E-020b — window-class optimum kernel D1 (quartic is optimal; control recovers MT)

08-18-2026 · 2 rows · script research/numerics/scripts/E-020b-window-optimum.py

Metadata

Validation checks

C1_control_recovers_MT	PASS
C2_D1_optimum_sane	PASS

Key values

R_opt_x	`1.3274994741768826`
R_MT	`1.3274992963205885`
R_opt_D1	`1.131359211780498`
R_quartic_D1	`1.1313601952861119`
cert_opt_D1	`0.868640788219502`
opt_coeffs_D1	`[1.4747096406032818, -0.11822069827325471, -0.3332111306955125, -0.05188711282919025, 0.018718518018636963, 0.014002590280189901, -0.014950796476394187]`

Parameters

K_poly	`6`
n_grid	`801`

Chart

Data preview (2 rows total)

kernel	R_opt	certificate_2_minus_R	reference
x	1.3274994742	0.6725005258	MT=1.3274992963
D1	1.1313592118	0.8686407882	quartic=1.1313601953