COMPUTER-ASSISTED PROOF:  Lambda <= t0 + y0^2/2 = 0.15399 + 0.2^2/2 = 0.17399 < 0.174

Criterion: Polymath, Thm 1.2 (arXiv:1904.12438).
(i)   RH verified up to 3e12 (Platt-Trudgian, arXiv:2004.09765); X/2 = 2999156664990.1567 < 3e12.
(iii) CERTIFIED (iii) [Arb]: barrier X=5998313329980.3135, t in [0,0.15399] (last step ends at 0.15399000000000002 >= t0), y0=0.2: no zeros of H_t; 73 steps, 39840 evaluations, min margin 0.3459, 55s
(ii)  eA+eB+eC0 <= 2.977e-07 for all x>=X+sqrt(1-y0^2), y in [y0,0.831877]
      certified y-intervals (each: all x >= X+sqrt(1-y0^2)):
        y in [0.20000, 0.20500]: 11 chunks, |f_t0| >= 0.00594
        y in [0.20500, 0.21500]:  9 chunks, |f_t0| >= 0.00966
        y in [0.21500, 0.23500]:  7 chunks, |f_t0| >= 0.01931
        y in [0.23500, 0.27500]:  5 chunks, |f_t0| >= 0.02836
        y in [0.27500, 0.35500]:  3 chunks, |f_t0| >= 0.01803
        y in [0.35500, 0.51500]:  2 chunks, |f_t0| >= 0.01855
        y in [0.51500, 0.83188]:  2 chunks, |f_t0| >= 0.14245
      union covers [0.2, 0.831877] = [y0, sqrt(1-2 t0)];  min certified |f_t0| = 0.00594

Inputs: X=5998313329980.3135 t0=0.15399 y0=0.2 ; weights lam_L0174.npy sha256=d71b379ee04a299191ec31c420d4dcca6bba3fc61c707eb9ee4c71c0c49b1235
        cert_region_ii.py sha256=8ca106d8a5609d7f093529cdb1614f5da773bdb78484afd30dba4dc5a481c4ec
        cert_barrier.py sha256=1882d2ce112ed1a551cff3d1ec4d7d131c2bfd46b628ec1b9cde8993921ea4fe
        common.py sha256=22361af17deaffa7c7761367f84cc90bc7dbf44d44267e32ab5ddc5273211e18
        certify_all.py sha256=a2ae5bc2137d4b96ce49e262a68c7ef1a58f0cdd9f0cfe12b5e09f461da1251a
Software: python 3.13.16, numpy 2.5.3, python-flint 0.9.0, Linux-6.18.44-fc-v139-x86_64-with-glibc2.39
Logs: logs_0.174_linux (second run of the unchanged scripts)