{ "status": "passed", "event_points": 62132, "intervals": 62131, "rounded_arithmetic_sum": 1243345293752876677540040193981, "rounding_denominator": "79228162514264337593543950336", "A_cert": "12507029707866288048422972493354331/790300921079786767495600904601600", "event_value_sha256": "d32a85cb0b94fe1c3b6242ec3fe4d4e4b74bbb0b1b91c9248d743bce2af607c0", "phase": { "status": "passed", "curvature_upper_bounds": [ "-78297686011890864483024931591098659957960951942296758344742727303/1003031212107426820953087107350011349993282887841202535875970705", "-553146279224391891266760912475794324021160006670674793022860620199/22672112142283391379489919069559134172177051533275574774985449830", "-12314551288787505310783262200406096596969262805174787599514995686749/1808615698822550313909524075820164755705650775774629130528790152800" ], "phi_x0_interval": [ "-1178967651293833503406538864617/39614081257132168796771975168", "-2357935302587667006813077729231/79228162514264337593543950336" ], "slope_x0_interval": [ "-117274437183052925880658087/79228162514264337593543950336", "-117274437183052925880658085/79228162514264337593543950336" ], "tangent_max_upper": "-2232095767/75000000", "certified_V": "-744/25", "Q_interval": [ "-5657002371982478064499943615/79228162514264337593543950336", "-2828501185991239032249971807/39614081257132168796771975168" ], "Q_strict_upper": "-357/5000", "method": "Rational atanh series with explicit positive remainder, 30 terms" }, "seconds": 5.274040996009717, "script_sha256": "e97645aa6103ce6db1dc88ced95297b169d9f12fd6f2751786ccc5a0d64b9c67", "scope": "Exact finite certificates; the prime-number-theorem transfer and elementary inequalities are mathematical arguments in the cited paper and the draft." }