E-021 — Exact S_inf(n) to n=5000 + |S_f(n)| curve + D-036 contour constants (A=0.9,B0=1.0); ALL CHECKS PASS (V1 4.8e-25 vs E-015, V2, V3 c0=-0.25)
08-18-2026 · 5000 rows · script
research/numerics/scripts/E-021-sinf-sf-curve.py
Metadata
Validation checks
| V1_lambda_vs_E015 | PASS |
| V2_R_bound_holds | PASS |
| V3_Sinf_residual_bounded | PASS |
Key values
| A_use | 0.9 |
| B0_use | 1.0 |
| R_max_sample | 4.7507714994958565 |
| C0_samples | {'1e2': 6.234438640727731, '1e4': 8.840233256550178, '1e6': 11.194201354663145} |
| eta_0 | -0.5772156649015328606065120900824024310 |
| Sinf_residual_fits | [[1000, -0.2500416666625], [2000, -0.2500208333328125], [3000, -0.25001388888873455], [4000, -0.25001041666660156], [5000, -0.2500083333333]] |
| V1_worst_rel | 0.000000000000000000000000479820218420929 |
| S_f_max_abs | 13.5229134371 |
| S_f_max_abs_n | 3298 |
Parameters
| n_max | 5000 |
| t_zeros | 5000.0 |
Chart
Data preview (5000 rows total)
| n | S_inf | S_f | lambda_n | abs_Sf |
|---|---|---|---|---|
| 1 | -1.55411995594 | -0.577215664902 | 0.0230957089661 | 0.577215664902 |
| 2 | -1.87453936173 | -0.966885096963 | 0.092345735228 | 0.966885096963 |
| 3 | -2.01305800766 | -1.22069692822 | 0.207638920554 | 1.22069692822 |
| 4 | -2.00679765238 | -1.37558813187 | 0.368790479492 | 1.37558813187 |
| 5 | -1.88272578574 | -1.4582685002 | 0.575542714461 | 1.4582685002 |
| 6 | -1.66073231493 | -1.48829832721 | 0.827566012282 | 1.48829832721 |
| 7 | -1.35573072267 | -1.48019084024 | 1.12446011757 | 1.48019084024 |
| 8 | -0.979100066972 | -1.44485574412 | 1.46575567715 | 1.44485574412 |
| 9 | -0.539680358409 | -1.39059640679 | 1.85091604838 | 1.39059640679 |
| 10 | -0.0444643205031 | -1.3238036837 | 2.27933936319 | 1.3238036837 |
| 11 | 0.500918062398 | -1.24944277582 | 2.75036083822 | 1.24944277582 |
| 12 | 1.09185707369 | -1.17139824694 | 3.26325532062 | 1.17139824694 |
| 13 | 1.72451874073 | -1.09272131711 | 3.81724005785 | 1.09272131711 |
| 14 | 2.39566826609 | -1.01580941259 | 4.41147767868 | 1.01580941259 |
| 15 | 3.10254095094 | -0.942538421086 | 5.04507937203 | 0.942538421086 |
| 16 | 3.84274658749 | -0.874361661381 | 5.71710824887 | 0.874361661381 |
| 17 | 4.61419765951 | -0.812385212605 | 6.42658287212 | 0.812385212605 |
| 18 | 5.41505465532 | -0.757426282975 | 7.17248093829 | 0.757426282975 |
| 19 | 6.24368381994 | -0.710059274376 | 7.95374309431 | 0.710059274376 |
| 20 | 7.09862405929 | -0.670652812799 | 8.76927687209 | 0.670652812799 |
| 21 | 7.97856066337 | -0.639400059776 | 9.61796072314 | 0.639400059776 |
| 22 | 8.8823041765 | -0.61634395843 | 10.4986481349 | 0.61634395843 |
| 23 | 9.80877320409 | -0.601398606428 | 11.4101718105 | 0.601398606428 |
| 24 | 10.7569802686 | -0.594367623933 | 12.3513478926 | 0.594367623933 |
| 25 | 11.726020058 | -0.594960154932 | 13.3209802129 | 0.594960154932 |