Checks · The unfolded zeros of the Riemann zeta function do not form a Riesz basis of exponentials

Recorded output over the first 10,000 zeros, 40 random tests

The same run with 40 tests of each identity and 600 continuation steps; like verify_10000.json, the file records neither these settings nor its date. The identity of Theorem 3.1 held to 7.11 × 10⁻²⁰ and the block-sum identity to 7.28 × 10⁻³⁴. Its keys are those of verify_10000.json, and its Kadec and Avdonin statistics are the same, since both runs cover the same 10,000 zeros. It lists the first 8 zeros and the first 5 windows tested; the worst residuals are over all of them.

Output of: Verification program for the displacement identities (checks/verify_identity.py), shown beside it on that page

Written by: verify_identity.py, a program by Claude Fable 5.1 (Anthropic)
Size: 3,679 bytes
SHA-256: 0e04172a6ca1578426cd2a77cdc1bef2ff4ccdc6c28652d81f7db7358e416aca

The paper's page Every file published with it This file on GitHub

Tables

A_worst_resid	7.113139113632402e-20
B_worst_resid	7.280724305602941e-34
first_cross_index	9
first_cross_gamma	48.00515088116716
sup_abs_d	0.9484712971877421
argmax_abs_d	8571
cstar	-0.04761543832514535
Dstar_centered_sup	0.9008558588625968
mean_d	2.4925939240449597e-06
rms_d	0.2887772086241074
D_peak_index	8571
D_peak_Sbar	0.9484712971877421

A_rows

35	111.87465917699264	0.6596452488315547	-0.34035474200271615	0.1596452534144193	-7.113139113632402e-20
151	321.1601343091136	0.1526397377158431	-0.8473602497616474	-0.34736025602290216	-2.4778148760786106e-20
366	633.5468582522518	0.7724910472383217	-0.22750893807658917	0.27249105458086625	-1.2560631787688726e-20
417	702.2273431457605	0.7713727086183512	-0.2286272763689448	0.2713727161247032	-1.1332154147877834e-20
465	766.0875400998362	0.3869264038783793	-0.6130735808318621	-0.11307358847674144	-1.0387518224731639e-20
476	780.3489250041816	0.46327284748681524	-0.5367271371647149	-0.036727144838949795	-1.0197679510561403e-20
502	814.045913607511	0.48925042021541965	-0.510749564301543	-0.010749572043061668	-9.77555199564414e-21
1034	1458.3937773686873	0.8796060435372085	-0.12039393912377122	0.3796060522067186	-5.4565149617825e-21

B_rows

4117.5275606061605	4230.967402421206	118	-0.30053637595213245	-0.30053637595213245	-4.150448425647165e-35
7112.64994600259	7239.668070162889	143	0.521540410415194	0.521540410415194	2.18997421499699e-34
5324.996837161511	5354.000182228051	31	-0.14390528053371704	-0.14390528053371704	1.026380998313372e-34
8337.479191655404	8433.268452029028	109	-0.5897801704939736	-0.5897801704939736	2.2095015409281745e-34
3653.4317100994813	3731.009553539676	78	-0.7918091147403796	-0.7918091147403796	-2.1076579271932556e-35

D_M

1	0.9484712971877421
2	0.673987960256783
4	0.34433772588831457
8	0.1459547397794406
16	0.10263498809093101
32	0.04382089380729032
64	0.021762030674296422
128	0.01153554548046435
256	0.006021135605918106
512	0.002804113440288177
1024	0.001457061653705308
2048	0.0007169921879641276
4096	0.0003234124191063116

D_M_centered

1	0.9008558588625968
2	0.6502031325398118
4	0.3419596081650264
8	0.14303466205253024
16	0.10109006126969201
32	0.04291524575610985
64	0.021673636991767553
128	0.011314759310655662
256	0.005611283759366805
512	0.002729151898030215
1024	0.0014342657339760309
2048	0.0007142299304169166
4096	0.00031843146303661864

D_rows(N: min Sbar in last N, block mean, A-N)

2	[0.39950462332582387, 0.673987960256783, -1.051528702812258]
4	[-0.23858728697931353, 0.29791766770217837, -3.051528702812258]
8	[-0.23858728697931353, 0.08741246852737836, -7.0515287028122575]
16	[-0.23858728697931353, 0.08856096460715922, -15.051528702812258]
32	[-0.54538572873013, 0.017807635941357768, -31.05152870281226]

JSON

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