string-pluck-v1

Plucked damped string: pickup velocity. Challenge specification. results.json. Generated 2026-09-17T18:03:09+00:00.

Errors are relative to the reference solution string-solutions/modal-series/modal-n1024, chosen by rule partial-order-agreement. Rows are sorted by the primary metric. Submissions are named as repository/submission.

Submission	Solution	Method	waveform_l2 (primary)	spectrogram_l2	Time (s)	Hardware	Claimed more accurate than	Output
modal-series string-solutions · Jeremy Magland	modal-n1024 (reference)	modal series, truncated `{"n_modes": 1024}`	0	0	2.33	13th Gen Intel(R) Core(TM) i7-1355U, single thread, Python 3.13.5 + numpy 2.4.4	modal-n256	wav fields code viz
modal-series string-solutions · Jeremy Magland	modal-n256	modal series, truncated `{"n_modes": 256}`	1.037e-06	5.628e-10	0.577	13th Gen Intel(R) Core(TM) i7-1355U, single thread, Python 3.13.5 + numpy 2.4.4	modal-n64	wav code viz
fd-second-order string-solutions · Jeremy Magland	fd-m16	finite differences, second order, implicit damping `{"oversampling": 16, "n_points": 3142, "dx_m": 0.000206940464820121, "dt_s": 1.3020833333333333e-06, "courant": 0.899766}`	0.000132	1.83e-05	111	13th Gen Intel(R) Core(TM) i7-1355U, single thread, Python 3.13.5 + numpy 2.4.4	fd-m8	wav fields code viz
fd-second-order string-solutions · Jeremy Magland	fd-m8	finite differences, second order, implicit damping `{"oversampling": 8, "n_points": 1571, "dx_m": 0.0004140127388535032, "dt_s": 2.6041666666666666e-06, "courant": 0.899479}`	0.0005295	7.296e-05	33.2	13th Gen Intel(R) Core(TM) i7-1355U, single thread, Python 3.13.5 + numpy 2.4.4	fd-m4	wav code viz
fd-second-order string-solutions · Jeremy Magland	fd-m4	finite differences, second order, implicit damping `{"oversampling": 4, "n_points": 786, "dx_m": 0.0008280254777070064, "dt_s": 5.208333333333333e-06, "courant": 0.899479}`	0.002116	0.0002882	11.4	13th Gen Intel(R) Core(TM) i7-1355U, single thread, Python 3.13.5 + numpy 2.4.4	fd-m2	wav code viz
modal-series string-solutions · Jeremy Magland	modal-n64	modal series, truncated `{"n_modes": 64}`	0.003219	0.0003154	0.126	13th Gen Intel(R) Core(TM) i7-1355U, single thread, Python 3.13.5 + numpy 2.4.4	modal-n32	wav code viz
fd-second-order string-solutions · Jeremy Magland	fd-m2	finite differences, second order, implicit damping `{"oversampling": 2, "n_points": 393, "dx_m": 0.0016581632653061226, "dt_s": 1.0416666666666666e-05, "courant": 0.898333}`	0.008528	0.001182	4.46	13th Gen Intel(R) Core(TM) i7-1355U, single thread, Python 3.13.5 + numpy 2.4.4	fd-m1	wav code viz
modal-series string-solutions · Jeremy Magland	modal-n32	modal series, truncated `{"n_modes": 32}`	0.01791	0.006947	0.0714	13th Gen Intel(R) Core(TM) i7-1355U, single thread, Python 3.13.5 + numpy 2.4.4	modal-n16	wav code viz
fd-second-order string-solutions · Jeremy Magland	fd-m1	finite differences, second order, implicit damping `{"oversampling": 1, "n_points": 197, "dx_m": 0.003316326530612245, "dt_s": 2.0833333333333333e-05, "courant": 0.898333}`	0.03189	0.00455	2.01	13th Gen Intel(R) Core(TM) i7-1355U, single thread, Python 3.13.5 + numpy 2.4.4		wav code viz
modal-series string-solutions · Jeremy Magland	modal-n16	modal series, truncated `{"n_modes": 16}`	0.04462	0.02968	0.0384	13th Gen Intel(R) Core(TM) i7-1355U, single thread, Python 3.13.5 + numpy 2.4.4	modal-n8	wav code viz
modal-series string-solutions · Jeremy Magland	modal-n8	modal series, truncated `{"n_modes": 8}`	0.1482	0.1338	0.0192	13th Gen Intel(R) Core(TM) i7-1355U, single thread, Python 3.13.5 + numpy 2.4.4	modal-n4	wav code viz
modal-series string-solutions · Jeremy Magland	modal-n4	modal series, truncated `{"n_modes": 4}`	0.1876	0.175	0.0079	13th Gen Intel(R) Core(TM) i7-1355U, single thread, Python 3.13.5 + numpy 2.4.4		wav code viz

Reference selection

Candidates are the maximal elements of each submission's asserted order. The score is the number of asserted pairs from other submissions whose order is preserved by the primary error to this candidate. Ties are broken first by the convergence gap (the primary error between the candidate and the nearest solution of its own submission asserted to be less accurate; smaller means a tighter convergence claim), then by the mean primary error to the other candidates.

Candidate	Pairs preserved	Convergence gap	Mean error to other candidates	Violated pairs
string-solutions/modal-series/modal-n1024	4/4	1.037e-06	0.000132
string-solutions/fd-second-order/fd-m16	6/6	0.0003975	0.000132

Order check against the chosen reference

All asserted accuracy orderings are preserved by both metrics under the chosen reference.

Pairwise errors (row vs column as reference)

waveform_l2

	string-solutions/modal-series/modal-n1024	string-solutions/modal-series/modal-n256	string-solutions/fd-second-order/fd-m16	string-solutions/fd-second-order/fd-m8	string-solutions/fd-second-order/fd-m4	string-solutions/modal-series/modal-n64	string-solutions/fd-second-order/fd-m2	string-solutions/modal-series/modal-n32	string-solutions/fd-second-order/fd-m1	string-solutions/modal-series/modal-n16	string-solutions/modal-series/modal-n8	string-solutions/modal-series/modal-n4
string-solutions/modal-series/modal-n1024	0	1.04e-06	0.000132	0.00053	0.00212	0.00322	0.00853	0.0179	0.0319	0.0447	0.15	0.191
string-solutions/modal-series/modal-n256	1.04e-06	0	0.000132	0.00053	0.00212	0.00322	0.00853	0.0179	0.0319	0.0447	0.15	0.191
string-solutions/fd-second-order/fd-m16	0.000132	0.000132	0	0.000398	0.00198	0.00322	0.0084	0.0179	0.0318	0.0447	0.15	0.191
string-solutions/fd-second-order/fd-m8	0.00053	0.00053	0.000398	0	0.00159	0.00325	0.00801	0.0179	0.0315	0.0446	0.15	0.191
string-solutions/fd-second-order/fd-m4	0.00212	0.00212	0.00198	0.00159	0	0.00378	0.00645	0.0179	0.0301	0.0446	0.15	0.191
string-solutions/modal-series/modal-n64	0.00322	0.00322	0.00322	0.00325	0.00378	0	0.00881	0.0176	0.0316	0.0445	0.15	0.191
string-solutions/fd-second-order/fd-m2	0.00853	0.00853	0.0084	0.00801	0.00645	0.00881	0	0.019	0.0245	0.0446	0.149	0.191
string-solutions/modal-series/modal-n32	0.0179	0.0179	0.0179	0.0179	0.0179	0.0176	0.019	0	0.033	0.0409	0.149	0.19
string-solutions/fd-second-order/fd-m1	0.0319	0.0319	0.0318	0.0314	0.0301	0.0316	0.0245	0.033	0	0.0489	0.149	0.19
string-solutions/modal-series/modal-n16	0.0446	0.0446	0.0446	0.0446	0.0446	0.0445	0.0446	0.0409	0.0489	0	0.143	0.186
string-solutions/modal-series/modal-n8	0.148	0.148	0.148	0.148	0.148	0.148	0.148	0.147	0.147	0.141	0	0.117
string-solutions/modal-series/modal-n4	0.188	0.188	0.188	0.188	0.188	0.188	0.187	0.187	0.187	0.182	0.116	0

spectrogram_l2

	string-solutions/modal-series/modal-n1024	string-solutions/modal-series/modal-n256	string-solutions/fd-second-order/fd-m16	string-solutions/fd-second-order/fd-m8	string-solutions/fd-second-order/fd-m4	string-solutions/modal-series/modal-n64	string-solutions/fd-second-order/fd-m2	string-solutions/modal-series/modal-n32	string-solutions/fd-second-order/fd-m1	string-solutions/modal-series/modal-n16	string-solutions/modal-series/modal-n8	string-solutions/modal-series/modal-n4
string-solutions/modal-series/modal-n1024	0	5.63e-10	1.83e-05	7.3e-05	0.000288	0.000315	0.00118	0.00695	0.00455	0.0297	0.135	0.178
string-solutions/modal-series/modal-n256	5.63e-10	0	1.83e-05	7.3e-05	0.000288	0.000315	0.00118	0.00695	0.00455	0.0297	0.135	0.178
string-solutions/fd-second-order/fd-m16	1.83e-05	1.83e-05	0	5.47e-05	0.00027	0.000316	0.00116	0.00695	0.00453	0.0297	0.135	0.178
string-solutions/fd-second-order/fd-m8	7.3e-05	7.3e-05	5.47e-05	0	0.000215	0.000323	0.00111	0.00694	0.00448	0.0297	0.135	0.178
string-solutions/fd-second-order/fd-m4	0.000288	0.000288	0.00027	0.000215	0	0.000425	0.000897	0.00694	0.00429	0.0297	0.135	0.178
string-solutions/modal-series/modal-n64	0.000315	0.000315	0.000316	0.000323	0.000425	0	0.00121	0.00694	0.00455	0.0297	0.135	0.178
string-solutions/fd-second-order/fd-m2	0.00118	0.00118	0.00116	0.00111	0.000897	0.00121	0	0.00692	0.00345	0.0295	0.135	0.177
string-solutions/modal-series/modal-n32	0.00695	0.00695	0.00695	0.00694	0.00694	0.00694	0.00692	0	0.00757	0.0289	0.135	0.178
string-solutions/fd-second-order/fd-m1	0.00455	0.00455	0.00453	0.00448	0.00429	0.00455	0.00345	0.00757	0	0.0292	0.134	0.177
string-solutions/modal-series/modal-n16	0.0297	0.0297	0.0297	0.0297	0.0296	0.0297	0.0295	0.0289	0.0292	0	0.132	0.175
string-solutions/modal-series/modal-n8	0.134	0.134	0.134	0.134	0.134	0.134	0.134	0.134	0.133	0.131	0	0.114
string-solutions/modal-series/modal-n4	0.175	0.175	0.175	0.175	0.175	0.175	0.175	0.175	0.174	0.172	0.114	0