E-032 — F-D side thread 6-R-0: TRUE complex right-tail horizontal integral of Lagarias Thm 6.1 at T=sqrt(n) vs the E-031 envelope
08-25-2026 · 9 rows · script
research/numerics/scripts/E-032-horizontal-true-integral.py
Metadata
Validation checks
| V0_envelope_reproduces_E031 | PASS |
| VA_mpmath_vs_dirichlet_le_1e-6 | PASS |
| VC_trapezoid_convergence | PASS |
| V3_repair_envelope_collapses | PASS |
Chart
Data preview (9 rows total)
| check | n | c | T | eps | clearance | Re_I_right | Im_I_right | abs_I_right | envelope | abs_over_env | Re_over_env | abs_over_sqrtn | hdelta | val_max_disc | abs_I_mid | envelope_mid | Re_I_full | abs_I_full |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| right_part | 1000 | 1.0 | 31.6727766 | 0.05 | 1.248 | 2.1287636 | -6.8620183 | 7.18463 | 50.8152 | 0.1414 | 0.04189 | 0.2272 | 9.5e-5 | 4.97e-10 | 4.38071 | 4.58947 | -2.2458021 | 7.44101 |
| right_part | 1000 | 1.5 | 47.4341649 | 0.0 | 0.571 | -1.0072954 | 0.49425851 | 1.12202 | 1.25123 | 0.8967 | 0.805 | 0.03548 | 4.76e-5 | 3.7e-10 | ||||
| right_part | 1000 | 2.0 | 63.2455532 | 0.0 | 1.867 | -0.62321194 | -0.0065248336 | 0.623246 | 0.628586 | 0.9915 | 0.9915 | 0.01971 | 4.91e-5 | 3.17e-10 | ||||
| right_part | 10000 | 1.0 | 100.05 | 0.05 | 1.219 | -11.887447 | -11.73172 | 16.7016 | 10258.0 | 0.001628 | 0.001159 | 0.167 | 5.03e-5 | 3.39e-10 | 5.22324 | 7.41556 | -16.646154 | 19.2052 |
| right_part | 10000 | 1.5 | 150.5 | 0.5 | 0.4253 | 0.8677629 | -0.7396482 | 1.14022 | 1.15893 | 0.9839 | 0.7488 | 0.0114 | 4.42e-5 | 3.95e-10 | ||||
| right_part | 10000 | 2.0 | 200.0 | 0.0 | 1.265 | 0.30987116 | 0.036921293 | 0.312063 | 0.312734 | 0.9979 | 0.9908 | 0.003121 | 1.08e-5 | 5.96e-10 | ||||
| right_part | 100000 | 1.0 | 316.627766 | 0.4 | 1.107 | -13.538954 | 22.464752 | 26.2292 | 4.70658e+10 | 5.573e-10 | 2.877e-10 | 0.08294 | 4.86e-5 | 3.33e-10 | 13.6968 | 14.739 | -25.972869 | 30.8894 |
| right_part | 100000 | 1.5 | 474.741649 | 0.4 | 0.8587 | 0.67084066 | 0.74100237 | 0.999556 | 1.00392 | 0.9957 | 0.6682 | 0.003161 | 1.06e-5 | 2.11e-10 | ||||
| right_part | 100000 | 2.0 | 632.905532 | 0.45 | 0.6413 | 0.35390459 | 0.014097658 | 0.354185 | 0.355357 | 0.9967 | 0.9959 | 0.00112 | 1.47e-5 | 3.66e-10 |