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The dataset generation failed
Error code: DatasetGenerationError
Exception: TypeError
Message: int() argument must be a string, a bytes-like object or a real number, not 'NoneType'
Traceback: Traceback (most recent call last):
File "/usr/local/lib/python3.14/site-packages/datasets/builder.py", line 1520, in _prepare_split_single
for key, record in generator:
^^^^^^^^^
File "/src/services/worker/src/worker/job_runners/config/parquet_and_info.py", line 613, in wrapped
for item in generator(*args, **kwargs):
~~~~~~~~~^^^^^^^^^^^^^^^^^
File "/usr/local/lib/python3.14/site-packages/datasets/packaged_modules/webdataset/webdataset.py", line 130, in _generate_examples
for example_idx, example in enumerate(self._get_pipeline_from_tar(tar_path, tar_iterator)):
~~~~~~~~~^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
File "/usr/local/lib/python3.14/site-packages/datasets/packaged_modules/webdataset/webdataset.py", line 34, in _get_pipeline_from_tar
for filename, f in tar_iterator:
^^^^^^^^^^^^
File "/usr/local/lib/python3.14/site-packages/datasets/utils/track.py", line 49, in __iter__
for x in self.generator(*self.args):
~~~~~~~~~~~~~~^^^^^^^^^^^^
File "/usr/local/lib/python3.14/site-packages/datasets/utils/file_utils.py", line 1405, in _iter_from_urlpath
with xopen(urlpath, "rb", download_config=download_config, block_size=0) as f:
~~~~~^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
File "/usr/local/lib/python3.14/site-packages/datasets/utils/file_utils.py", line 982, in xopen
file_obj = fs.open(paths[0], mode)
File "<string>", line 3, in open
File "/usr/local/lib/python3.14/unittest/mock.py", line 1176, in __call__
return self._mock_call(*args, **kwargs)
~~~~~~~~~~~~~~~^^^^^^^^^^^^^^^^^
File "/usr/local/lib/python3.14/unittest/mock.py", line 1180, in _mock_call
return self._execute_mock_call(*args, **kwargs)
~~~~~~~~~~~~~~~~~~~~~~~^^^^^^^^^^^^^^^^^
File "/usr/local/lib/python3.14/unittest/mock.py", line 1247, in _execute_mock_call
result = effect(*args, **kwargs)
File "/src/services/worker/src/worker/job_runners/config/parquet_and_info.py", line 786, in wrapped
tracker.files[urlpath] = {"read": 0, "size": int(f.size)}
~~~^^^^^^^^
TypeError: int() argument must be a string, a bytes-like object or a real number, not 'NoneType'
The above exception was the direct cause of the following exception:
Traceback (most recent call last):
File "/src/services/worker/src/worker/job_runners/config/parquet_and_info.py", line 1369, in compute_config_parquet_and_info_response
parquet_operations, partial, estimated_dataset_info = stream_convert_to_parquet(
~~~~~~~~~~~~~~~~~~~~~~~~~^
builder, max_dataset_size_bytes=max_dataset_size_bytes
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
)
^
File "/src/services/worker/src/worker/job_runners/config/parquet_and_info.py", line 948, in stream_convert_to_parquet
builder._prepare_split(split_generator=splits_generators[split], file_format="parquet")
~~~~~~~~~~~~~~~~~~~~~~^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
File "/usr/local/lib/python3.14/site-packages/datasets/builder.py", line 1382, in _prepare_split
for job_id, done, content in self._prepare_split_single(
~~~~~~~~~~~~~~~~~~~~~~~~~~^
gen_kwargs=gen_kwargs, job_id=job_id, **_prepare_split_args
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
):
^
File "/usr/local/lib/python3.14/site-packages/datasets/builder.py", line 1560, in _prepare_split_single
raise DatasetGenerationError("An error occurred while generating the dataset") from e
datasets.exceptions.DatasetGenerationError: An error occurred while generating the datasetNeed help to make the dataset viewer work? Make sure to review how to configure the dataset viewer, and open a discussion for direct support.
png image | json dict | __key__ string | __url__ string |
|---|---|---|---|
{
"height": 50,
"id": "CMER-Bench_easy_0706_0207_19",
"source": "CMER-Bench",
"tex": "\\langle\\psi|e^{-Q}|\\psi\\rangle=1.(19)",
"tokens": 1,
"width": 350
} | CMER-Bench_easy_0706_0207_19 | hf://datasets/Baitlo/math_total@1a80ace131210139a18b431c1232c83334fc82fc/labels-000000.tar | |
{
"height": 64,
"id": "CMER-Bench_easy_0706_2428_9",
"source": "CMER-Bench",
"tex": "(1.6) \\left\\{ \\theta_j, \\theta_k \\right\\} = 0, \\quad \\left\\{ \\theta_j, \\frac{1}{2} \\log[\\mu_k/\\mu_n] \\right\\} = \\delta_{jk},",
"tokens": 15,
"width": 801
} | CMER-Bench_easy_0706_2428_9 | hf://datasets/Baitlo/math_total@1a80ace131210139a18b431c1232c83334fc82fc/labels-000000.tar | |
{
"height": 116,
"id": "CMER-Bench_easy_0707_1945_9",
"source": "CMER-Bench",
"tex": "ds^2 = \\frac{U^2}{\\rho^2} (dt - P d\\phi)^2 - \\frac{\\sin^2 \\theta}{\\rho^2} \\left[ (F + l^2) \\, d\\phi - a dt \\right]^2 - \\frac{\\rho^2}{U^2} dr^2 - \\rho^2 d\\theta^2 \\quad (4)",
"tokens": 28,
"width": 1312
} | CMER-Bench_easy_0707_1945_9 | hf://datasets/Baitlo/math_total@1a80ace131210139a18b431c1232c83334fc82fc/labels-000000.tar | |
{
"height": 66,
"id": "CMER-Bench_easy_0707_2579_10",
"source": "CMER-Bench",
"tex": "\\langle\\langle \\mathcal{E}_{\\beta\\beta}^{(j)} | \\mathcal{O} | \\mathcal{D}_{\\alpha}^{(i)} \\rangle\\rangle = 0 \\quad (\\lambda_{\\alpha} \\neq \\lambda_{\\beta}) . (9)",
"tokens": 15,
"width": 643
} | CMER-Bench_easy_0707_2579_10 | hf://datasets/Baitlo/math_total@1a80ace131210139a18b431c1232c83334fc82fc/labels-000000.tar | |
{
"height": 65,
"id": "CMER-Bench_easy_0707_3327_12",
"source": "CMER-Bench",
"tex": "G = \\left\\{ (x, x_{n+1}) \\mid u_1(x) < x_{n+1} < u_2(x) \\right\\}",
"tokens": 12,
"width": 738
} | CMER-Bench_easy_0707_3327_12 | hf://datasets/Baitlo/math_total@1a80ace131210139a18b431c1232c83334fc82fc/labels-000000.tar | |
{
"height": 118,
"id": "CMER-Bench_easy_0707_4247_10",
"source": "CMER-Bench",
"tex": "w = \\frac{p}{2X \\frac{\\partial p}{\\partial X} - p}.(11)",
"tokens": 8,
"width": 383
} | CMER-Bench_easy_0707_4247_10 | hf://datasets/Baitlo/math_total@1a80ace131210139a18b431c1232c83334fc82fc/labels-000000.tar | |
{
"height": 125,
"id": "CMER-Bench_easy_0711_1095_65",
"source": "CMER-Bench",
"tex": "1 - p(\\omega) := P_{\\omega}^{b}(\\tau(d) < \\tau^{+}(b)) = \\omega_{b} \\frac{\\mathrm{e}^{V(b)}}{\\sum_{x=b}^{d-1} \\mathrm{e}^{V(x)}},",
"tokens": 11,
"width": 860
} | CMER-Bench_easy_0711_1095_65 | hf://datasets/Baitlo/math_total@1a80ace131210139a18b431c1232c83334fc82fc/labels-000000.tar | |
{
"height": 124,
"id": "CMER-Bench_easy_0711_2469_1",
"source": "CMER-Bench",
"tex": "f^{a} = \\lim_{\\epsilon \\to 0} q^{2} \\int_{-\\infty}^{\\tau - \\epsilon} \\nabla^{a} G_{ret} \\left( x, x' \\right) d\\tau'(2)",
"tokens": 16,
"width": 693
} | CMER-Bench_easy_0711_2469_1 | hf://datasets/Baitlo/math_total@1a80ace131210139a18b431c1232c83334fc82fc/labels-000000.tar | |
{
"height": 99,
"id": "CMER-Bench_easy_0711_3396_22",
"source": "CMER-Bench",
"tex": "\\mathcal{M}_{l \\pm}^{\\alpha} = \\frac{1}{2} [\\tau_\\alpha, \\tau_0] \\mathcal{M}_{l \\pm}^{(-)} + \\frac{1}{2} \\{\\tau_\\alpha, \\tau_0\\} \\mathcal{M}_{l \\pm}^{(+)} + \\tau_\\alpha \\mathcal{M}_{l \\pm}^{(0)}, \\quad (1... | CMER-Bench_easy_0711_3396_22 | hf://datasets/Baitlo/math_total@1a80ace131210139a18b431c1232c83334fc82fc/labels-000000.tar | |
{
"height": 108,
"id": "CMER-Bench_easy_0711_4559_123",
"source": "CMER-Bench",
"tex": "c_{12} = \\left[ -\\frac{1}{2} \\left( \\frac{\\partial^2 F}{\\partial \\kappa^2} \\right)_c \\right]^{1/2} \\left( \\frac{\\partial \\kappa}{\\partial \\nu_2} \\right)_c,",
"tokens": 15,
"width": 516
} | CMER-Bench_easy_0711_4559_123 | hf://datasets/Baitlo/math_total@1a80ace131210139a18b431c1232c83334fc82fc/labels-000000.tar | |
{
"height": 47,
"id": "CMER-Bench_easy_0712_3103_33",
"source": "CMER-Bench",
"tex": "\\xi = u + V - V_{\\infty}.",
"tokens": 7,
"width": 306
} | CMER-Bench_easy_0712_3103_33 | hf://datasets/Baitlo/math_total@1a80ace131210139a18b431c1232c83334fc82fc/labels-000000.tar | |
{
"height": 100,
"id": "CMER-Bench_easy_0801_0077_27",
"source": "CMER-Bench",
"tex": "C_{\\infty} = \\bigcap_{R} \\Omega_{R}(C). = \\bigcap_{d} \\Omega_{d}^{K}(C).",
"tokens": 7,
"width": 555
} | CMER-Bench_easy_0801_0077_27 | hf://datasets/Baitlo/math_total@1a80ace131210139a18b431c1232c83334fc82fc/labels-000000.tar | |
{
"height": 47,
"id": "CMER-Bench_easy_0801_0438_56",
"source": "CMER-Bench",
"tex": "\\rho(H(z, S)) = \\langle H(z, \\pi(S))\\xi, \\xi\\rangle_{\\mathcal{H}}",
"tokens": 7,
"width": 562
} | CMER-Bench_easy_0801_0438_56 | hf://datasets/Baitlo/math_total@1a80ace131210139a18b431c1232c83334fc82fc/labels-000000.tar | |
{
"height": 215,
"id": "CMER-Bench_easy_0801_1366_16",
"source": "CMER-Bench",
"tex": "{ \\varphi } _ { 1 } = \\frac { i ( { p } _ { 2 } - p ) } { { p } _ { 3 } } { \\varphi } _ { 1 } ^ { \\prime } , { \\varphi } _ { 2 } ^ { \\prime } = \\frac { i ( { p } _ { 2 } + p ) } { { p } _ { 3 } } { \\varphi } _ { 2 } .... | CMER-Bench_easy_0801_1366_16 | hf://datasets/Baitlo/math_total@1a80ace131210139a18b431c1232c83334fc82fc/labels-000000.tar | |
{
"height": 60,
"id": "CMER-Bench_easy_0801_2895_35",
"source": "CMER-Bench",
"tex": "(x^2 - a^2)(1 - dx) < 2(1 - a^2)x(x - d), \\text{ i.e.,}",
"tokens": 13,
"width": 772
} | CMER-Bench_easy_0801_2895_35 | hf://datasets/Baitlo/math_total@1a80ace131210139a18b431c1232c83334fc82fc/labels-000000.tar | |
{
"height": 99,
"id": "CMER-Bench_easy_0801_3702_26",
"source": "CMER-Bench",
"tex": "D_c = \\sigma^2 P_e (N_u) \\left[ \\frac{\\gamma + \\beta}{\\gamma} \\ln \\left( 1 + \\frac{\\gamma}{\\beta} \\right) - \\frac{1}{\\gamma} + \\frac{1}{2} \\right], \\quad (20)",
"tokens": 22,
"width": 926
} | CMER-Bench_easy_0801_3702_26 | hf://datasets/Baitlo/math_total@1a80ace131210139a18b431c1232c83334fc82fc/labels-000000.tar | |
{
"height": 99,
"id": "CMER-Bench_easy_0802_0067_19",
"source": "CMER-Bench",
"tex": "V = C \\frac{4\\pi}{3} R_1 R_2 R_3 (18)",
"tokens": 8,
"width": 402
} | CMER-Bench_easy_0802_0067_19 | hf://datasets/Baitlo/math_total@1a80ace131210139a18b431c1232c83334fc82fc/labels-000000.tar | |
{
"height": 108,
"id": "CMER-Bench_easy_0802_0340_14",
"source": "CMER-Bench",
"tex": "\\frac{v_{gj}}{v_{Dj}} \\approx \\frac{g}{\\Omega_j} \\frac{\\Omega_j L}{C_{sj}^2} \\approx \\frac{L}{H}, \\quad (15)",
"tokens": 9,
"width": 465
} | CMER-Bench_easy_0802_0340_14 | hf://datasets/Baitlo/math_total@1a80ace131210139a18b431c1232c83334fc82fc/labels-000000.tar | |
{
"height": 104,
"id": "CMER-Bench_easy_0802_2408_76",
"source": "CMER-Bench",
"tex": "\\partial_t \\int_{\\mathbf{R}} \\Psi_A(x - x(t)) \\varepsilon^2 \\le -c \\int_{\\mathbf{R}} (\\varepsilon^2 + \\varepsilon_x^2) e^{-|x - x(t)|/A}",
"tokens": 15,
"width": 914
} | CMER-Bench_easy_0802_2408_76 | hf://datasets/Baitlo/math_total@1a80ace131210139a18b431c1232c83334fc82fc/labels-000000.tar | |
{
"height": 99,
"id": "CMER-Bench_easy_0802_2445_4",
"source": "CMER-Bench",
"tex": "\\frac{42}{4097}, \\frac{54}{4097}, \\frac{134}{4097}, \\frac{190}{4097}.",
"tokens": 4,
"width": 469
} | CMER-Bench_easy_0802_2445_4 | hf://datasets/Baitlo/math_total@1a80ace131210139a18b431c1232c83334fc82fc/labels-000000.tar | |
{
"height": 125,
"id": "CMER-Bench_easy_0802_3537_20",
"source": "CMER-Bench",
"tex": "\\Delta Q = - { \\oint } _ { 0 } ^ { 2 \\pi } 𝑑 { k } _ { y } \\frac { \\partial { P } _ { x } ( { k } _ { y } ) } { \\partial { k } _ { y } } . ( 1 7 ) ",
"tokens": 59,
"width": 555
} | CMER-Bench_easy_0802_3537_20 | hf://datasets/Baitlo/math_total@1a80ace131210139a18b431c1232c83334fc82fc/labels-000000.tar | |
{
"height": 50,
"id": "CMER-Bench_easy_0803_2360_66",
"source": "CMER-Bench",
"tex": "v_0 = 220 \\pm 20 \\text{km/s}(64)",
"tokens": 6,
"width": 423
} | CMER-Bench_easy_0803_2360_66 | hf://datasets/Baitlo/math_total@1a80ace131210139a18b431c1232c83334fc82fc/labels-000000.tar | |
{
"height": 119,
"id": "CMER-Bench_easy_0803_3766_96",
"source": "CMER-Bench",
"tex": "\\int_{Y} \\gamma = \\frac{1}{2} \\int_{\\widehat{Y}} \\widehat{\\gamma} = \\frac{1}{2t} \\int_{\\widehat{S}} \\widehat{\\gamma}.",
"tokens": 10,
"width": 456
} | CMER-Bench_easy_0803_3766_96 | hf://datasets/Baitlo/math_total@1a80ace131210139a18b431c1232c83334fc82fc/labels-000000.tar | |
{
"height": 58,
"id": "CMER-Bench_easy_0804_4241_16",
"source": "CMER-Bench",
"tex": "\\{\\alpha\\}_{-(N+1)} = K(\\alpha, q^N). (2.15)",
"tokens": 5,
"width": 535
} | CMER-Bench_easy_0804_4241_16 | hf://datasets/Baitlo/math_total@1a80ace131210139a18b431c1232c83334fc82fc/labels-000000.tar | |
{
"height": 131,
"id": "CMER-Bench_easy_0805_0964_3",
"source": "CMER-Bench",
"tex": "\\langle\\langle n_j \\rangle\\rangle = \\sum_{i=1}^{5} R_i \\langle n_j \\rangle_{q_i} (21)",
"tokens": 10,
"width": 440
} | CMER-Bench_easy_0805_0964_3 | hf://datasets/Baitlo/math_total@1a80ace131210139a18b431c1232c83334fc82fc/labels-000000.tar | |
{
"height": 131,
"id": "CMER-Bench_easy_0805_1971_37",
"source": "CMER-Bench",
"tex": "L_\\alpha(x) = \\sup \\left\\{ \\theta \\in [0, 1] \\text{ such that } \\sum_{i=x}^n \\binom{n}{i} \\theta^i (1 - \\theta)^{n-i} \\ge \\alpha \\right\\}",
"tokens": 21,
"width": 1104
} | CMER-Bench_easy_0805_1971_37 | hf://datasets/Baitlo/math_total@1a80ace131210139a18b431c1232c83334fc82fc/labels-000000.tar | |
{
"height": 99,
"id": "CMER-Bench_easy_0805_3094_26",
"source": "CMER-Bench",
"tex": "y_i = \\sum_j \\mathcal{H}_{ij} z_j . (28)",
"tokens": 7,
"width": 344
} | CMER-Bench_easy_0805_3094_26 | hf://datasets/Baitlo/math_total@1a80ace131210139a18b431c1232c83334fc82fc/labels-000000.tar | |
{
"height": 99,
"id": "CMER-Bench_easy_0805_4403_1",
"source": "CMER-Bench",
"tex": "\\frac{\\partial u}{\\partial t} = \\Delta u + u^p - V(x)u",
"tokens": 10,
"width": 425
} | CMER-Bench_easy_0805_4403_1 | hf://datasets/Baitlo/math_total@1a80ace131210139a18b431c1232c83334fc82fc/labels-000000.tar | |
{
"height": 140,
"id": "CMER-Bench_easy_0806_3338_11",
"source": "CMER-Bench",
"tex": "\\Psi(x_1, t_2) = \\frac{\\sqrt{2}\\eta e^{i(\\kappa x_1 + (\\kappa^2 - \\eta^2)t_2/2)}}{\\cosh(\\eta(x_1 + \\kappa t_2))}.",
"tokens": 13,
"width": 638
} | CMER-Bench_easy_0806_3338_11 | hf://datasets/Baitlo/math_total@1a80ace131210139a18b431c1232c83334fc82fc/labels-000000.tar | |
{
"height": 70,
"id": "CMER-Bench_easy_0807_2523_16",
"source": "CMER-Bench",
"tex": "(\\tilde{D}_\\rho T^\\lambda_{\\mu\\nu}) \\xi^\\rho = (h^{\\sigma\\lambda} T^\\rho_{\\mu\\nu} + h^{\\sigma}_{\\mu} T^{\\lambda\\rho}{}_{\\nu} + h^{\\sigma}_{\\nu} T^{\\lambda}{}_{\\mu}{}^{\\rho}) \\tilde{D}_{[\\rho} \\xi_{\\si... | CMER-Bench_easy_0807_2523_16 | hf://datasets/Baitlo/math_total@1a80ace131210139a18b431c1232c83334fc82fc/labels-000000.tar | |
{
"height": 136,
"id": "CMER-Bench_easy_0807_4832_17",
"source": "CMER-Bench",
"tex": "= \\frac{1}{\\| a_n \\|_2} \\int_0^\\infty e^{-t} \\int_{\\{\\| x \\|_{a_n}=t\\}} \\left( \\prod_{i=1}^n |x_i|^{a_{i,n}s} \\right) d\\mathcal{H}^{n-1}(x) dt",
"tokens": 15,
"width": 998
} | CMER-Bench_easy_0807_4832_17 | hf://datasets/Baitlo/math_total@1a80ace131210139a18b431c1232c83334fc82fc/labels-000000.tar | |
{
"height": 112,
"id": "CMER-Bench_easy_0808_0696_47",
"source": "CMER-Bench",
"tex": "\\tilde{p}(\\kappa) = \\frac{m}{k} \\left[ Z \\left( \\text{sn}^{-1} \\left( \\sqrt{-1 + \\frac{1}{k^2} + \\frac{\\kappa^2}{m^2}}, k \\right), k \\right) + \\frac{\\pi}{2\\mathbf{K}} \\right] \\quad (48)",
"tokens": 22,
"... | CMER-Bench_easy_0808_0696_47 | hf://datasets/Baitlo/math_total@1a80ace131210139a18b431c1232c83334fc82fc/labels-000000.tar | |
{
"height": 65,
"id": "CMER-Bench_easy_0808_2029_3",
"source": "CMER-Bench",
"tex": "\\mathbf{q}_{eff} = \\hat{k}_i \\left[ k_i - \\delta k \\right] - \\hat{k}_f \\left[ k_f - \\delta k \\right].(4)",
"tokens": 17,
"width": 676
} | CMER-Bench_easy_0808_2029_3 | hf://datasets/Baitlo/math_total@1a80ace131210139a18b431c1232c83334fc82fc/labels-000000.tar | |
{
"height": 125,
"id": "CMER-Bench_easy_0809_0190_63",
"source": "CMER-Bench",
"tex": "\\int_{0}^{\\infty} d E E^{s}",
"tokens": 4,
"width": 188
} | CMER-Bench_easy_0809_0190_63 | hf://datasets/Baitlo/math_total@1a80ace131210139a18b431c1232c83334fc82fc/labels-000000.tar | |
{
"height": 49,
"id": "CMER-Bench_easy_0809_0306_105",
"source": "CMER-Bench",
"tex": "x_p \\ge 0_p,",
"tokens": 3,
"width": 154
} | CMER-Bench_easy_0809_0306_105 | hf://datasets/Baitlo/math_total@1a80ace131210139a18b431c1232c83334fc82fc/labels-000000.tar | |
{
"height": 103,
"id": "CMER-Bench_easy_0809_2305_14",
"source": "CMER-Bench",
"tex": "\\left( \\frac{Z_{crust}}{Z_{lith}} \\right) = \\frac{7}{110} \\left( \\frac{Q}{Q_{Earth}} \\right) \\left( \\frac{Z_{crust}}{Z_{crust, Earth}} \\right) . (15)",
"tokens": 14,
"width": 896
} | CMER-Bench_easy_0809_2305_14 | hf://datasets/Baitlo/math_total@1a80ace131210139a18b431c1232c83334fc82fc/labels-000000.tar | |
{
"height": 66,
"id": "CMER-Bench_easy_0809_2342_1",
"source": "CMER-Bench",
"tex": "\\hat{\\chi}(x) = A_0 + A_1x + A_2x^2 + A_3x^{d\\nu-1} + \\cdots , \\quad (2)",
"tokens": 14,
"width": 844
} | CMER-Bench_easy_0809_2342_1 | hf://datasets/Baitlo/math_total@1a80ace131210139a18b431c1232c83334fc82fc/labels-000000.tar | |
{
"height": 46,
"id": "CMER-Bench_easy_0809_3326_9",
"source": "CMER-Bench",
"tex": "R(y) = C(\\alpha_s) \\Sigma(y, \\alpha_s) + D(y, \\alpha_s), (10)",
"tokens": 9,
"width": 735
} | CMER-Bench_easy_0809_3326_9 | hf://datasets/Baitlo/math_total@1a80ace131210139a18b431c1232c83334fc82fc/labels-000000.tar | |
{
"height": 111,
"id": "CMER-Bench_easy_0810_0094_8",
"source": "CMER-Bench",
"tex": "E_{syn,cut} \\approx 3 \\times 10^{-3} B_{100} \\left( \\frac{E_{e,max}}{\\mathrm{TeV}} \\right)^{2} \\mathrm{keV}, \\quad (9)",
"tokens": 12,
"width": 811
} | CMER-Bench_easy_0810_0094_8 | hf://datasets/Baitlo/math_total@1a80ace131210139a18b431c1232c83334fc82fc/labels-000000.tar | |
{
"height": 107,
"id": "CMER-Bench_easy_0810_0525_12",
"source": "CMER-Bench",
"tex": "\\phi_1 \\simeq \\pm \\frac{2}{3} \\sqrt{\\frac{7}{3}} y^{-1/2} + O(y^{-1}). (13)",
"tokens": 9,
"width": 602
} | CMER-Bench_easy_0810_0525_12 | hf://datasets/Baitlo/math_total@1a80ace131210139a18b431c1232c83334fc82fc/labels-000000.tar | |
{
"height": 104,
"id": "CMER-Bench_easy_0810_3029_14",
"source": "CMER-Bench",
"tex": "p_i = P(\\sigma_i = 1) = \\frac{e^{U_g}}{e^{U_g} + e^{-U_g}}, \\quad (4.3)",
"tokens": 11,
"width": 638
} | CMER-Bench_easy_0810_3029_14 | hf://datasets/Baitlo/math_total@1a80ace131210139a18b431c1232c83334fc82fc/labels-000000.tar | |
{
"height": 57,
"id": "CMER-Bench_easy_0811_1540_1",
"source": "CMER-Bench",
"tex": "f^{efg}{}_{b} f^{cba}{}_{d} + f^{fea}{}_{b} f^{cbg}{}_{d} + f^{*gaf}{}_{b} f^{ceb}{}_{d} + f^{*age}{}_{b} f^{cfb}{}_{d} = 0 \\text{ .}(2.2)",
"tokens": 15,
"width": 1132
} | CMER-Bench_easy_0811_1540_1 | hf://datasets/Baitlo/math_total@1a80ace131210139a18b431c1232c83334fc82fc/labels-000000.tar | |
{
"height": 132,
"id": "CMER-Bench_easy_0811_2856_25",
"source": "CMER-Bench",
"tex": "|\\varphi_{i}(t)\\rangle = \\sum_{\\beta=1}^{N} |\\psi_{\\beta}(t)\\rangle v_{\\beta i}(t) \\quad , \\quad \\sum_{\\alpha} v_{\\alpha i}^*(t) v_{\\alpha j}^*(t) = \\delta_{ij} \\cdot (18)",
"tokens": 18,
"width": 1059
} | CMER-Bench_easy_0811_2856_25 | hf://datasets/Baitlo/math_total@1a80ace131210139a18b431c1232c83334fc82fc/labels-000000.tar | |
{
"height": 112,
"id": "CMER-Bench_easy_0812_1081_19",
"source": "CMER-Bench",
"tex": "\\frac{\\Gamma_{0}}{\\alpha^{3}}<3\\left[\\frac{17}{24}\\right]^{3 / 2} \\frac{1}{\\kappa(1-n s)^{3 / 2}} .(21)",
"tokens": 8,
"width": 629
} | CMER-Bench_easy_0812_1081_19 | hf://datasets/Baitlo/math_total@1a80ace131210139a18b431c1232c83334fc82fc/labels-000000.tar | |
{
"height": 103,
"id": "CMER-Bench_easy_0812_2467_23",
"source": "CMER-Bench",
"tex": "\\partial_\\theta K = \\kappa(r, \\theta). \\quad \\frac{\\partial_r K}{\\partial_\\theta K} = \\lambda(r, \\theta), \\quad (24)",
"tokens": 14,
"width": 658
} | CMER-Bench_easy_0812_2467_23 | hf://datasets/Baitlo/math_total@1a80ace131210139a18b431c1232c83334fc82fc/labels-000000.tar | |
{
"height": 58,
"id": "CMER-Bench_easy_0901_0421_55",
"source": "CMER-Bench",
"tex": "\\Phi_u(r) \\geq \\mu - Cr_0^\\epsilon",
"tokens": 5,
"width": 304
} | CMER-Bench_easy_0901_0421_55 | hf://datasets/Baitlo/math_total@1a80ace131210139a18b431c1232c83334fc82fc/labels-000000.tar | |
{
"height": 54,
"id": "CMER-Bench_easy_0901_1171_315",
"source": "CMER-Bench",
"tex": "\\|\\varphi(t)^{-1}\\psi(t)\\| \\le 1 \\quad (t \\in \\Omega_0)",
"tokens": 7,
"width": 502
} | CMER-Bench_easy_0901_1171_315 | hf://datasets/Baitlo/math_total@1a80ace131210139a18b431c1232c83334fc82fc/labels-000000.tar | |
{
"height": 106,
"id": "CMER-Bench_easy_0901_3835_37",
"source": "CMER-Bench",
"tex": "\\frac{S_{q_{r-1}}}{S_{q_r}} \\le r^{-2}.(3.6)",
"tokens": 3,
"width": 319
} | CMER-Bench_easy_0901_3835_37 | hf://datasets/Baitlo/math_total@1a80ace131210139a18b431c1232c83334fc82fc/labels-000000.tar | |
{
"height": 43,
"id": "CMER-Bench_easy_0902_0079_70",
"source": "CMER-Bench",
"tex": "\\dot{\\gamma} = \\gamma \\times \\omega(t), \\quad (5.30)",
"tokens": 7,
"width": 354
} | CMER-Bench_easy_0902_0079_70 | hf://datasets/Baitlo/math_total@1a80ace131210139a18b431c1232c83334fc82fc/labels-000000.tar | |
{
"height": 58,
"id": "CMER-Bench_easy_0902_0238_18",
"source": "CMER-Bench",
"tex": "\\langle A \\rangle_{cl} = p_{\\uparrow} A_{\\uparrow} + p_{\\downarrow} A_{\\downarrow}, \\quad \\langle A^2 \\rangle_{cl} = p_{\\uparrow} A_{\\uparrow}^2 + p_{\\downarrow} A_{\\downarrow}^2 . (20)",
"tokens": 21,
"width"... | CMER-Bench_easy_0902_0238_18 | hf://datasets/Baitlo/math_total@1a80ace131210139a18b431c1232c83334fc82fc/labels-000000.tar | |
{
"height": 66,
"id": "CMER-Bench_easy_0902_1306_1",
"source": "CMER-Bench",
"tex": "f(r, u_0, \\dots, u_d) = a(\\lambda, d) \\, \\Delta_d \\, r^{d^2-1} \\exp \\left( -\\lambda w_d r^d \\right)",
"tokens": 17,
"width": 892
} | CMER-Bench_easy_0902_1306_1 | hf://datasets/Baitlo/math_total@1a80ace131210139a18b431c1232c83334fc82fc/labels-000000.tar | |
{
"height": 104,
"id": "CMER-Bench_easy_0902_2965_20",
"source": "CMER-Bench",
"tex": "d \\ln p_l = \\left( \\mu_{\\text{riskless}} + l \\mu_{\\text{excess}} - \\frac{l^2 \\sigma_M^2}{2} \\right) dt + l \\sigma_M dW_t. (17)",
"tokens": 19,
"width": 1012
} | CMER-Bench_easy_0902_2965_20 | hf://datasets/Baitlo/math_total@1a80ace131210139a18b431c1232c83334fc82fc/labels-000000.tar | |
{
"height": 99,
"id": "CMER-Bench_easy_0903_0529_97",
"source": "CMER-Bench",
"tex": "(3.27) \\dot{h} \\le -h \\left( 1 - \\frac{|\\dot{a}|}{a} \\right) + |\\dot{a}| \\|V_\\delta\\|.",
"tokens": 12,
"width": 622
} | CMER-Bench_easy_0903_0529_97 | hf://datasets/Baitlo/math_total@1a80ace131210139a18b431c1232c83334fc82fc/labels-000000.tar | |
{
"height": 99,
"id": "CMER-Bench_easy_0903_1079_1",
"source": "CMER-Bench",
"tex": "\\langle S_{z} \\rangle = S(1 + \\frac{J\\rho}{2} + O(J^{2})), \\quad (1)",
"tokens": 11,
"width": 556
} | CMER-Bench_easy_0903_1079_1 | hf://datasets/Baitlo/math_total@1a80ace131210139a18b431c1232c83334fc82fc/labels-000000.tar | |
{
"height": 131,
"id": "CMER-Bench_easy_0903_4222_0",
"source": "CMER-Bench",
"tex": "A \\varnothing \\stackrel { D } { \\to } \\varnothing A , \\varnothing A \\stackrel { D } { \\to } A \\varnothing , A A \\stackrel { p } { \\to } \\varnothing \\varnothing , A A \\varnothing \\varnothing \\stackrel { { \\sigma... | CMER-Bench_easy_0903_4222_0 | hf://datasets/Baitlo/math_total@1a80ace131210139a18b431c1232c83334fc82fc/labels-000000.tar | |
{
"height": 54,
"id": "CMER-Bench_easy_0903_5062_57",
"source": "CMER-Bench",
"tex": "\\rho = \\pm \\sqrt{2/b} \\sqrt[4]{(a + b\\sigma^{1})^{2} + 1}, \\quad \\psi = \\pm \\arctan(a + b\\sigma^{1})/2 + \\phi, \\quad b > 0. (43)",
"tokens": 23,
"width": 1347
} | CMER-Bench_easy_0903_5062_57 | hf://datasets/Baitlo/math_total@1a80ace131210139a18b431c1232c83334fc82fc/labels-000000.tar | |
{
"height": 132,
"id": "CMER-Bench_easy_0904_0714_85",
"source": "CMER-Bench",
"tex": "S := \\sum_{c=1}^{q} \\Delta(N, q, c)^2,",
"tokens": 6,
"width": 370
} | CMER-Bench_easy_0904_0714_85 | hf://datasets/Baitlo/math_total@1a80ace131210139a18b431c1232c83334fc82fc/labels-000000.tar | |
{
"height": 99,
"id": "CMER-Bench_easy_0904_1891_81",
"source": "CMER-Bench",
"tex": "d_{\\mathrm{CE}}(\\omega)^{j} = \\frac{j(j-1)}{2} [\\omega, \\omega] \\wedge (\\omega)^{j-2} = -j(j-1) d\\omega \\wedge (\\omega)^{j-2} = -j d(\\omega^{j-1}).",
"tokens": 15,
"width": 1328
} | CMER-Bench_easy_0904_1891_81 | hf://datasets/Baitlo/math_total@1a80ace131210139a18b431c1232c83334fc82fc/labels-000000.tar | |
{
"height": 92,
"id": "CMER-Bench_easy_0904_2751_71",
"source": "CMER-Bench",
"tex": "\\sup_{v \\in \\mathcal{B}_{q \\times q}^{\\delta, \\epsilon}} \\mathcal{H}(v) + c\\mathcal{E}(v) \\leq \\mathcal{H}(\\bar{v}) + \\alpha\\mathcal{E}(\\bar{v}).",
"tokens": 13,
"width": 674
} | CMER-Bench_easy_0904_2751_71 | hf://datasets/Baitlo/math_total@1a80ace131210139a18b431c1232c83334fc82fc/labels-000000.tar | |
{
"height": 42,
"id": "CMER-Bench_easy_0905_1579_75",
"source": "CMER-Bench",
"tex": "x = (r \\cos \\theta, r \\sin \\theta)",
"tokens": 8,
"width": 346
} | CMER-Bench_easy_0905_1579_75 | hf://datasets/Baitlo/math_total@1a80ace131210139a18b431c1232c83334fc82fc/labels-000000.tar | |
{
"height": 109,
"id": "CMER-Bench_easy_0905_2513_29",
"source": "CMER-Bench",
"tex": "S(\\epsilon) = v_a(\\epsilon) \\frac{L}{\\sqrt{2\\pi v}} \\exp \\left[ -\\frac{\\epsilon^2}{2v} \\right], \\quad (30)",
"tokens": 11,
"width": 640
} | CMER-Bench_easy_0905_2513_29 | hf://datasets/Baitlo/math_total@1a80ace131210139a18b431c1232c83334fc82fc/labels-000000.tar | |
{
"height": 51,
"id": "CMER-Bench_easy_0905_3484_67",
"source": "CMER-Bench",
"tex": "(4.1) \\Psi_{(ij)} = A_{ij(i)} \\Psi_{(i)} + A_{ji(j)} \\Psi_{(j)} + (1 - A_{ij(i)} - A_{ji(j)}) \\Psi, \\quad i \\neq j,",
"tokens": 19,
"width": 1284
} | CMER-Bench_easy_0905_3484_67 | hf://datasets/Baitlo/math_total@1a80ace131210139a18b431c1232c83334fc82fc/labels-000000.tar | |
{
"height": 155,
"id": "CMER-Bench_easy_0906_0107_7",
"source": "CMER-Bench",
"tex": "c_1 2^{n+1}(n+1)! \\le \\int_{-\\infty}^{+\\infty} \\dots \\int_{-\\infty}^{+\\infty} \\frac{dx_1 \\dots dx_n}{\\sqrt{(1+x_1^2)(1+(x_2-x_1)^2) \\dots (1+(x_n-x_{n-1})^2)(1+x_n^2)}} \\le",
"tokens": 12,
"width": 1562
} | CMER-Bench_easy_0906_0107_7 | hf://datasets/Baitlo/math_total@1a80ace131210139a18b431c1232c83334fc82fc/labels-000000.tar | |
{
"height": 155,
"id": "CMER-Bench_easy_0906_2919_26",
"source": "CMER-Bench",
"tex": "A_{1} = \\frac{8}{3} \\int_{-\\infty}^{+\\infty} \\left(a''(s)\\right)^{2} a(s) \\, ds . (29)",
"tokens": 10,
"width": 576
} | CMER-Bench_easy_0906_2919_26 | hf://datasets/Baitlo/math_total@1a80ace131210139a18b431c1232c83334fc82fc/labels-000000.tar | |
{
"height": 99,
"id": "CMER-Bench_easy_0906_4157_18",
"source": "CMER-Bench",
"tex": "(2.1) \\frac{\\partial g}{\\partial t} = -2Rc + \\frac{2}{3}Rg, \\quad g(0) = g_0,",
"tokens": 12,
"width": 656
} | CMER-Bench_easy_0906_4157_18 | hf://datasets/Baitlo/math_total@1a80ace131210139a18b431c1232c83334fc82fc/labels-000000.tar | |
{
"height": 116,
"id": "CMER-Bench_easy_0906_4297_9",
"source": "CMER-Bench",
"tex": "f(t) = \\frac{1}{\\lambda} \\sum_{n} f\\left(\\frac{n}{\\lambda}\\right) g\\left(t - \\frac{n}{\\lambda}\\right). (1.2)",
"tokens": 9,
"width": 614
} | CMER-Bench_easy_0906_4297_9 | hf://datasets/Baitlo/math_total@1a80ace131210139a18b431c1232c83334fc82fc/labels-000000.tar | |
{
"height": 104,
"id": "CMER-Bench_easy_0906_4939_27",
"source": "CMER-Bench",
"tex": "\\int_{\\Omega} \\langle a(x, Du), D\\varphi \\rangle \\, \\mathrm{d}x = \\int_{\\Omega} \\varphi \\, \\mathrm{d}\\mu",
"tokens": 13,
"width": 563
} | CMER-Bench_easy_0906_4939_27 | hf://datasets/Baitlo/math_total@1a80ace131210139a18b431c1232c83334fc82fc/labels-000000.tar | |
{
"height": 49,
"id": "CMER-Bench_easy_0907_3608_116",
"source": "CMER-Bench",
"tex": "R_1 = R_2 = R_3 , \\quad P_{Ab} = Q_{Ab} = 0 , \\quad P_{DcAb} = 0",
"tokens": 17,
"width": 940
} | CMER-Bench_easy_0907_3608_116 | hf://datasets/Baitlo/math_total@1a80ace131210139a18b431c1232c83334fc82fc/labels-000000.tar | |
{
"height": 114,
"id": "CMER-Bench_easy_0907_5606_116",
"source": "CMER-Bench",
"tex": "\\frac{H \\circ \\psi^{w_{k,T}}}{w_{k,T}^2}",
"tokens": 3,
"width": 173
} | CMER-Bench_easy_0907_5606_116 | hf://datasets/Baitlo/math_total@1a80ace131210139a18b431c1232c83334fc82fc/labels-000000.tar | |
{
"height": 131,
"id": "CMER-Bench_easy_0908_0344_45",
"source": "CMER-Bench",
"tex": "\\text{Term} \\le N^{-2+} \\prod_{i=1}^{6} \\| I \\phi_i \\|_{X_{1, \\frac{1}{2}+}^{\\delta}},",
"tokens": 9,
"width": 563
} | CMER-Bench_easy_0908_0344_45 | hf://datasets/Baitlo/math_total@1a80ace131210139a18b431c1232c83334fc82fc/labels-000000.tar | |
{
"height": 136,
"id": "CMER-Bench_easy_0908_1079_6",
"source": "CMER-Bench",
"tex": "\\Phi = \\frac{1}{\\sqrt{2}} \\begin{pmatrix} v + h + i\\phi^0 & i\\sqrt{2} \\ \\phi^+ \\\\ i\\sqrt{2} \\ \\phi^- & v + h - i\\phi^0 \\end{pmatrix} . (7)",
"tokens": 26,
"width": 798
} | CMER-Bench_easy_0908_1079_6 | hf://datasets/Baitlo/math_total@1a80ace131210139a18b431c1232c83334fc82fc/labels-000000.tar | |
{
"height": 156,
"id": "CMER-Bench_easy_0908_1300_7",
"source": "CMER-Bench",
"tex": "\\sigma(u_0, v) = \\sigma(u_0, v_0) + \\int_{v_0}^{v} \\frac{r_{,vv} - r \\left(\\Psi_{,v}\\right)^2 + r \\left(\\Phi_{,v}\\right)^2}{2 \\, r_{,v}} dv \\quad (8)",
"tokens": 19,
"width": 1017
} | CMER-Bench_easy_0908_1300_7 | hf://datasets/Baitlo/math_total@1a80ace131210139a18b431c1232c83334fc82fc/labels-000000.tar | |
{
"height": 100,
"id": "CMER-Bench_easy_0909_1024_20",
"source": "CMER-Bench",
"tex": "\\phi\\phi\\Omega = c_{\\phi}\\mathbf{1}\\Omega + (\\phi + \\sum_{l=2,4,\\dots} \\phi_{\\mu_1\\dots\\mu_l})\\Omega",
"tokens": 8,
"width": 668
} | CMER-Bench_easy_0909_1024_20 | hf://datasets/Baitlo/math_total@1a80ace131210139a18b431c1232c83334fc82fc/labels-000000.tar | |
{
"height": 118,
"id": "CMER-Bench_easy_0909_1052_0",
"source": "CMER-Bench",
"tex": "y_{ij} = \\frac{2\\min(E_i^2, E_j^2)(1 - \\cos \\theta_{ij})}{E_{vis}^2}, \\quad (1)",
"tokens": 9,
"width": 653
} | CMER-Bench_easy_0909_1052_0 | hf://datasets/Baitlo/math_total@1a80ace131210139a18b431c1232c83334fc82fc/labels-000000.tar | |
{
"height": 199,
"id": "CMER-Bench_easy_0909_4272_36",
"source": "CMER-Bench",
"tex": "\\begin{aligned}\nF_{jk} &= \\frac{1}{2} \\varepsilon_{ijk} \\frac{x_i}{r^3} T_{\\vec{m}}, \\\\\n\\Phi_9 &= \\frac{1}{2r} T_{\\vec{m}}, \\quad (5.6)\n\\end{aligned}",
"tokens": 15,
"width": 339
} | CMER-Bench_easy_0909_4272_36 | hf://datasets/Baitlo/math_total@1a80ace131210139a18b431c1232c83334fc82fc/labels-000000.tar | |
{
"height": 99,
"id": "CMER-Bench_easy_0909_4926_175",
"source": "CMER-Bench",
"tex": "\\eta \\max_{1 \\le i \\le d} \\rho_i(\\mathcal{H}, L) \\le \\frac{1}{2} \\max_{1 \\le i \\le d} \\rho_i(\\mathcal{H}, L) \\le \\min_{1 \\le i \\le d} \\rho_i(\\mathcal{H}, L).",
"tokens": 25,
"width": 952
} | CMER-Bench_easy_0909_4926_175 | hf://datasets/Baitlo/math_total@1a80ace131210139a18b431c1232c83334fc82fc/labels-000000.tar | |
{
"height": 110,
"id": "CMER-Bench_easy_0909_5442_3",
"source": "CMER-Bench",
"tex": "t^{\\text{rec}} = m \\cdot \\frac{\\vec{d} \\cdot \\vec{p}}{|\\text{p}|^2}, (4)",
"tokens": 8,
"width": 336
} | CMER-Bench_easy_0909_5442_3 | hf://datasets/Baitlo/math_total@1a80ace131210139a18b431c1232c83334fc82fc/labels-000000.tar | |
{
"height": 81,
"id": "CMER-Bench_easy_0910_4002_114",
"source": "CMER-Bench",
"tex": "(3.27) \\quad \\max_{\\partial B_1} |u_j| = 1, \\quad \\text{so } 0 < -u_j \\le |x|^{-\\alpha_j}.",
"tokens": 15,
"width": 776
} | CMER-Bench_easy_0910_4002_114 | hf://datasets/Baitlo/math_total@1a80ace131210139a18b431c1232c83334fc82fc/labels-000000.tar | |
{
"height": 109,
"id": "CMER-Bench_easy_0911_0901_10",
"source": "CMER-Bench",
"tex": "A^+ := \\bigcup_{i \\in I^+} A_i, \\quad A^- := \\bigcup_{i \\in I^-} A_i.",
"tokens": 13,
"width": 633
} | CMER-Bench_easy_0911_0901_10 | hf://datasets/Baitlo/math_total@1a80ace131210139a18b431c1232c83334fc82fc/labels-000000.tar | |
{
"height": 140,
"id": "CMER-Bench_easy_0911_3174_2",
"source": "CMER-Bench",
"tex": "\\psi(t) = \\cos(t\\sqrt{A})f + \\frac{\\sin(t\\sqrt{A})}{\\sqrt{A}}g",
"tokens": 5,
"width": 570
} | CMER-Bench_easy_0911_3174_2 | hf://datasets/Baitlo/math_total@1a80ace131210139a18b431c1232c83334fc82fc/labels-000000.tar | |
{
"height": 155,
"id": "CMER-Bench_easy_0911_4201_16",
"source": "CMER-Bench",
"tex": "|J_{xy}| > \\min \\left\\{ \\sum_{z:\\langle z,x \\rangle \\in E, z \\neq y} |J_{xz}|, \\sum_{z:\\langle z,y \\rangle \\in E, z \\neq x} |J_{yz}| \\right\\}, (10)",
"tokens": 24,
"width": 1039
} | CMER-Bench_easy_0911_4201_16 | hf://datasets/Baitlo/math_total@1a80ace131210139a18b431c1232c83334fc82fc/labels-000000.tar | |
{
"height": 104,
"id": "CMER-Bench_easy_0911_4206_27",
"source": "CMER-Bench",
"tex": "H_{-} = -\\frac{d^{2}}{dx^{2}} + V_{-}(x) - E_{0}^{-} (6lmnqrs)",
"tokens": 8,
"width": 683
} | CMER-Bench_easy_0911_4206_27 | hf://datasets/Baitlo/math_total@1a80ace131210139a18b431c1232c83334fc82fc/labels-000000.tar | |
{
"height": 64,
"id": "CMER-Bench_easy_0911_4478_51",
"source": "CMER-Bench",
"tex": "\\Omega^k \\operatorname{coker} J \\longrightarrow \\Omega^k Q_0 S^0 \\longrightarrow \\Omega^k J.",
"tokens": 10,
"width": 586
} | CMER-Bench_easy_0911_4478_51 | hf://datasets/Baitlo/math_total@1a80ace131210139a18b431c1232c83334fc82fc/labels-000000.tar | |
{
"height": 99,
"id": "CMER-Bench_easy_0912_1142_64",
"source": "CMER-Bench",
"tex": "f_N(\\zeta) > -\\frac{B_3}{\\text{Im } \\zeta}",
"tokens": 5,
"width": 274
} | CMER-Bench_easy_0912_1142_64 | hf://datasets/Baitlo/math_total@1a80ace131210139a18b431c1232c83334fc82fc/labels-000000.tar | |
{
"height": 49,
"id": "CMER-Bench_easy_0912_2096_4",
"source": "CMER-Bench",
"tex": "T_{\\mu\\nu} = \\rho_0 h u_\\mu u_\\nu + P g_{\\mu\\nu} \\, ,",
"tokens": 11,
"width": 445
} | CMER-Bench_easy_0912_2096_4 | hf://datasets/Baitlo/math_total@1a80ace131210139a18b431c1232c83334fc82fc/labels-000000.tar | |
{
"height": 102,
"id": "CMER-Bench_easy_1001_1677_0",
"source": "CMER-Bench",
"tex": "H = \\sum_{i} h_{i}^{\\text{JC}} - \\mu N - J \\sum_{\\langle ij \\rangle} a_{i}^{\\dagger} a_{j}, \\quad (1)",
"tokens": 16,
"width": 650
} | CMER-Bench_easy_1001_1677_0 | hf://datasets/Baitlo/math_total@1a80ace131210139a18b431c1232c83334fc82fc/labels-000000.tar | |
{
"height": 115,
"id": "CMER-Bench_easy_1001_5217_10",
"source": "CMER-Bench",
"tex": "\\left[ f_{\\mathrm{NL}} \\frac{\\mathcal{F}(\\vec{k}_1, \\vec{k}_2)}{D(z)} + J(\\vec{k}_1, \\vec{k}_2) + \\frac{b_2(z)}{2b_1(z)} \\right] + \\text{cyc.}",
"tokens": 12,
"width": 792
} | CMER-Bench_easy_1001_5217_10 | hf://datasets/Baitlo/math_total@1a80ace131210139a18b431c1232c83334fc82fc/labels-000000.tar | |
{
"height": 226,
"id": "CMER-Bench_easy_1002_0030_112",
"source": "CMER-Bench",
"tex": "(51) \\text{Prob}(A_{u,a}) = \\text{Prob} \\left( \\left\\{ \\|w\\|_{\\infty} > \\frac{u}{a} + O(aS^2) \\right\\} \\right) \\\\\n+ O \\left( \\exp \\left( \\alpha_f S - \\frac{S^2}{2\\sigma_f^2} \\right) + \\exp \\left( \\al... | CMER-Bench_easy_1002_0030_112 | hf://datasets/Baitlo/math_total@1a80ace131210139a18b431c1232c83334fc82fc/labels-000000.tar | |
{
"height": 83,
"id": "CMER-Bench_easy_1002_2990_4",
"source": "CMER-Bench",
"tex": "u_0(x) = 1, \\quad u_1(x) = \\sqrt{3}(1 - 2x), \\quad u_2(x) = \\sqrt{5}(1 - 6x + 6x^2), \\dots (3.5)",
"tokens": 19,
"width": 1228
} | CMER-Bench_easy_1002_2990_4 | hf://datasets/Baitlo/math_total@1a80ace131210139a18b431c1232c83334fc82fc/labels-000000.tar | |
{
"height": 133,
"id": "CMER-Bench_easy_1003_0667_21",
"source": "CMER-Bench",
"tex": "N(\\gamma, t) \\approx q_0 t \\gamma^{-p} \\left[ 1 - \\frac{t_0}{t} \\left( 1 - \\frac{\\gamma t_0}{\\tau_{s0}} \\ln \\left( \\frac{t}{t_0} \\right) \\right)^{p-2} \\right], \\quad (22)",
"tokens": 23,
"width": 976
} | CMER-Bench_easy_1003_0667_21 | hf://datasets/Baitlo/math_total@1a80ace131210139a18b431c1232c83334fc82fc/labels-000000.tar | |
{
"height": 125,
"id": "CMER-Bench_easy_1003_2681_14",
"source": "CMER-Bench",
"tex": "\\mathcal{V}^{(0,0)} = \\mathcal{V}^{(1,0)} = \\begin{bmatrix} ++ \\\\ +- \\end{bmatrix} ; \\mathcal{V}^{(1,1)} = \\begin{bmatrix} ++ +- \\\\ ++ -+ \\end{bmatrix}",
"tokens": 19,
"width": 1285
} | CMER-Bench_easy_1003_2681_14 | hf://datasets/Baitlo/math_total@1a80ace131210139a18b431c1232c83334fc82fc/labels-000000.tar | |
{
"height": 47,
"id": "CMER-Bench_easy_1003_2793_17",
"source": "CMER-Bench",
"tex": "\\Delta_{\\xi\\eta} f = f(\\cdot, \\xi) - f(\\cdot, \\eta).",
"tokens": 8,
"width": 430
} | CMER-Bench_easy_1003_2793_17 | hf://datasets/Baitlo/math_total@1a80ace131210139a18b431c1232c83334fc82fc/labels-000000.tar | |
{
"height": 124,
"id": "CMER-Bench_easy_1003_2960_22",
"source": "CMER-Bench",
"tex": "|\\mathcal{A}| \\le \\frac{2^n}{\\sum_{i=0}^{k} \\binom{n}{i}} \\binom{n}{k}",
"tokens": 5,
"width": 374
} | CMER-Bench_easy_1003_2960_22 | hf://datasets/Baitlo/math_total@1a80ace131210139a18b431c1232c83334fc82fc/labels-000000.tar | |
{
"height": 130,
"id": "CMER-Bench_easy_1004_1665_4",
"source": "CMER-Bench",
"tex": "\\phi(\\mathbf{r}; \\omega) = \\sum_{n=-\\infty}^{\\infty} \\int \\frac{d^2\\mathbf{q}_{\\|}}{(2\\pi)^2} \\left[ e^{-q_n z} - g_n(\\mathbf{q}_{\\|}; \\omega) e^{q_n z} \\right] e^{i q_{x,n}x + i q_y y} \\quad \\text{for } z \\... | CMER-Bench_easy_1004_1665_4 | hf://datasets/Baitlo/math_total@1a80ace131210139a18b431c1232c83334fc82fc/labels-000000.tar | |
{
"height": 58,
"id": "CMER-Bench_easy_1004_3189_3",
"source": "CMER-Bench",
"tex": "V_{x,y}(t) = S_{x,y}(t) + V_{x,y}^{S}(t)(7)",
"tokens": 5,
"width": 522
} | CMER-Bench_easy_1004_3189_3 | hf://datasets/Baitlo/math_total@1a80ace131210139a18b431c1232c83334fc82fc/labels-000000.tar | |
{
"height": 133,
"id": "CMER-Bench_easy_1004_4630_13",
"source": "CMER-Bench",
"tex": "{ ( - 1 ) } ^ { { \\nu } _ { i } } = \\prod _ { { n } _ { i } = 1 , { n } _ { j \\ne i } = 0 , 1 } \\prod _ { m = 1 } ^ { 2 } { \\xi } _ { m } ( { 𝚪 } _ { { 𝐧 } _ { \\mathrm { � � } } { 𝐧 } _ { \\mathrm { � � } } { 𝐧 } _ ... | CMER-Bench_easy_1004_4630_13 | hf://datasets/Baitlo/math_total@1a80ace131210139a18b431c1232c83334fc82fc/labels-000000.tar | |
{
"height": 130,
"id": "CMER-Bench_easy_1005_0865_1",
"source": "CMER-Bench",
"tex": "\\dot{S} = \\frac{1}{2} \\sum_{i,j} \\left[ \\omega_i^j P_j(t) - \\omega_j^i P_i(t) \\right] \\ln \\left[ \\frac{\\omega_i^j P_j(t)}{\\omega_j^i P_i(t)} \\right] . (2)",
"tokens": 19,
"width": 860
} | CMER-Bench_easy_1005_0865_1 | hf://datasets/Baitlo/math_total@1a80ace131210139a18b431c1232c83334fc82fc/labels-000000.tar | |
{
"height": 100,
"id": "CMER-Bench_easy_1005_2206_43",
"source": "CMER-Bench",
"tex": "2\\gamma r_{2} < \\frac{R - r}{2} . (4)",
"tokens": 8,
"width": 315
} | CMER-Bench_easy_1005_2206_43 | hf://datasets/Baitlo/math_total@1a80ace131210139a18b431c1232c83334fc82fc/labels-000000.tar | |
{
"height": 145,
"id": "CMER-Bench_easy_1005_4345_41",
"source": "CMER-Bench",
"tex": "(C^{-1}) = \\begin{pmatrix} 2.305 & 29.698 & -1.333 \\\\ 29.698 & 6825.27 & -113.180 \\\\ -1.333 & -113.180 & 3.414 \\end{pmatrix}. (42)",
"tokens": 22,
"width": 919
} | CMER-Bench_easy_1005_4345_41 | hf://datasets/Baitlo/math_total@1a80ace131210139a18b431c1232c83334fc82fc/labels-000000.tar | |
{
"height": 63,
"id": "CMER-Bench_easy_1006_0791_31",
"source": "CMER-Bench",
"tex": "A_{i}^{(3)} = \\partial_{j} \\left[ \\Psi^{\\dagger} * I_{ji} \\Psi \\right].(30)",
"tokens": 9,
"width": 465
} | CMER-Bench_easy_1006_0791_31 | hf://datasets/Baitlo/math_total@1a80ace131210139a18b431c1232c83334fc82fc/labels-000000.tar |
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