E-005 — Oversampled third-moment decider (lambda,q) sinc-Gram CMS bounds

08-17-2026 · 8 rows · script research/numerics/scripts/E-005-oversampled-third-moment.py

Metadata

3-moment one-sided bounds for (lambda,q) sinc-Gram matrices over the sine process; decides whether an unconditional third moment (lambda <= 2/3) can beat 2/3

Parameters

N_GUE	`400`
W	`500`
lambdas	`[0.5, 0.6666666666666666, 0.8, 1.0]`
qs	`[1, 2]`
n_samples	`30`
seed	`20260817`

Chart

Data preview (8 rows total)

lambda	q	d_over_N	mu1	mu2	mu3	mu4	CMS2	MARKOV3	CMS4	baseline_2moment	cap_q*lambda	heuristic_cert_MARK3*8/9
0.5000	1	0.5000	2.0082	4.3010	9.8021	23.4711	0.9376	0.9599	1.0047	-0.1667	0.5000	0.8532
0.5000	2	1.0000	0.9994	2.1392	4.8782	11.6859	0.4669	0.4782	0.5017	-0.1667	1.0000	0.4251
0.6667	1	0.6667	1.5065	2.5644	4.7789	9.5152	0.8850	0.9098	0.9821	0.2778	0.6667	0.8087
0.6667	2	1.3333	0.7510	1.2773	2.3807	4.7409	0.4416	0.4541	0.4910	0.2778	1.3333	0.4036
0.8000	1	0.8000	1.2566	1.8827	3.1402	5.6410	0.8387	0.8634	0.9514	0.4833	0.8000	0.7674
0.8000	2	1.6000	0.6263	0.9375	1.5640	2.8106	0.4184	0.4308	0.4755	0.4833	1.6000	0.3829
1.0000	1	1.0000	1.0062	1.3258	1.9625	3.1439	0.7636	0.7851	0.8757	0.6667	1.0000	0.6978
1.0000	2	2.0000	0.5015	0.6601	0.9772	1.5661	0.3811	0.3919	0.4378	0.6667	2.0000	0.3483