files / problems / riemann-hypothesis / compute / q1 / fresh / tail_arb_512.log
P1113 Arb verifier: precision=512, N1=3840000, M=153814 [PASS] exact rational target and y-hull containments [PASS] exact target identity t0+y0^2/2 = 893927/5000000 [PASS] domain: 0 < t <= 1/2 [PASS] domain: 0 < ybox <= yext <= 1 [PASS] domain: N1 > MHEAD > MERR > 1 [PASS] P1113 has lambda_1 = 1 [PASS] exact P1113 vector normalization sum|lambda|=9918746/1000000 [PASS] domain: X_N(t) > 200 and all error denominators positive [PASS] domain: log(N^2-t/16) > 2 [PASS] domain: 0 < t/(16N^2) < 1 [PASS] SC1: sigma1 > (t/2) log N on box and extended hull [PASS] SC2: sigma2 > (t/2) log N on box and extended hull [PASS] SC3: sigma1,sigma2 > 1 on extended hull [PASS] window log gate: N(1-t/(16N^2)) > 1 [PASS] delta and kappa cutoff monotonicity premises: t>=0, X_N>12 [PASS] sigma N-slope t/2 is positive [PASS] G N-monotonicity premises: y>0 and N^2-t/16>0 [PASS] GN-TR: every fixed-left routed cap decreases for all N>=N1 [PASS] OVW: floor(N/d)>=N/(d+1), and moving caps decrease by sigma>1 [PASS] Mmax is strictly positive [PASS] GN-AB: fixed-left MHEAD A-cap decreases for all N>=N1 [PASS] YM: D decreases above the lower y-box [PASS] GN-error: both MERR=3000 caps decrease for all N>=N1 [PASS] Delta N-monotonicity gate: (t^2/16)L(L-2)+0.626 > 0 [PASS] eC0 quotient N-monotonicity gate: 3 < 10.50 and X_N>12 [PASS] P corridor 0.170227 < P < 0.170229 [PASS] TR corridor 0.262900 < TR < 0.262902 [PASS] OV corridor 0.039241 < OV < 0.039243 [PASS] Mmax corridor 1.608288 < Mmax < 1.608290 [PASS] AB corridor 0.327893 < AB < 0.327895 [PASS] D corridor 0.999719 < D < 0.999721 [PASS] P interval width is smaller than 1-D [PASS] decisive contraction D < 1 [PASS] flow corridor 0.0001735 < flow < 0.0001740 [PASS] error corridor 1.1670e-8 < err < 1.1672e-8 [PASS] decisive normalized margin flow > error > 0 Directed Arb enclosures: P upper point = [0.170228023678122342286328162340 +/- 4.41e-31] TR upper point = [0.262901330124790894596039723464 +/- 4.37e-31] OV upper point = [0.0392426812101768641638975708089 +/- 1.10e-32] Mmax upper point = [1.60828914495414090322020715102 +/- 3.70e-30] AB upper point = [0.327894319270990003368094008613 +/- 2.18e-31] D upper point = [0.999720909388750699545691864037 +/- 4.11e-31] flow lower point = [0.000173532608937218501848333877396 +/- 3.22e-35] eAB upper point = [4.93807921086187247227924285051e-13 +/- 3.21e-43] eC0 upper point = [1.16711096273536263367986975936e-8 +/- 2.20e-38] error upper point = [1.16716034352747125240459255179e-8 +/- 6.97e-39] flow-error lower point = [0.000173520937333783227135809831471 +/- 4.86e-34] P enclosure width = [5.44525141643603660668304655701e-9 +/- 7.80e-40] TOTAL CHECKS: 36; FAILURES: 0 RESULT: ALL ARB TAIL CHECKS PASS