Datasets:

cahlen
/

cfd-chaotic-advection

k_index int64 0 2.05k	K float64 0 5	mean_lyapunov float64 0 0.96	std_lyapunov float64 0 0.25	min_lyapunov float64 -0 0	max_lyapunov float64 0 1	fraction_positive float64 0 1
0	0	0	0	0	0	0
1	0.002443	0.000082	0.000024	-0.000089	0.000194	0.994019
2	0.004885	0.000095	0.000024	-0.000052	0.000237	0.996948
3	0.007328	0.000103	0.000024	-0.000078	0.000246	0.997314
4	0.00977	0.000109	0.000023	-0.000058	0.000242	0.998535
5	0.012213	0.000112	0.000024	-0.000041	0.000259	0.999146
6	0.014656	0.000116	0.000024	-0.000074	0.000254	0.998535
7	0.017098	0.000119	0.000023	-0.000069	0.000231	0.999023
8	0.019541	0.000121	0.000024	-0.000093	0.000253	0.998657
9	0.021983	0.000124	0.000024	-0.000052	0.000282	0.999023
10	0.024426	0.000126	0.000023	-0.000031	0.000235	0.999268
11	0.026869	0.000128	0.000024	-0.000056	0.000286	0.998901
12	0.029311	0.000129	0.000024	-0.000048	0.000228	0.998901
13	0.031754	0.000131	0.000023	-0.000034	0.000303	0.99939
14	0.034196	0.000132	0.000024	-0.000042	0.000258	0.99939
15	0.036639	0.000133	0.000024	-0.000095	0.000251	0.998413
16	0.039082	0.000135	0.000024	-0.000048	0.000282	0.99939
17	0.041524	0.000136	0.000024	-0.000098	0.000264	0.99939
18	0.043967	0.000137	0.000023	-0.000054	0.000255	0.999634
19	0.046409	0.000137	0.000024	-0.000068	0.000238	0.999146
20	0.048852	0.000139	0.000024	-0.000057	0.000299	0.999146
21	0.051295	0.00014	0.000024	-0.000139	0.000287	0.999512
22	0.053737	0.00014	0.000024	-0.000034	0.000273	0.999268
23	0.05618	0.000141	0.000024	-0.000049	0.00027	0.99939
24	0.058622	0.000142	0.000024	-0.000039	0.000257	0.999146
25	0.061065	0.000142	0.000024	-0.00009	0.000261	0.999634
26	0.063508	0.000144	0.000024	-0.000022	0.000255	0.999512
27	0.06595	0.000144	0.000024	-0.000001	0.000299	0.999878
28	0.068393	0.000145	0.000024	-0.000028	0.000267	0.999878
29	0.070835	0.000145	0.000024	-0.000011	0.000281	0.999878
30	0.073278	0.000146	0.000024	-0.000051	0.000294	0.999756
31	0.075721	0.000146	0.000024	-0.000025	0.000268	0.999634
32	0.078163	0.000147	0.000024	-0.000056	0.00028	0.999634
33	0.080606	0.000148	0.000024	-0.000033	0.000262	0.999634
34	0.083048	0.000148	0.000024	-0.000059	0.00025	0.999756
35	0.085491	0.000149	0.000024	-0.00003	0.000284	0.999512
36	0.087934	0.000149	0.000024	-0.000032	0.000306	0.999634
37	0.090376	0.00015	0.000024	-0.00006	0.000274	0.999634
38	0.092819	0.00015	0.000025	-0.000035	0.000268	0.99939
39	0.095261	0.00015	0.000025	-0.000042	0.000273	0.999146
40	0.097704	0.000151	0.000025	-0.000013	0.000299	0.999512
41	0.100147	0.000151	0.000025	-0.000045	0.000267	0.999146
42	0.102589	0.000152	0.000024	-0.000017	0.000293	0.999756
43	0.105032	0.000152	0.000025	-0.000075	0.000293	0.999268
44	0.107474	0.000152	0.000024	-0.000035	0.000279	0.999878
45	0.109917	0.000153	0.000025	-0.00004	0.000267	0.99939
46	0.11236	0.000153	0.000024	0.000013	0.000291	1
47	0.114802	0.000154	0.000025	-0.000006	0.000272	0.999878
48	0.117245	0.000154	0.000025	-0.000072	0.000265	0.999512
49	0.119687	0.000154	0.000025	-0.000075	0.00028	0.999146
50	0.12213	0.000155	0.000025	-0.000048	0.000274	0.999756
51	0.124573	0.000155	0.000026	-0.000024	0.000276	0.999512
52	0.127015	0.000155	0.000025	-0.000016	0.000275	0.999634
53	0.129458	0.000156	0.000025	-0.000045	0.000275	0.999512
54	0.1319	0.000156	0.000025	-0.000037	0.000281	0.99939
55	0.134343	0.000156	0.000025	-0.000029	0.000261	0.999634
56	0.136786	0.000156	0.000025	-0.00003	0.000267	0.99939
57	0.139228	0.000157	0.000026	-0.000035	0.000303	0.99939
58	0.141671	0.000158	0.000025	-0.000019	0.000324	0.999878
59	0.144113	0.000158	0.000025	-0.000016	0.000288	0.999878
60	0.146556	0.000158	0.000025	-0.000012	0.000312	0.999634
61	0.148999	0.000158	0.000025	-0.000007	0.000285	0.999878
62	0.151441	0.000158	0.000026	-0.000037	0.000288	0.999634
63	0.153884	0.000159	0.000025	-0.000061	0.000273	0.999512
64	0.156326	0.000159	0.000026	-0.000027	0.000299	0.999634
65	0.158769	0.000159	0.000026	-0.000025	0.000276	0.999756
66	0.161212	0.00016	0.000026	-0.000005	0.000295	0.999756
67	0.163654	0.00016	0.000026	-0.000064	0.000285	0.999634
68	0.166097	0.00016	0.000025	-0.000005	0.000315	0.999878
69	0.168539	0.00016	0.000026	-0.000021	0.000299	0.999634
70	0.170982	0.000161	0.000041	-0.000081	0.003089	0.999512
71	0.173425	0.000161	0.000026	-0.000035	0.000303	0.999268
72	0.175867	0.000161	0.000026	-0.00002	0.000302	0.999512
73	0.17831	0.000162	0.000026	-0.000035	0.000311	0.999756
74	0.180752	0.000165	0.000304	-0.000058	0.027625	0.999634
75	0.183195	0.000161	0.000026	-0.000004	0.000277	0.999878
76	0.185638	0.000162	0.000026	-0.000083	0.000282	0.999634
77	0.18808	0.000162	0.000026	-0.000065	0.000331	0.999756
78	0.190523	0.000164	0.000187	-0.000015	0.016969	0.999756
79	0.192965	0.000165	0.000197	-0.000022	0.017877	0.999512
80	0.195408	0.000163	0.000026	-0.000036	0.000285	0.999634
81	0.197851	0.000163	0.000026	-0.000014	0.000291	0.999634
82	0.200293	0.000163	0.000026	-0.00002	0.000309	0.999512
83	0.202736	0.000163	0.000026	-0.000016	0.000264	0.999634
84	0.205178	0.000163	0.000026	-0.000039	0.000304	0.999878
85	0.207621	0.000168	0.000344	-0.000045	0.029301	0.999634
86	0.210064	0.000164	0.000026	-0.00002	0.000269	0.999756
87	0.212506	0.000164	0.000026	-0.00003	0.000269	0.999512
88	0.214949	0.000164	0.000026	-0.000012	0.00032	0.999634
89	0.217391	0.000164	0.000027	-0.000019	0.000296	0.999512
90	0.219834	0.000169	0.000428	-0.000029	0.038872	0.999756
91	0.222277	0.000164	0.000027	-0.000029	0.000278	0.999756
92	0.224719	0.000164	0.000027	-0.000031	0.000278	0.999634
93	0.227162	0.000166	0.000064	-0.00006	0.005469	0.999756
94	0.229604	0.000165	0.000027	-0.00005	0.000307	0.99939
95	0.232047	0.000165	0.000028	-0.000016	0.000288	0.999268
96	0.234489	0.000165	0.000027	-0.000037	0.00028	0.99939
97	0.236932	0.000166	0.000028	-0.000067	0.000301	0.999512
98	0.239375	0.000165	0.000027	-0.000019	0.000279	0.999756
99	0.241817	0.000168	0.000221	-0.000022	0.020035	0.999634

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Chirikov Standard Map Lyapunov Spectrum

Maximal Lyapunov exponent Λ(K) for the Chirikov standard map on T², computed with a custom CUDA Benettin kernel on NVIDIA RTX 5090 (sm_120).

Part of the bigcompute.science CFD conjecture program — GPU-accelerated exploration of open questions in fluid mixing and dynamical systems.

Quick Start

from datasets import load_dataset

ds = load_dataset("cahlen/cfd-chaotic-advection", "deep_sweep", split="train")
row = ds[1200]
print(f"K={row['K']:.4f}, mean Λ={row['mean_lyapunov']:.6f}")

What's In This Dataset

Each row is one coupling parameter K on a uniform grid in [0, K_max]:

Column	Type	Description
`k_index`	int	Grid index
`K`	float	Standard map coupling parameter
`mean_lyapunov`	float	Mean maximal Lyapunov exponent over ICs
`std_lyapunov`	float	Standard deviation across ICs
`min_lyapunov`	float	Minimum over ICs
`max_lyapunov`	float	Maximum over ICs
`fraction_positive`	float	Fraction of ICs with Λ > 0

Configurations

Config	n_k	n_ic	n_iters	K_max	Trajectories	Wall time
`deep_sweep`	2048	8192	50000	5.0	16,777,216	116.6 s
`standard_sweep`	512	4096	20000	5.0	2,097,152	5.9 s
`smoke_test`	64	512	5000	2.0	32,768	~1 s

Certifying logs are in logs/. Claim-validation artifacts in validation/ (convergence at $K=5$, convergence_k5_gpu.json). Metadata in metadata.json.

Validation artifacts

File	Description
`validation/convergence_k5_gpu.json`	GPU mean Λ at $K=5$ for 5k–100k iterations (65,536 ICs)
`validation/lyapunov_k2_ic65536_iter*.csv`	Per-iteration-count sweeps at $K=0$ and $K=5$ only

Generated by validate_claims.py — see finding claim-validation table.

Key Results (deep_sweep)

Λ(0) = 0 (integrable limit validated)
At literature K_crit ≈ 0.971635406: mean Λ ≈ 0.0446, >99.9% ICs positive
At K = 5: mean Λ ≈ 0.956
Zero NaN/Inf across all trajectories

Reproduction

git clone https://github.com/cahlen/idontknow.git
cd idontknow
./scripts/experiments/cfd-chaotic-advection/run.sh 2048 8192 50000 5.0

CUDA kernel: cahlen/bigcompute-cuda-kernels (cfd-chaotic-advection/standard_map_lyapunov.cu)

Experiment: bigcompute.science/experiments/cfd-chaotic-advection
Finding: Standard Map Chaos Onset

Citation

@misc{humphreys2026cfdchaoticadvection,
  author = {Humphreys, Cahlen},
  title = {Chirikov Standard Map Lyapunov Spectrum (GPU-Computed)},
  year = {2026},
  publisher = {Hugging Face},
  howpublished = {\\url{https://huggingface.co/datasets/cahlen/cfd-chaotic-advection}}
}

Human–AI collaborative research. Not peer-reviewed. All code and data open for verification.