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E-022 — spectral-measure convergence (D-035 D2): Clark weights 1/K(z_k,z_k) for Suzuki D_{a,pi}

08-19-2026 · 3815 rows · script research/numerics/scripts/E-022-spectral-measure.py

Metadata

Validation checks

V0_schur_vs_solve_v PASS
V1_weights_positive PASS
V2_refinement PASS
V3_lattice_and_z1law PASS

Key values

4{'n_zeros': 381, 'z1': 1.1260734006983593, 'z1_times_a': 4.504293602793437, 'lattice_expected': 381.9718634205488, 'mass_total_Zmetric': 184.02432245308052, 'O1_cumulative_Linf': 0.030472775278319375, 'O1_cumulative_L2': 0.015369322417422383, 'O2_logw_slope': 0.004773175983096674, 'O2_logw_R2': 0.17155831473911887, 'O2_logw_std_resid': 0.8476672146023767, 'O3_weak_metric': 0.010527875427328966, 'O5_mass_near_gamma': 1.6069393990772483, 'O5_mass_near_random': 1.239913792291073, 'O5_ratio': 1.2960089718076262, 'elapsed_s': 2.9}
6{'n_zeros': 572, 'z1': 0.7499016225074712, 'z1_times_a': 4.499409735044827, 'lattice_expected': 572.9577951308232, 'mass_total_Zmetric': 184.01489106241632, 'O1_cumulative_Linf': 0.02723380344436621, 'O1_cumulative_L2': 0.015298102993183555, 'O2_logw_slope': 0.004573680792971365, 'O2_logw_R2': 0.13177706690264612, 'O2_logw_std_resid': 0.9483241546589634, 'O3_weak_metric': 0.010569164981132785, 'O5_mass_near_gamma': 1.6173747450375149, 'O5_mass_near_random': 1.257329769139859, 'O5_ratio': 1.2863568371120038, 'elapsed_s': 4.8}
8{'n_zeros': 763, 'z1': 0.5621012628096893, 'z1_times_a': 4.4968101024775144, 'lattice_expected': 763.9437268410976, 'mass_total_Zmetric': 184.13312237431055, 'O1_cumulative_Linf': 0.027258094320286474, 'O1_cumulative_L2': 0.015486596743652112, 'O2_logw_slope': 0.004185396789595135, 'O2_logw_R2': 0.10532818940743971, 'O2_logw_std_resid': 0.986518773772079, 'O3_weak_metric': 0.010568959142405882, 'O5_mass_near_gamma': 1.6196075350475192, 'O5_mass_near_random': 1.2561234028070363, 'O5_ratio': 1.2893697636937673, 'elapsed_s': 8.2}
10{'n_zeros': 954, 'z1': 0.44959701245436284, 'z1_times_a': 4.4959701245436285, 'lattice_expected': 954.9296585513721, 'mass_total_Zmetric': 184.1239991524169, 'O1_cumulative_Linf': 0.024844169503423608, 'O1_cumulative_L2': 0.015446208652370818, 'O2_logw_slope': 0.0038097364559334847, 'O2_logw_R2': 0.08653440341105123, 'O2_logw_std_resid': 1.0006504172097648, 'O3_weak_metric': 0.010581710686957842, 'O5_mass_near_gamma': 1.6290317856739722, 'O5_mass_near_random': 1.2562149964535079, 'O5_ratio': 1.2967778527345915, 'elapsed_s': 13.4}
12{'n_zeros': 1145, 'z1': 0.3746087478472408, 'z1_times_a': 4.495304974166889, 'lattice_expected': 1145.9155902616465, 'mass_total_Zmetric': 184.10483484645468, 'O1_cumulative_Linf': 0.028584131798192303, 'O1_cumulative_L2': 0.015417413187446537, 'O2_logw_slope': 0.003682406300531162, 'O2_logw_R2': 0.08233450272296328, 'O2_logw_std_resid': 0.9935774298804366, 'O3_weak_metric': 0.010592268896428007, 'O5_mass_near_gamma': 1.6165573705799765, 'O5_mass_near_random': 1.2532365071394718, 'O5_ratio': 1.2899060643148588, 'elapsed_s': 20.9}
O4_trend{'a': [4.0, 6.0, 8.0, 10.0, 12.0], 'd_a': [0.010527875427328966, 0.010569164981132785, 0.010568959142405882, 0.010581710686957842, 0.010592268896428007], 'monotone_decreasing': False}
V0_max_dev0.00000000000003560323900663321
V2_rel0.0011243096862693027

Parameters

a_list[4.0, 6.0, 8.0, 10.0, 12.0]
h0.01
lam-1.0
z_max300.0
z_metric280.0
sigma_bump8.0
n_grid40000

Chart

Data preview (3815 rows total)

akz_kw_k
411.1260734006981.3150969738e-01
421.9360080382471.2740670325e-01
432.7326943685661.2636621211e-01
443.5252108749531.2595312341e-01
454.3159001714241.2575252173e-01
465.1056578341081.2564554270e-01
475.8949135996621.2558829852e-01
486.6839144012741.2556250831e-01
497.4728312269721.2556100101e-01
4108.2618118608511.2558322675e-01
4119.0510197519861.2563499919e-01
4129.8406824127671.2573202239e-01
41310.6311880007061.2591308387e-01
41411.4233354394981.2628281622e-01
41512.2191987616341.2720705733e-01
41613.0267696882191.3082036040e-01
41714.0235206782367.4562634887e-01
41814.3184944991434.8317221263e-01
41915.2938856077071.3081752958e-01
42016.1017861005441.2729956533e-01
42116.8984467540061.2644831498e-01
42217.6919316001861.2618381164e-01
42318.4846693678371.2619664153e-01
42419.2784654032991.2656797621e-01
42520.0777675836411.2838024329e-01