files / problems / riemann-hypothesis / compute / q2 / certificate / analytic / prop410 / prop410_arb_512.log
Prop410 Arb verifier: precision=512, N0=690988, m0=2000 PARAM t0 = 129/800 PARAM tbox_lo = 161250000/1000000000 PARAM tbox_hi = 161250001/1000000000 PARAM y0^2 = 87677/2500000 PARAM ymax^2 = 271/400 PARAM N0 = 690988 PARAM m0 = 2000 PARAM Tmin = 791366/1000000000000 PARAM budget_Emax = 234/1000000000 PARAM stated_eAB = 206/100000000000000 PARAM stated_eC0 = 233492848188649183/10^24 PARAM stated_Emax = 233494905212337849/10^24 [PASS] exact candidate identity t0+y0^2/2 = 893927/5000000 [PASS] exact t-box: t0 = tbox_lo < tbox_hi <= 1/4 [PASS] exact y0^2 identity 87677/2500000 = 350708/10^7 [PASS] exact floor exceeds coarse budget: 791366/10^12 > 234/10^9 [PASS] domain: 0 < t/(16 N0^2) < 1 and 1 - t/(16 N0^2) > 0 [PASS] domain: x0 > 12, x0 > 6.66, x0 > 6 [PASS] domain: log N0 - log m0 > 0 [PASS] domain: N0 - 1/8 > 0 [PASS] gate G0_positive_part: 8/x0^2 < 3 y0 [PASS] gate sigma1_positive: sigma1 > 0 [PASS] gate Y1_negative: Y1 < 0 [PASS] gate kappa_domain: 0 < kappa < 1 [PASS] gate G2a_ratio: N0^2/(N0^2-t/16) > 1 [PASS] gate U1_log_domain: log(N0^2-t/16) > 2 [PASS] gate U2_logN: log N0 > 1/2 [PASS] gate U3a_tail_decrease: (1+y0)/2 - delta1 > 0 [PASS] gate Y_range (exact): 0 < y0^2 < ymax^2 <= 1 [PASS] gate U3b_first_endpoint: g_t1 < 0 [PASS] gate U3c_second_endpoint: g_t2 < 0 [PASS] gate U5_last_factor (exact): 3/10.50 < 1 [PASS] majorant domain: log n > 0 for all head terms, log m0 > 0 [PASS] majorant domain: tlo > 0 and lower(log0^2) > 0 [PASS] eAB corridor 2.057e-12 < eAB < 2.058e-12 [PASS] eC0 corridor 2.33492848e-7 < eC0 < 2.33492849e-7 [PASS] Emax corridor 2.33494905e-7 < Emax < 2.33494906e-7 [PASS] decisive eAB < 206/10^14 [PASS] decisive eC0 < 233492848188649183/10^24 [PASS] decisive Emax < 233494905212337849/10^24 [PASS] decisive coarse budget Emax < 234/10^9 [PASS] decisive finite margin Tmin - Emax > 0 [PASS] decisive binding floor Tmin - Emax > 557/10^9 Directed Arb enclosures: delta1 upper point = [8.50899889846674100236672464318e-16 +/- 1.66e-46] kappa upper point = [1.34375117103022393313684222211e-14 +/- 2.19e-44] sigma1 enclosure = [1.67770989321524226316357665287 +/- 3.37e-9] Y1 enclosure = [-6.70293886823147901130462711684 +/- 3.28e-23] g_t1 enclosure = [-0.441735640408169908607809683727 +/- 1.91e-9] g_t2 enclosure = [-0.506622770922606166492249723339 +/- 3.37e-9] U1max upper point = [3.00202962917846552863796139950e-13 +/- 1.00e-44] Pmax upper point = [2.02020134002695090625827654559 +/- 2.81e-30] head upper point = [1.44876762495760293674693740052 +/- 3.25e-30] cap upper point = [0.943027908358772630207471199068 +/- 3.95e-31] Smax upper point = [3.39179553331637556695440859958 +/- 4.36e-30] eAB upper point = [2.05702368866621440130649806893e-12 +/- 1.23e-42] eC0 upper point = [2.33492848188649182679145092376e-7 +/- 4.23e-37] Emax upper point = [2.33494905212337848893546398874e-7 +/- 3.54e-37] Tmin-Emax lower point = [5.57871094787662151106453601126e-7 +/- 3.54e-37] TOTAL CHECKS: 31; FAILURES: 0 RESULT: ALL ARB PROP410 CHECKS PASS