "1": {
        "absolute_error_bound": "1/5000",
        "passed": true
      },
      "8": {
        "absolute_error_bound": "1/5000",
        "passed": true
      },
      "32": {
        "absolute_error_bound": "1/5000",
        "passed": true
      },
      "256": {
        "absolute_error_bound": "1/5000",
        "passed": true
      }
    }
  },
  "versions": {
    "sage": "10.9",
    "numberdb": "0.1.10"
  }
}