Datasets:
id stringlengths 19 19 | split stringclasses 1
value | task_type stringclasses 3
values | gold_spec dict | gold_answer unknown | tags dict | meta unknown | param_hash stringlengths 16 16 | text stringlengths 229 506 |
|---|---|---|---|---|---|---|---|---|
T1_527247b6ee042289 | train | T1 | {
"dim": 2,
"dt": 0.05,
"horizon": 2,
"objects": [
{
"id": "o0",
"mass": 2.2558413567,
"position": [
-3.9750482383,
2.4066774467
],
"velocity": [
0.907330675,
1.809850249
],
"force": [
-18.7286928207,
-16.2521904055
... | {
"objects": [
{
"id": "o0",
"position": [
-3.9050709442000002,
2.5696512422
],
"velocity": [
0.0770997385,
1.0894010757
]
},
{
"id": "o1",
"position": [
1.4496253033,
1.0134589539
],
"velocity": [
... | {
"horizon": 2,
"n_obj": 2,
"n_col": 0,
"ood_axis": "id",
"dim": 2
} | {} | 527247b6ee042289 | Consider the following physical system.
Time step Δt = 0.05 s. Predict the state after 2 steps.
Object o0 has mass 2.256 kg, position [-3.975, 2.407] m, velocity [0.9073, 1.81] m/s, and force [-18.73, -16.25] N.
Object o1 has mass 3094 g, position [1.02, 0.6125] m, velocity [4.32, 4.026] m/s, and force [-3.219, -2.032]... |
T1_1aae825683b12a83 | train | T1 | {
"dim": 2,
"dt": 0.05,
"horizon": 1,
"objects": [
{
"id": "o0",
"mass": 4.4193457057,
"position": [
-1.4102061952,
-1.5604427752
],
"velocity": [
-4.7095826556,
-9.1309911415
],
"force": [
-1.6230048131,
-15.006953485... | {
"objects": [
{
"id": "o0",
"position": [
-1.6456853278999999,
-2.0169923323
],
"velocity": [
-4.7279451567,
-9.3007781924
]
},
{
"id": "o1",
"position": [
-4.0833582197,
-1.6827654380000001
],
"velocity... | {
"horizon": 1,
"n_obj": 2,
"n_col": 0,
"ood_axis": "id",
"dim": 2
} | {} | 1aae825683b12a83 | Here is a Newtonian point-mass scene.
Time step Δt = 0.05 s. Predict the state after 1 steps.
Object o0 has mass 4419 g, position [-1.41, -1.56] m, velocity [-4.71, -9.131] m/s, and force [-1.623, -15.01] N.
Object o1 has mass 9.301 kg, position [-4.212, -2.068] m, velocity [2.573, 7.709] m/s, and force [-5.535, -12.31... |
T3_dd39691094a815e5 | train | T3 | {
"dim": 1,
"dt": 0.1,
"horizon": 3,
"objects": [
{
"id": "o0",
"mass": 6.7211599984,
"position": [
-1.3516782103
],
"velocity": [
-2.5963806577
],
"force": [
-11.6197187691
]
}
],
"walls": [
-8,
8
],
"collisions": f... | "YES" | {
"horizon": 3,
"n_obj": 1,
"n_col": 0,
"ood_axis": "id",
"dim": 1
} | {
"claim": "After 3 steps, object o0 ends at position[0] ≈ -2.182 (within 1%).",
"label": "YES",
"true_x0": -2.1824571993
} | dd39691094a815e5 | Answer yes or no: is this outcome physically feasible?
Object o0 has mass 6.721 kg, position -1.352 m, velocity -2.596 m/s, and constant force -11.62 N.
Claim: After 3 steps, object o0 ends at position[0] ≈ -2.182 (within 1%).
Answer with exactly YES or NO. |
T1_49a92e31430c685f | train | T1 | {
"dim": 1,
"dt": 0.05,
"horizon": 3,
"objects": [
{
"id": "o0",
"mass": 3.0614326477,
"position": [
-4.678997561
],
"velocity": [
-3.6909390388
],
"force": [
-9.290364961
]
}
],
"walls": [
-8,
8
],
"collisions": fal... | {
"objects": [
{
"id": "o0",
"position": [
-5.2553982633
],
"velocity": [
-4.1461359693
]
}
]
} | {
"horizon": 3,
"n_obj": 1,
"n_col": 0,
"ood_axis": "id",
"dim": 1
} | {} | 49a92e31430c685f | You are given this physics setup.
Time step Δt = 0.05 s. Predict the state after 3 steps.
Object o0 has mass 3.061 kg, position -467.9 cm, velocity -369.1 cm/s, and constant force -9.29 N.
Walls at [-8.0, 8.0].
Return JSON with keys objects (list of {id, position, velocity}), using SI units (m, m/s). |
T1_00d640023073f438 | train | T1 | {
"dim": 2,
"dt": 0.1,
"horizon": 5,
"objects": [
{
"id": "o0",
"mass": 9.0804059524,
"position": [
-1.0059949486,
-2.8067924084
],
"velocity": [
9.9507521299,
0.1905258735
],
"force": [
-16.363623513,
-18.115344983
... | {
"objects": [
{
"id": "o0",
"position": [
3.7891730552,
-2.911028757
],
"velocity": [
9.0497118241,
-0.8069705533
]
},
{
"id": "o1",
"position": [
0.2577307097,
-0.4451154244
],
"velocity": [
-2.... | {
"horizon": 5,
"n_obj": 2,
"n_col": 0,
"ood_axis": "id",
"dim": 2
} | {} | 00d640023073f438 | Consider the following physical system.
Time step Δt = 0.1 s. Predict the state after 5 steps.
Object o0 has mass 9.08 kg, position [-1.006, -2.807] m, velocity [9.951, 0.1905] m/s, and force [-16.36, -18.12] N.
Object o1 has mass 1987 g, position [1.274, 2.921] m, velocity [-1.557, -8.729] m/s, and force [-4.735, 19.8... |
T2_6c339440d9d95935 | train | T2 | {
"dim": 1,
"dt": 0.05,
"horizon": 4,
"objects": [
{
"id": "o0",
"mass": 5.083513357,
"position": [
4.5381592752
],
"velocity": [
7.5170588076
],
"force": [
-9.46443797
]
}
],
"walls": null,
"collisions": false,
"gravity": n... | 5.083513357 | {
"horizon": 4,
"n_obj": 1,
"n_col": 0,
"ood_axis": "id",
"dim": 1
} | {
"unknown": {
"object_id": "o0",
"field": "mass",
"value": 5.083513357
},
"observation": {
"objects": [
{
"id": "o0",
"position": [
6.013644176
],
"velocity": [
7.1447006645
]
}
]
}
} | 6c339440d9d95935 | Infer the unknown quantity from the observed trajectory.
Time step Δt = 0.05 s, horizon = 4.
Object o0 has unknown mass, position 4.538 m, velocity 751.7 cm/s, constant force -9.464 N.
After 4 steps the observed state is: {'objects': [{'id': 'o0', 'position': [6.013644175991542], 'velocity': [7.144700664470072]}]}.
Wha... |
T1_c2e861dc11a97907 | train | T1 | {
"dim": 1,
"dt": 0.1,
"horizon": 5,
"objects": [
{
"id": "o0",
"mass": 5.3974513723,
"position": [
-3.8813227468
],
"velocity": [
-2.7403846564
],
"force": [
19.4128551578
]
}
],
"walls": null,
"collisions": false,
"gravity... | {
"objects": [
{
"id": "o0",
"position": [
-4.8918480059
],
"velocity": [
-0.9420493108
]
}
]
} | {
"horizon": 5,
"n_obj": 1,
"n_col": 0,
"ood_axis": "id",
"dim": 1
} | {} | c2e861dc11a97907 | Here is a Newtonian point-mass scene.
Time step Δt = 0.1 s. Predict the state after 5 steps.
Object o0 has mass 5.397 kg, position -3.881 m, velocity -2.74 m/s, and constant force 19.41 N.
Return JSON with keys objects (list of {id, position, velocity}), using SI units (m, m/s). |
T2_040ef820f8722fec | train | T2 | {
"dim": 1,
"dt": 0.2,
"horizon": 2,
"objects": [
{
"id": "o0",
"mass": 5.2775414029,
"position": [
0.4980359349
],
"velocity": [
-4.6988674212
],
"force": [
14.8973216434
]
}
],
"walls": null,
"collisions": false,
"gravity"... | 5.2775414029 | {
"horizon": 2,
"n_obj": 1,
"n_col": 0,
"ood_axis": "id",
"dim": 1
} | {
"unknown": {
"object_id": "o0",
"field": "mass",
"value": 5.2775414029
},
"observation": {
"objects": [
{
"id": "o0",
"position": [
-1.2685999599
],
"velocity": [
-3.5697566853
]
}
]
}
} | 040ef820f8722fec | Infer the unknown quantity from the observed trajectory.
Time step Δt = 0.2 s, horizon = 2.
Object o0 has unknown mass, position 0.498 m, velocity -469.9 cm/s, constant force 14.9 N.
After 2 steps the observed state is: {'objects': [{'id': 'o0', 'position': [-1.2685999599361877], 'velocity': [-3.5697566852598084]}]}.
W... |
T3_6685d4efd64e38cb | train | T3 | {
"dim": 1,
"dt": 0.1,
"horizon": 5,
"objects": [
{
"id": "o0",
"mass": 2.0890377628,
"position": [
-2.7530266297
],
"velocity": [
-3.2382887571
],
"force": [
3.5323487383
]
}
],
"walls": [
-8,
8
],
"collisions": fal... | "NO" | {
"horizon": 5,
"n_obj": 1,
"n_col": 0,
"ood_axis": "id",
"dim": 1
} | {
"claim": "After 5 steps, object o0 has position[0] > 0.",
"label": "NO",
"true_x0": -4.2030812578
} | 6685d4efd64e38cb | Decide whether the proposed outcome is physically possible.
Object o0 has mass 2.089 kg, position -2.753 m, velocity -3.238 m/s, and constant force 3.532 N.
Claim: After 5 steps, object o0 has position[0] > 0.
Answer with exactly YES or NO. |
T3_175f8f02fb3bf42e | train | T3 | {
"dim": 1,
"dt": 0.2,
"horizon": 3,
"objects": [
{
"id": "o0",
"mass": 5.3687304924,
"position": [
0.3923393139
],
"velocity": [
4.4670513176
],
"force": [
15.2953230056
]
}
],
"walls": null,
"collisions": false,
"gravity":... | "YES" | {
"horizon": 3,
"n_obj": 1,
"n_col": 0,
"ood_axis": "id",
"dim": 1
} | {
"claim": "After 3 steps, object o0 has position[0] > 0.",
"label": "YES",
"true_x0": 3.4144458540000002
} | 175f8f02fb3bf42e | Is the following claim consistent with Newtonian mechanics?
Object o0 has mass 5369 g, position 0.3923 m, velocity 4.467 m/s, and constant force 15.3 N.
Claim: After 3 steps, object o0 has position[0] > 0.
Answer with exactly YES or NO. |
T1_da0a6ce11fefb56c | train | T1 | {
"dim": 1,
"dt": 0.2,
"horizon": 4,
"objects": [
{
"id": "o0",
"mass": 1.4875406851,
"position": [
1.5345548827
],
"velocity": [
2.9235950259
],
"force": [
-17.5754930369
]
},
{
"id": "o1",
"mass": 7.553922296,
... | {
"objects": [
{
"id": "o0",
"position": [
-9.6734591954
],
"velocity": [
-22.2987422357
]
},
{
"id": "o1",
"position": [
-1.5649820755000001
],
"velocity": [
-6.0155883092
]
}
]
} | {
"horizon": 4,
"n_obj": 2,
"n_col": 1,
"ood_axis": "id",
"dim": 1
} | {} | da0a6ce11fefb56c | Here is a Newtonian point-mass scene.
Time step Δt = 0.2 s. Predict the state after 4 steps.
Object o0 has mass 1488 g, position 1.535 m, velocity 292.4 cm/s, and constant force -17.58 N.
Object o1 has mass 7.554 kg, position 3.006 m, velocity -781.5 cm/s, and constant force -12.34 N.
Objects collide elastically when t... |
T1_1666c17ee5cae765 | train | T1 | {
"dim": 1,
"dt": 0.05,
"horizon": 1,
"objects": [
{
"id": "o0",
"mass": 2.4967999954,
"position": [
-0.1435887455
],
"velocity": [
-5.725054016
],
"force": [
-3.958388298
]
}
],
"walls": [
-8,
8
],
"collisions": fal... | {
"objects": [
{
"id": "o0",
"position": [
-0.42984144630000004
],
"velocity": [
-5.8043232467
]
}
]
} | {
"horizon": 1,
"n_obj": 1,
"n_col": 0,
"ood_axis": "id",
"dim": 1
} | {} | 1666c17ee5cae765 | Simulate the evolution of the system below.
Time step Δt = 0.05 s. Predict the state after 1 steps.
Object o0 has mass 2.497 kg, position -14.36 cm, velocity -572.5 cm/s, and constant force -3.958 N.
Walls at [-8.0, 8.0].
Return JSON with keys objects (list of {id, position, velocity}), using SI units (m, m/s). |
T1_561496759b2c5891 | train | T1 | {
"dim": 1,
"dt": 0.05,
"horizon": 2,
"objects": [
{
"id": "o0",
"mass": 3.6703704295,
"position": [
4.6870936497
],
"velocity": [
1.5836058163
],
"force": [
1.687808055
]
},
{
"id": "o1",
"mass": 7.7317800434,
... | {
"objects": [
{
"id": "o0",
"position": [
4.8466038483
],
"velocity": [
1.6295904952
]
},
{
"id": "o1",
"position": [
-4.2599552162
],
"velocity": [
1.6850265214
]
}
]
} | {
"horizon": 2,
"n_obj": 2,
"n_col": 0,
"ood_axis": "id",
"dim": 1
} | {} | 561496759b2c5891 | Here is a Newtonian point-mass scene.
Time step Δt = 0.05 s. Predict the state after 2 steps.
Object o0 has mass 3.67 kg, position 4.687 m, velocity 1.584 m/s, and constant force 1.688 N.
Object o1 has mass 7.732 kg, position -4.428 m, velocity 168.4 cm/s, and constant force 0.114 N.
Objects collide elastically when th... |
T3_f964c4a683c1db0a | train | T3 | {
"dim": 1,
"dt": 0.05,
"horizon": 5,
"objects": [
{
"id": "o0",
"mass": 4.773024238,
"position": [
0.8367228929
],
"velocity": [
0.4556543106
],
"force": [
17.3882503095
]
}
],
"walls": [
-8,
8
],
"collisions": fals... | "NO" | {
"horizon": 5,
"n_obj": 1,
"n_col": 0,
"ood_axis": "id",
"dim": 1
} | {
"claim": "After 5 steps, object o0 ends at position[0] = 6.042.",
"label": "NO",
"true_x0": 1.0417121149
} | f964c4a683c1db0a | Is the following claim consistent with Newtonian mechanics?
Object o0 has mass 4.773 kg, position 83.67 cm, velocity 45.57 cm/s, and constant force 17.39 N.
Claim: After 5 steps, object o0 ends at position[0] = 6.042.
Answer with exactly YES or NO. |
T3_c832a435ec680e6a | train | T3 | {
"dim": 1,
"dt": 0.2,
"horizon": 4,
"objects": [
{
"id": "o0",
"mass": 9.9860899677,
"position": [
4.9609644786
],
"velocity": [
-8.534785578
],
"force": [
-11.4738275093
]
}
],
"walls": [
-8,
8
],
"collisions": fal... | "YES" | {
"horizon": 4,
"n_obj": 1,
"n_col": 0,
"ood_axis": "id",
"dim": 1
} | {
"claim": "After 4 steps, object o0 ends at position[0] ≈ -2.143 (within 1%).",
"label": "YES",
"true_x0": -2.1426194208
} | c832a435ec680e6a | Decide whether the proposed outcome is physically possible.
Object o0 has mass 9986 g, position 496.1 cm, velocity -8.535 m/s, and constant force -11.47 N.
Claim: After 4 steps, object o0 ends at position[0] ≈ -2.143 (within 1%).
Answer with exactly YES or NO. |
T2_423c80e155074365 | train | T2 | {
"dim": 1,
"dt": 0.1,
"horizon": 5,
"objects": [
{
"id": "o0",
"mass": 9.3858043549,
"position": [
-3.9641349808
],
"velocity": [
7.5625392995
],
"force": [
-9.4213631405
]
}
],
"walls": null,
"collisions": false,
"gravity"... | 9.3858043549 | {
"horizon": 5,
"n_obj": 1,
"n_col": 0,
"ood_axis": "id",
"dim": 1
} | {
"unknown": {
"object_id": "o0",
"field": "mass",
"value": 9.3858043549
},
"observation": {
"objects": [
{
"id": "o0",
"position": [
-0.2832441882
],
"velocity": [
7.060645014
]
}
]
}
} | 423c80e155074365 | Use the observed motion to find the missing value.
Time step Δt = 0.1 s, horizon = 5.
Object o0 has unknown mass, position -3.964 m, velocity 756.3 cm/s, constant force -9.421 N.
After 5 steps the observed state is: {'objects': [{'id': 'o0', 'position': [-0.2832441881755645], 'velocity': [7.060645014003836]}]}.
What is... |
T1_684fe41162e6624c | train | T1 | {
"dim": 1,
"dt": 0.2,
"horizon": 3,
"objects": [
{
"id": "o0",
"mass": 5.3967866693,
"position": [
4.0533649108
],
"velocity": [
6.9220742659
],
"force": [
-16.3080612915
]
}
],
"walls": null,
"collisions": false,
"gravity"... | {
"objects": [
{
"id": "o0",
"position": [
7.8439923289
],
"velocity": [
5.1089885587
]
}
]
} | {
"horizon": 3,
"n_obj": 1,
"n_col": 0,
"ood_axis": "id",
"dim": 1
} | {} | 684fe41162e6624c | You are given this physics setup.
Time step Δt = 0.2 s. Predict the state after 3 steps.
Object o0 has mass 5.397 kg, position 4.053 m, velocity 692.2 cm/s, and constant force -16.31 N.
Return JSON with keys objects (list of {id, position, velocity}), using SI units (m, m/s). |
T1_2100c3668bbe8a71 | train | T1 | {
"dim": 1,
"dt": 0.2,
"horizon": 5,
"objects": [
{
"id": "o0",
"mass": 4.8491822708,
"position": [
-4.9033030039
],
"velocity": [
-8.4951227985
],
"force": [
15.324255732
]
},
{
"id": "o1",
"mass": 9.135357144,
... | {
"objects": [
{
"id": "o0",
"position": [
-3.0353271427
],
"velocity": [
9.2677782952
]
},
{
"id": "o1",
"position": [
7.2937423367
],
"velocity": [
7.05317611
]
}
]
} | {
"horizon": 5,
"n_obj": 2,
"n_col": 1,
"ood_axis": "id",
"dim": 1
} | {} | 2100c3668bbe8a71 | Here is a Newtonian point-mass scene.
Time step Δt = 0.2 s. Predict the state after 5 steps.
Object o0 has mass 4.849 kg, position -490.3 cm, velocity -849.5 cm/s, and constant force 15.32 N.
Object o1 has mass 9135 g, position 0.4559 m, velocity 6.692 m/s, and constant force 3.3 N.
Walls at [-8.0, 8.0].
Objects collid... |
T1_3b06fae3642c9969 | train | T1 | {
"dim": 1,
"dt": 0.2,
"horizon": 5,
"objects": [
{
"id": "o0",
"mass": 2.390980045,
"position": [
4.2988101569
],
"velocity": [
7.2921139244
],
"force": [
19.0482413172
]
},
{
"id": "o1",
"mass": 8.2969454795,
... | {
"objects": [
{
"id": "o0",
"position": [
2.7960968351
],
"velocity": [
-6.4068504864
]
},
{
"id": "o1",
"position": [
-5.2260306513
],
"velocity": [
-8.363783302
]
}
]
} | {
"horizon": 5,
"n_obj": 2,
"n_col": 1,
"ood_axis": "id",
"dim": 1
} | {} | 3b06fae3642c9969 | Simulate the evolution of the system below.
Time step Δt = 0.2 s. Predict the state after 5 steps.
Object o0 has mass 2.391 kg, position 429.9 cm, velocity 7.292 m/s, and constant force 19.05 N.
Object o1 has mass 8297 g, position 3.814 m, velocity -950.4 cm/s, and constant force 9.463 N.
Walls at [-8.0, 8.0].
Objects ... |
T1_e958068f45c7d339 | train | T1 | {
"dim": 1,
"dt": 0.05,
"horizon": 3,
"objects": [
{
"id": "o0",
"mass": 3.0063119249,
"position": [
1.6003318275
],
"velocity": [
-2.0306804287
],
"force": [
-8.8558775591
]
},
{
"id": "o1",
"mass": 1.624786792,
... | {
"objects": [
{
"id": "o0",
"position": [
1.2736365528
],
"velocity": [
-2.4725446354000002
]
},
{
"id": "o1",
"position": [
2.2884414219
],
"velocity": [
-2.9423442131
]
}
]
} | {
"horizon": 3,
"n_obj": 2,
"n_col": 0,
"ood_axis": "id",
"dim": 1
} | {} | e958068f45c7d339 | You are given this physics setup.
Time step Δt = 0.05 s. Predict the state after 3 steps.
Object o0 has mass 3.006 kg, position 1.6 m, velocity -203.1 cm/s, and constant force -8.856 N.
Object o1 has mass 1625 g, position 2.733 m, velocity -2.977 m/s, and constant force 0.3762 N.
Objects collide elastically when they m... |
T1_f404b1ffbbb9148e | train | T1 | {
"dim": 1,
"dt": 0.2,
"horizon": 5,
"objects": [
{
"id": "o0",
"mass": 2.0408120563,
"position": [
3.9950473291
],
"velocity": [
-6.19842451
],
"force": [
-18.2245386515
]
},
{
"id": "o1",
"mass": 4.9245176391,
... | {
"objects": [
{
"id": "o0",
"position": [
9.6086020015
],
"velocity": [
6.5194070217
]
},
{
"id": "o1",
"position": [
0.5397542469000001
],
"velocity": [
-1.3232956979
]
}
]
} | {
"horizon": 5,
"n_obj": 2,
"n_col": 1,
"ood_axis": "id",
"dim": 1
} | {} | f404b1ffbbb9148e | Here is a Newtonian point-mass scene.
Time step Δt = 0.2 s. Predict the state after 5 steps.
Object o0 has mass 2041 g, position 399.5 cm, velocity -6.198 m/s, and constant force -18.22 N.
Object o1 has mass 4925 g, position 0.1992 m, velocity 613 cm/s, and constant force 7.474 N.
Objects collide elastically when they ... |
T1_db336e1d710754b5 | train | T1 | {
"dim": 1,
"dt": 0.05,
"horizon": 5,
"objects": [
{
"id": "o0",
"mass": 2.7265608369,
"position": [
1.6492943421
],
"velocity": [
-2.4170944575
],
"force": [
9.9253824064
]
},
{
"id": "o1",
"mass": 2.5662460889,
... | {
"objects": [
{
"id": "o0",
"position": [
1.1360271549
],
"velocity": [
-1.5070301861000002
]
},
{
"id": "o1",
"position": [
0.3514724949
],
"velocity": [
-0.5780556003
]
}
]
} | {
"horizon": 5,
"n_obj": 2,
"n_col": 0,
"ood_axis": "id",
"dim": 1
} | {} | db336e1d710754b5 | Here is a Newtonian point-mass scene.
Time step Δt = 0.05 s. Predict the state after 5 steps.
Object o0 has mass 2727 g, position 164.9 cm, velocity -241.7 cm/s, and constant force 9.925 N.
Object o1 has mass 2566 g, position 0.6911 m, velocity -187.8 cm/s, and constant force 13.35 N.
Walls at [-8.0, 8.0].
Objects coll... |
T1_fc89689c8680a919 | train | T1 | {
"dim": 1,
"dt": 0.05,
"horizon": 1,
"objects": [
{
"id": "o0",
"mass": 7.055161035,
"position": [
-2.75359334
],
"velocity": [
-6.0174013455
],
"force": [
-19.0229844909
]
},
{
"id": "o1",
"mass": 3.2035828967,
... | {
"objects": [
{
"id": "o0",
"position": [
-3.0544634073
],
"velocity": [
-6.1522174354
]
},
{
"id": "o1",
"position": [
0.1011011368
],
"velocity": [
6.7280701296
]
}
]
} | {
"horizon": 1,
"n_obj": 2,
"n_col": 0,
"ood_axis": "id",
"dim": 1
} | {} | fc89689c8680a919 | Here is a Newtonian point-mass scene.
Time step Δt = 0.05 s. Predict the state after 1 steps.
Object o0 has mass 7055 g, position -275.4 cm, velocity -601.7 cm/s, and constant force -19.02 N.
Object o1 has mass 3.204 kg, position -0.2486 m, velocity 6.995 m/s, and constant force -17.09 N.
Objects collide elastically wh... |
T1_a6e53bc27e6dc77d | train | T1 | {
"dim": 1,
"dt": 0.2,
"horizon": 1,
"objects": [
{
"id": "o0",
"mass": 3.2427845169,
"position": [
3.4833634735
],
"velocity": [
-0.8707634906
],
"force": [
12.0566640689
]
},
{
"id": "o1",
"mass": 7.0081995933,
... | {
"objects": [
{
"id": "o0",
"position": [
3.3092107754
],
"velocity": [
-0.1271640312
]
},
{
"id": "o1",
"position": [
5.2607338045
],
"velocity": [
2.4227755832
]
}
]
} | {
"horizon": 1,
"n_obj": 2,
"n_col": 0,
"ood_axis": "id",
"dim": 1
} | {} | a6e53bc27e6dc77d | Simulate the evolution of the system below.
Time step Δt = 0.2 s. Predict the state after 1 steps.
Object o0 has mass 3243 g, position 3.483 m, velocity -87.08 cm/s, and constant force 12.06 N.
Object o1 has mass 7008 g, position 4.879 m, velocity 190.9 cm/s, and constant force 18 N.
Objects collide elastically when th... |
T1_46db150288d548a0 | train | T1 | {
"dim": 1,
"dt": 0.05,
"horizon": 3,
"objects": [
{
"id": "o0",
"mass": 3.4454359637,
"position": [
-1.8029043158
],
"velocity": [
0.8030444504
],
"force": [
-14.4650375394
]
}
],
"walls": [
-8,
8
],
"collisions": f... | {
"objects": [
{
"id": "o0",
"position": [
-1.7139350370000002
],
"velocity": [
0.1732966757
]
}
]
} | {
"horizon": 3,
"n_obj": 1,
"n_col": 0,
"ood_axis": "id",
"dim": 1
} | {} | 46db150288d548a0 | Here is a Newtonian point-mass scene.
Time step Δt = 0.05 s. Predict the state after 3 steps.
Object o0 has mass 3.445 kg, position -1.803 m, velocity 80.3 cm/s, and constant force -14.47 N.
Walls at [-8.0, 8.0].
Return JSON with keys objects (list of {id, position, velocity}), using SI units (m, m/s). |
T1_a7dc86d26124fa3b | train | T1 | {
"dim": 1,
"dt": 0.1,
"horizon": 2,
"objects": [
{
"id": "o0",
"mass": 4.505291314,
"position": [
2.6979577231
],
"velocity": [
8.9212406718
],
"force": [
-19.2187217305
]
}
],
"walls": null,
"collisions": false,
"gravity":... | {
"objects": [
{
"id": "o0",
"position": [
4.4395477464
],
"velocity": [
8.0680784503
]
}
]
} | {
"horizon": 2,
"n_obj": 1,
"n_col": 0,
"ood_axis": "id",
"dim": 1
} | {} | a7dc86d26124fa3b | Simulate the evolution of the system below.
Time step Δt = 0.1 s. Predict the state after 2 steps.
Object o0 has mass 4505 g, position 2.698 m, velocity 892.1 cm/s, and constant force -19.22 N.
Return JSON with keys objects (list of {id, position, velocity}), using SI units (m, m/s). |
T2_541df757052dc976 | train | T2 | {
"dim": 1,
"dt": 0.2,
"horizon": 5,
"objects": [
{
"id": "o0",
"mass": 7.6117065468,
"position": [
2.9986817094
],
"velocity": [
7.956226948
],
"force": [
-0.470820898
]
}
],
"walls": null,
"collisions": false,
"gravity": n... | 7.6117065468 | {
"horizon": 5,
"n_obj": 1,
"n_col": 0,
"ood_axis": "id",
"dim": 1
} | {
"unknown": {
"object_id": "o0",
"field": "mass",
"value": 7.6117065468
},
"observation": {
"objects": [
{
"id": "o0",
"position": [
10.930166721
],
"velocity": [
7.894372107
]
}
]
}
} | 541df757052dc976 | An unknown parameter must be recovered from the data below.
Time step Δt = 0.2 s, horizon = 5.
Object o0 has unknown mass, position 2.999 m, velocity 795.6 cm/s, constant force -0.4708 N.
After 5 steps the observed state is: {'objects': [{'id': 'o0', 'position': [10.930166721007168], 'velocity': [7.894372107010367]}]}.... |
T1_4822c0c0e39ad318 | train | T1 | {
"dim": 1,
"dt": 0.05,
"horizon": 4,
"objects": [
{
"id": "o0",
"mass": 9.8264977977,
"position": [
0.3412362953
],
"velocity": [
8.1385772517
],
"force": [
3.6757110251
]
}
],
"walls": null,
"collisions": false,
"gravity":... | {
"objects": [
{
"id": "o0",
"position": [
1.9745626629
],
"velocity": [
8.2133894809
]
}
]
} | {
"horizon": 4,
"n_obj": 1,
"n_col": 0,
"ood_axis": "id",
"dim": 1
} | {} | 4822c0c0e39ad318 | Consider the following physical system.
Time step Δt = 0.05 s. Predict the state after 4 steps.
Object o0 has mass 9826 g, position 0.3412 m, velocity 813.9 cm/s, and constant force 3.676 N.
Return JSON with keys objects (list of {id, position, velocity}), using SI units (m, m/s). |
T1_c42ff532f6a39b42 | train | T1 | {
"dim": 1,
"dt": 0.1,
"horizon": 4,
"objects": [
{
"id": "o0",
"mass": 4.0375049327,
"position": [
3.79639986
],
"velocity": [
-4.4348676872
],
"force": [
18.0481647944
]
}
],
"walls": null,
"collisions": false,
"gravity": ... | {
"objects": [
{
"id": "o0",
"position": [
2.2906604792
],
"velocity": [
-2.6468163936
]
}
]
} | {
"horizon": 4,
"n_obj": 1,
"n_col": 0,
"ood_axis": "id",
"dim": 1
} | {} | c42ff532f6a39b42 | Consider the following physical system.
Time step Δt = 0.1 s. Predict the state after 4 steps.
Object o0 has mass 4038 g, position 3.796 m, velocity -4.435 m/s, and constant force 18.05 N.
Return JSON with keys objects (list of {id, position, velocity}), using SI units (m, m/s). |
T1_2ed86c3d1ec71e28 | train | T1 | {
"dim": 2,
"dt": 0.05,
"horizon": 1,
"objects": [
{
"id": "o0",
"mass": 2.7942461413,
"position": [
-4.7961998268,
-3.4761765422
],
"velocity": [
-7.4755805025,
3.3891768924
],
"force": [
2.5587832772,
-11.2814183637
... | {
"objects": [
{
"id": "o0",
"position": [
-5.1699788519,
-3.3067176975
],
"velocity": [
-7.4297938547,
3.187308163
]
}
]
} | {
"horizon": 1,
"n_obj": 1,
"n_col": 0,
"ood_axis": "id",
"dim": 2
} | {} | 2ed86c3d1ec71e28 | You are given this physics setup.
Time step Δt = 0.05 s. Predict the state after 1 steps.
Object o0 has mass 2.794 kg, position [-4.796, -3.476] m, velocity [-7.476, 3.389] m/s, and force [2.559, -11.28] N.
Return JSON with keys objects (list of {id, position, velocity}), using SI units (m, m/s). |
T1_193eb6e5795da7d6 | train | T1 | {
"dim": 1,
"dt": 0.1,
"horizon": 2,
"objects": [
{
"id": "o0",
"mass": 1.9728887469,
"position": [
-4.743215745
],
"velocity": [
-3.7608551121
],
"force": [
7.093891474
]
}
],
"walls": null,
"collisions": false,
"gravity": ... | {
"objects": [
{
"id": "o0",
"position": [
-5.4594298921
],
"velocity": [
-3.0417176052
]
}
]
} | {
"horizon": 2,
"n_obj": 1,
"n_col": 0,
"ood_axis": "id",
"dim": 1
} | {} | 193eb6e5795da7d6 | Simulate the evolution of the system below.
Time step Δt = 0.1 s. Predict the state after 2 steps.
Object o0 has mass 1.973 kg, position -4.743 m, velocity -3.761 m/s, and constant force 7.094 N.
Return JSON with keys objects (list of {id, position, velocity}), using SI units (m, m/s). |
T1_8ff19aa1cfdc8d08 | train | T1 | {
"dim": 1,
"dt": 0.05,
"horizon": 5,
"objects": [
{
"id": "o0",
"mass": 4.1248338878,
"position": [
-0.7162198677
],
"velocity": [
-2.5885824756
],
"force": [
0.2384315871
]
}
],
"walls": [
-8,
8
],
"collisions": fa... | {
"objects": [
{
"id": "o0",
"position": [
-1.3619203884
],
"velocity": [
-2.5741314945
]
}
]
} | {
"horizon": 5,
"n_obj": 1,
"n_col": 0,
"ood_axis": "id",
"dim": 1
} | {} | 8ff19aa1cfdc8d08 | Simulate the evolution of the system below.
Time step Δt = 0.05 s. Predict the state after 5 steps.
Object o0 has mass 4125 g, position -0.7162 m, velocity -258.9 cm/s, and constant force 0.2384 N.
Walls at [-8.0, 8.0].
Return JSON with keys objects (list of {id, position, velocity}), using SI units (m, m/s). |
T1_60eac4006a3a02f4 | train | T1 | {
"dim": 1,
"dt": 0.05,
"horizon": 4,
"objects": [
{
"id": "o0",
"mass": 7.6041577361,
"position": [
4.6547373124
],
"velocity": [
-4.5983520723
],
"force": [
12.3279687523
]
}
],
"walls": null,
"collisions": false,
"gravity... | {
"objects": [
{
"id": "o0",
"position": [
3.7593851114
],
"velocity": [
-4.2741092256
]
}
]
} | {
"horizon": 4,
"n_obj": 1,
"n_col": 0,
"ood_axis": "id",
"dim": 1
} | {} | 60eac4006a3a02f4 | Simulate the evolution of the system below.
Time step Δt = 0.05 s. Predict the state after 4 steps.
Object o0 has mass 7604 g, position 465.5 cm, velocity -459.8 cm/s, and constant force 12.33 N.
Return JSON with keys objects (list of {id, position, velocity}), using SI units (m, m/s). |
T3_04ea6f672eceb8cb | train | T3 | {
"dim": 1,
"dt": 0.1,
"horizon": 3,
"objects": [
{
"id": "o0",
"mass": 3.1947709527,
"position": [
-0.352915334
],
"velocity": [
2.2066340846
],
"force": [
-4.8404278349
]
}
],
"walls": [
-8,
8
],
"collisions": fals... | "NO" | {
"horizon": 3,
"n_obj": 1,
"n_col": 0,
"ood_axis": "id",
"dim": 1
} | {
"claim": "After 3 steps, object o0 ends at position[0] = 5.264.",
"label": "NO",
"true_x0": 0.26362160630000003
} | 04ea6f672eceb8cb | Decide whether the proposed outcome is physically possible.
Object o0 has mass 3195 g, position -35.29 cm, velocity 220.7 cm/s, and constant force -4.84 N.
Claim: After 3 steps, object o0 ends at position[0] = 5.264.
Answer with exactly YES or NO. |
T3_822076e4938a29a2 | train | T3 | {
"dim": 1,
"dt": 0.05,
"horizon": 5,
"objects": [
{
"id": "o0",
"mass": 5.6496452654,
"position": [
-3.0894357647
],
"velocity": [
-5.1728789925
],
"force": [
-3.7428750132
]
}
],
"walls": null,
"collisions": false,
"gravit... | "NO" | {
"horizon": 5,
"n_obj": 1,
"n_col": 0,
"ood_axis": "id",
"dim": 1
} | {
"claim": "After 5 steps, object o0 has position[0] > 0.",
"label": "NO",
"true_x0": -4.3992179466
} | 822076e4938a29a2 | Is the following claim consistent with Newtonian mechanics?
Object o0 has mass 5650 g, position -308.9 cm, velocity -5.173 m/s, and constant force -3.743 N.
Claim: After 5 steps, object o0 has position[0] > 0.
Answer with exactly YES or NO. |
T1_4150277cc48bd88c | train | T1 | {
"dim": 1,
"dt": 0.2,
"horizon": 3,
"objects": [
{
"id": "o0",
"mass": 6.234000268,
"position": [
-0.2673951124
],
"velocity": [
0.6184386229
],
"force": [
-2.9798474918
]
}
],
"walls": null,
"collisions": false,
"gravity":... | {
"objects": [
{
"id": "o0",
"position": [
0.0463081506
],
"velocity": [
0.3316390691
]
}
]
} | {
"horizon": 3,
"n_obj": 1,
"n_col": 0,
"ood_axis": "id",
"dim": 1
} | {} | 4150277cc48bd88c | You are given this physics setup.
Time step Δt = 0.2 s. Predict the state after 3 steps.
Object o0 has mass 6234 g, position -26.74 cm, velocity 61.84 cm/s, and constant force -2.98 N.
Return JSON with keys objects (list of {id, position, velocity}), using SI units (m, m/s). |
T1_47f7c34a5a8b8563 | train | T1 | {
"dim": 2,
"dt": 0.05,
"horizon": 3,
"objects": [
{
"id": "o0",
"mass": 7.6859295728,
"position": [
4.5087756039,
1.9016355414
],
"velocity": [
-6.1691805398,
4.7720930702
],
"force": [
-8.9400149213,
3.5834762384
... | {
"objects": [
{
"id": "o0",
"position": [
3.5746747751,
2.6209462906
],
"velocity": [
-6.3436554976,
4.8420288445
]
}
]
} | {
"horizon": 3,
"n_obj": 1,
"n_col": 0,
"ood_axis": "id",
"dim": 2
} | {} | 47f7c34a5a8b8563 | You are given this physics setup.
Time step Δt = 0.05 s. Predict the state after 3 steps.
Object o0 has mass 7.686 kg, position [4.509, 1.902] m, velocity [-6.169, 4.772] m/s, and force [-8.94, 3.583] N.
Return JSON with keys objects (list of {id, position, velocity}), using SI units (m, m/s). |
T2_2acbb4ae600e1417 | train | T2 | {
"dim": 1,
"dt": 0.1,
"horizon": 2,
"objects": [
{
"id": "o0",
"mass": 1.1273353053,
"position": [
0.3413508927
],
"velocity": [
-4.5137734643
],
"force": [
18.9717972441
]
}
],
"walls": null,
"collisions": false,
"gravity"... | 1.1273353053 | {
"horizon": 2,
"n_obj": 1,
"n_col": 0,
"ood_axis": "id",
"dim": 1
} | {
"unknown": {
"object_id": "o0",
"field": "mass",
"value": 1.1273353053
},
"observation": {
"objects": [
{
"id": "o0",
"position": [
-0.39311494100000005
],
"velocity": [
-1.1479962808
]
}
]
}
} | 2acbb4ae600e1417 | Use the observed motion to find the missing value.
Time step Δt = 0.1 s, horizon = 2.
Object o0 has unknown mass, position 0.3414 m, velocity -451.4 cm/s, constant force 18.97 N.
After 2 steps the observed state is: {'objects': [{'id': 'o0', 'position': [-0.393114941012026], 'velocity': [-1.1479962807692248]}]}.
What i... |
T3_8036db6c69138e34 | train | T3 | {
"dim": 1,
"dt": 0.1,
"horizon": 4,
"objects": [
{
"id": "o0",
"mass": 4.066353393,
"position": [
4.6549764314
],
"velocity": [
-4.9504321901
],
"force": [
14.4689185851
]
}
],
"walls": [
-8,
8
],
"collisions": fals... | "YES" | {
"horizon": 4,
"n_obj": 1,
"n_col": 0,
"ood_axis": "id",
"dim": 1
} | {
"claim": "After 4 steps, object o0 has position[0] > 0.",
"label": "YES",
"true_x0": 2.8882958496
} | 8036db6c69138e34 | Is the following claim consistent with Newtonian mechanics?
Object o0 has mass 4.066 kg, position 4.655 m, velocity -4.95 m/s, and constant force 14.47 N.
Claim: After 4 steps, object o0 has position[0] > 0.
Answer with exactly YES or NO. |
T2_0ba300c58b7ef921 | train | T2 | {
"dim": 1,
"dt": 0.05,
"horizon": 2,
"objects": [
{
"id": "o0",
"mass": 6.0226573116,
"position": [
-0.8382597859
],
"velocity": [
1.9225369082
],
"force": [
4.7367340999
]
}
],
"walls": null,
"collisions": false,
"gravity"... | 6.0226573116 | {
"horizon": 2,
"n_obj": 1,
"n_col": 0,
"ood_axis": "id",
"dim": 1
} | {
"unknown": {
"object_id": "o0",
"field": "mass",
"value": 6.0226573116
},
"observation": {
"objects": [
{
"id": "o0",
"position": [
-0.6440398807000001
],
"velocity": [
2.0011854823
]
}
]
}
} | 0ba300c58b7ef921 | An unknown parameter must be recovered from the data below.
Time step Δt = 0.05 s, horizon = 2.
Object o0 has unknown mass, position -83.83 cm, velocity 192.3 cm/s, constant force 4.737 N.
After 2 steps the observed state is: {'objects': [{'id': 'o0', 'position': [-0.6440398807235753], 'velocity': [2.0011854823240944]}... |
T3_1407fd20ea9afb81 | train | T3 | {
"dim": 1,
"dt": 0.2,
"horizon": 5,
"objects": [
{
"id": "o0",
"mass": 1.5420727394,
"position": [
4.6010877743
],
"velocity": [
-8.0153285045
],
"force": [
10.5094841742
]
}
],
"walls": null,
"collisions": false,
"gravity"... | "NO" | {
"horizon": 5,
"n_obj": 1,
"n_col": 0,
"ood_axis": "id",
"dim": 1
} | {
"claim": "After 5 steps, object o0 has position[0] > 0.",
"label": "NO",
"true_x0": -0.6881736891
} | 1407fd20ea9afb81 | Decide whether the proposed outcome is physically possible.
Object o0 has mass 1.542 kg, position 4.601 m, velocity -8.015 m/s, and constant force 10.51 N.
Claim: After 5 steps, object o0 has position[0] > 0.
Answer with exactly YES or NO. |
T1_96b0d5f26f261a55 | train | T1 | {
"dim": 1,
"dt": 0.05,
"horizon": 3,
"objects": [
{
"id": "o0",
"mass": 3.083286111,
"position": [
2.0695582988
],
"velocity": [
4.0597511619
],
"force": [
-1.8387469437
]
},
{
"id": "o1",
"mass": 7.1864642806,
... | {
"objects": [
{
"id": "o0",
"position": [
2.6740482769
],
"velocity": [
3.9702972378
]
},
{
"id": "o1",
"position": [
5.1078150895
],
"velocity": [
5.8609718281
]
}
]
} | {
"horizon": 3,
"n_obj": 2,
"n_col": 0,
"ood_axis": "id",
"dim": 1
} | {} | 96b0d5f26f261a55 | Here is a Newtonian point-mass scene.
Time step Δt = 0.05 s. Predict the state after 3 steps.
Object o0 has mass 3083 g, position 2.07 m, velocity 4.06 m/s, and constant force -1.839 N.
Object o1 has mass 7186 g, position 4.239 m, velocity 5.757 m/s, and constant force 5.002 N.
Objects collide elastically when they mee... |
T1_6deaaf82eaf3786e | train | T1 | {
"dim": 1,
"dt": 0.05,
"horizon": 4,
"objects": [
{
"id": "o0",
"mass": 5.2182817325,
"position": [
-1.9590880946
],
"velocity": [
-1.9498296167
],
"force": [
-9.1101522742
]
},
{
"id": "o1",
"mass": 5.8598340634,
... | {
"objects": [
{
"id": "o0",
"position": [
-2.3752412364
],
"velocity": [
-2.2989925306
]
},
{
"id": "o1",
"position": [
-0.1903909362
],
"velocity": [
2.4923836392
]
}
]
} | {
"horizon": 4,
"n_obj": 2,
"n_col": 0,
"ood_axis": "id",
"dim": 1
} | {} | 6deaaf82eaf3786e | You are given this physics setup.
Time step Δt = 0.05 s. Predict the state after 4 steps.
Object o0 has mass 5.218 kg, position -1.959 m, velocity -1.95 m/s, and constant force -9.11 N.
Object o1 has mass 5860 g, position -0.6224 m, velocity 1.961 m/s, and constant force 15.58 N.
Objects collide elastically when they m... |
T1_42620846d823eff5 | train | T1 | {
"dim": 1,
"dt": 0.2,
"horizon": 2,
"objects": [
{
"id": "o0",
"mass": 4.9229648837,
"position": [
3.1424494454
],
"velocity": [
9.3811047213
],
"force": [
-1.1995842016
]
},
{
"id": "o1",
"mass": 4.6751328409,
... | {
"objects": [
{
"id": "o0",
"position": [
6.8851444905
],
"velocity": [
9.2836362867
]
},
{
"id": "o1",
"position": [
-5.0686963992
],
"velocity": [
-9.0687826631
]
}
]
} | {
"horizon": 2,
"n_obj": 2,
"n_col": 0,
"ood_axis": "id",
"dim": 1
} | {} | 42620846d823eff5 | Simulate the evolution of the system below.
Time step Δt = 0.2 s. Predict the state after 2 steps.
Object o0 has mass 4923 g, position 314.2 cm, velocity 9.381 m/s, and constant force -1.2 N.
Object o1 has mass 4.675 kg, position -178.9 cm, velocity -790.8 cm/s, and constant force -13.57 N.
Objects collide elastically ... |
T1_6a29a025145dd312 | train | T1 | {
"dim": 1,
"dt": 0.1,
"horizon": 5,
"objects": [
{
"id": "o0",
"mass": 4.7192281372,
"position": [
-3.1241745861
],
"velocity": [
-2.764412817
],
"force": [
10.2577261622
]
}
],
"walls": null,
"collisions": false,
"gravity"... | {
"objects": [
{
"id": "o0",
"position": [
-4.2890207427
],
"velocity": [
-1.6776115579000002
]
}
]
} | {
"horizon": 5,
"n_obj": 1,
"n_col": 0,
"ood_axis": "id",
"dim": 1
} | {} | 6a29a025145dd312 | Consider the following physical system.
Time step Δt = 0.1 s. Predict the state after 5 steps.
Object o0 has mass 4.719 kg, position -312.4 cm, velocity -2.764 m/s, and constant force 10.26 N.
Return JSON with keys objects (list of {id, position, velocity}), using SI units (m, m/s). |
T1_2bda285067ba23b0 | train | T1 | {
"dim": 1,
"dt": 0.2,
"horizon": 1,
"objects": [
{
"id": "o0",
"mass": 6.4798450037,
"position": [
-2.6070253767
],
"velocity": [
-6.8324367239
],
"force": [
2.0335602801
]
}
],
"walls": null,
"collisions": false,
"gravity"... | {
"objects": [
{
"id": "o0",
"position": [
-3.9735127215
],
"velocity": [
-6.7696710164
]
}
]
} | {
"horizon": 1,
"n_obj": 1,
"n_col": 0,
"ood_axis": "id",
"dim": 1
} | {} | 2bda285067ba23b0 | Consider the following physical system.
Time step Δt = 0.2 s. Predict the state after 1 steps.
Object o0 has mass 6.48 kg, position -2.607 m, velocity -683.2 cm/s, and constant force 2.034 N.
Return JSON with keys objects (list of {id, position, velocity}), using SI units (m, m/s). |
T1_26a7eb74a33c4166 | train | T1 | {
"dim": 2,
"dt": 0.2,
"horizon": 5,
"objects": [
{
"id": "o0",
"mass": 3.4608240704,
"position": [
3.3472394558,
4.802446326
],
"velocity": [
-5.1253818785,
1.0253015376
],
"force": [
-4.6565594701,
16.8747259973
... | {
"objects": [
{
"id": "o0",
"position": [
-2.3163448133,
7.778118718
],
"velocity": [
-6.4708878549,
5.9012286734
]
},
{
"id": "o1",
"position": [
-0.9259372573,
10.6868524145
],
"velocity": [
-5... | {
"horizon": 5,
"n_obj": 2,
"n_col": 0,
"ood_axis": "id",
"dim": 2
} | {} | 26a7eb74a33c4166 | Consider the following physical system.
Time step Δt = 0.2 s. Predict the state after 5 steps.
Object o0 has mass 3461 g, position [3.347, 4.802] m, velocity [-5.125, 1.025] m/s, and force [-4.657, 16.87] N.
Object o1 has mass 5574 g, position [3.793, 3.64] m, velocity [-4.475, 5.8] m/s, and force [-3.402, 17.37] N.
Ob... |
T2_ebf151a761421792 | train | T2 | {
"dim": 1,
"dt": 0.1,
"horizon": 2,
"objects": [
{
"id": "o0",
"mass": 5.8472251993,
"position": [
-1.5487605831
],
"velocity": [
1.0383483414
],
"force": [
1.7372025183
]
}
],
"walls": null,
"collisions": false,
"gravity":... | 5.8472251993 | {
"horizon": 2,
"n_obj": 1,
"n_col": 0,
"ood_axis": "id",
"dim": 1
} | {
"unknown": {
"object_id": "o0",
"field": "mass",
"value": 5.8472251993
},
"observation": {
"objects": [
{
"id": "o0",
"position": [
-1.3381199286
],
"velocity": [
1.0977680647999999
]
}
]
}
} | ebf151a761421792 | An unknown parameter must be recovered from the data below.
Time step Δt = 0.1 s, horizon = 2.
Object o0 has unknown mass, position -1.549 m, velocity 1.038 m/s, constant force 1.737 N.
After 2 steps the observed state is: {'objects': [{'id': 'o0', 'position': [-1.3381199286195247], 'velocity': [1.0977680647593382]}]}.... |
T1_5eb1e01cd2486876 | train | T1 | {
"dim": 1,
"dt": 0.2,
"horizon": 3,
"objects": [
{
"id": "o0",
"mass": 5.2567862522,
"position": [
4.1343016782
],
"velocity": [
-2.3753770611
],
"force": [
19.5365600776
]
}
],
"walls": null,
"collisions": false,
"gravity"... | {
"objects": [
{
"id": "o0",
"position": [
3.1550489122
],
"velocity": [
-0.1455097078
]
}
]
} | {
"horizon": 3,
"n_obj": 1,
"n_col": 0,
"ood_axis": "id",
"dim": 1
} | {} | 5eb1e01cd2486876 | Here is a Newtonian point-mass scene.
Time step Δt = 0.2 s. Predict the state after 3 steps.
Object o0 has mass 5257 g, position 4.134 m, velocity -2.375 m/s, and constant force 19.54 N.
Return JSON with keys objects (list of {id, position, velocity}), using SI units (m, m/s). |
T3_1b74e87709bcbbe3 | train | T3 | {
"dim": 1,
"dt": 0.2,
"horizon": 1,
"objects": [
{
"id": "o0",
"mass": 9.1939750993,
"position": [
-4.8465240208
],
"velocity": [
-7.1168916807
],
"force": [
14.837318854
]
}
],
"walls": null,
"collisions": false,
"gravity"... | "NO" | {
"horizon": 1,
"n_obj": 1,
"n_col": 0,
"ood_axis": "id",
"dim": 1
} | {
"claim": "After 1 steps, object o0 has position[0] > 0.",
"label": "NO",
"true_x0": -6.269902357
} | 1b74e87709bcbbe3 | Is the following claim consistent with Newtonian mechanics?
Object o0 has mass 9194 g, position -484.7 cm, velocity -7.117 m/s, and constant force 14.84 N.
Claim: After 1 steps, object o0 has position[0] > 0.
Answer with exactly YES or NO. |
T3_51d5438cb5c1c95c | train | T3 | {
"dim": 1,
"dt": 0.2,
"horizon": 3,
"objects": [
{
"id": "o0",
"mass": 7.468456827,
"position": [
2.5940180933
],
"velocity": [
7.447660348
],
"force": [
-18.5640360065
]
}
],
"walls": [
-8,
8
],
"collisions": false... | "YES" | {
"horizon": 3,
"n_obj": 1,
"n_col": 0,
"ood_axis": "id",
"dim": 1
} | {
"claim": "After 3 steps, object o0 ends at position[0] ≈ 6.764 (within 1%).",
"label": "YES",
"true_x0": 6.7643352369
} | 51d5438cb5c1c95c | Decide whether the proposed outcome is physically possible.
Object o0 has mass 7.468 kg, position 259.4 cm, velocity 7.448 m/s, and constant force -18.56 N.
Claim: After 3 steps, object o0 ends at position[0] ≈ 6.764 (within 1%).
Answer with exactly YES or NO. |
T1_2dcfeefca16835d8 | train | T1 | {
"dim": 1,
"dt": 0.1,
"horizon": 1,
"objects": [
{
"id": "o0",
"mass": 8.1652911865,
"position": [
-2.0663222403
],
"velocity": [
-2.5031782045
],
"force": [
-14.177208172
]
}
],
"walls": null,
"collisions": false,
"gravity... | {
"objects": [
{
"id": "o0",
"position": [
-2.3166400608
],
"velocity": [
-2.6768059154
]
}
]
} | {
"horizon": 1,
"n_obj": 1,
"n_col": 0,
"ood_axis": "id",
"dim": 1
} | {} | 2dcfeefca16835d8 | Here is a Newtonian point-mass scene.
Time step Δt = 0.1 s. Predict the state after 1 steps.
Object o0 has mass 8.165 kg, position -2.066 m, velocity -2.503 m/s, and constant force -14.18 N.
Return JSON with keys objects (list of {id, position, velocity}), using SI units (m, m/s). |
T1_e99724a48dc64051 | train | T1 | {
"dim": 2,
"dt": 0.1,
"horizon": 2,
"objects": [
{
"id": "o0",
"mass": 6.741141679,
"position": [
-0.4042950082,
1.6684071727
],
"velocity": [
7.978170634,
-0.6949348895
],
"force": [
-8.4947333701,
1.8639255041
... | {
"objects": [
{
"id": "o0",
"position": [
1.1787377911,
1.5321851945
],
"velocity": [
7.726144085,
-0.6396348945
]
}
]
} | {
"horizon": 2,
"n_obj": 1,
"n_col": 0,
"ood_axis": "id",
"dim": 2
} | {} | e99724a48dc64051 | You are given this physics setup.
Time step Δt = 0.1 s. Predict the state after 2 steps.
Object o0 has mass 6741 g, position [-0.4043, 1.668] m, velocity [7.978, -0.6949] m/s, and force [-8.495, 1.864] N.
Walls at [-8.0, 8.0, -8.0, 8.0].
Return JSON with keys objects (list of {id, position, velocity}), using SI units (... |
T1_a71e94452dc00f17 | train | T1 | {
"dim": 1,
"dt": 0.1,
"horizon": 4,
"objects": [
{
"id": "o0",
"mass": 2.792952992,
"position": [
-1.1530675103
],
"velocity": [
-0.3358387788
],
"force": [
-10.5117719229
]
},
{
"id": "o1",
"mass": 6.1473042312,
... | {
"objects": [
{
"id": "o0",
"position": [
-1.51322362
],
"velocity": [
-1.8413094334000002
]
},
{
"id": "o1",
"position": [
4.6097106583
],
"velocity": [
9.3208742558
]
}
]
} | {
"horizon": 4,
"n_obj": 2,
"n_col": 0,
"ood_axis": "id",
"dim": 1
} | {} | a71e94452dc00f17 | Simulate the evolution of the system below.
Time step Δt = 0.1 s. Predict the state after 4 steps.
Object o0 has mass 2793 g, position -1.153 m, velocity -0.3358 m/s, and constant force -10.51 N.
Object o1 has mass 6147 g, position 0.7481 m, velocity 985.4 cm/s, and constant force -8.191 N.
Objects collide elastically ... |
T1_86444c17a11f5113 | train | T1 | {
"dim": 1,
"dt": 0.2,
"horizon": 1,
"objects": [
{
"id": "o0",
"mass": 6.81706548,
"position": [
-1.9106711605
],
"velocity": [
-1.1835361967
],
"force": [
3.1829522147
]
}
],
"walls": null,
"collisions": false,
"gravity": ... | {
"objects": [
{
"id": "o0",
"position": [
-2.1473783998
],
"velocity": [
-1.0901543091
]
}
]
} | {
"horizon": 1,
"n_obj": 1,
"n_col": 0,
"ood_axis": "id",
"dim": 1
} | {} | 86444c17a11f5113 | Consider the following physical system.
Time step Δt = 0.2 s. Predict the state after 1 steps.
Object o0 has mass 6817 g, position -191.1 cm, velocity -118.4 cm/s, and constant force 3.183 N.
Return JSON with keys objects (list of {id, position, velocity}), using SI units (m, m/s). |
T1_c41aee9f5b412016 | train | T1 | {
"dim": 1,
"dt": 0.2,
"horizon": 5,
"objects": [
{
"id": "o0",
"mass": 9.2213827703,
"position": [
3.3047261957
],
"velocity": [
-4.8605983087
],
"force": [
12.9875925017
]
},
{
"id": "o1",
"mass": 5.3366304689,
... | {
"objects": [
{
"id": "o0",
"position": [
-0.9925035674
],
"velocity": [
-3.4521769445
]
},
{
"id": "o1",
"position": [
-1.9138790142
],
"velocity": [
-6.1101389176
]
}
]
} | {
"horizon": 5,
"n_obj": 2,
"n_col": 0,
"ood_axis": "id",
"dim": 1
} | {} | c41aee9f5b412016 | Here is a Newtonian point-mass scene.
Time step Δt = 0.2 s. Predict the state after 5 steps.
Object o0 has mass 9.221 kg, position 330.5 cm, velocity -486.1 cm/s, and constant force 12.99 N.
Object o1 has mass 5337 g, position 2.466 m, velocity -322.6 cm/s, and constant force -15.39 N.
Objects collide elastically when ... |
T1_c25d46f57373596d | train | T1 | {
"dim": 1,
"dt": 0.1,
"horizon": 5,
"objects": [
{
"id": "o0",
"mass": 8.401755711,
"position": [
4.4029189178
],
"velocity": [
-7.833077956
],
"force": [
-10.6471239115
]
},
{
"id": "o1",
"mass": 1.2252218468,
... | {
"objects": [
{
"id": "o0",
"position": [
1.4786214636000001
],
"velocity": [
-5.9684715842
]
},
{
"id": "o1",
"position": [
-1.8488488667
],
"velocity": [
-9.1245987146
]
}
]
} | {
"horizon": 5,
"n_obj": 2,
"n_col": 1,
"ood_axis": "id",
"dim": 1
} | {} | c25d46f57373596d | Consider the following physical system.
Time step Δt = 0.1 s. Predict the state after 5 steps.
Object o0 has mass 8402 g, position 440.3 cm, velocity -783.3 cm/s, and constant force -10.65 N.
Object o1 has mass 1.225 kg, position 3.842 m, velocity 1.228 m/s, and constant force 16.61 N.
Walls at [-8.0, 8.0].
Objects col... |
T3_fa62828c2d1a1a9c | train | T3 | {
"dim": 1,
"dt": 0.05,
"horizon": 5,
"objects": [
{
"id": "o0",
"mass": 4.4978124804,
"position": [
-1.2898848451
],
"velocity": [
8.9876153682
],
"force": [
7.8593596655
]
}
],
"walls": null,
"collisions": false,
"gravity"... | "YES" | {
"horizon": 5,
"n_obj": 1,
"n_col": 0,
"ood_axis": "id",
"dim": 1
} | {
"claim": "After 5 steps, object o0 ends at position[0] ≈ 1.001 (within 1%).",
"label": "YES",
"true_x0": 1.0007033418
} | fa62828c2d1a1a9c | Is the following claim consistent with Newtonian mechanics?
Object o0 has mass 4.498 kg, position -129 cm, velocity 898.8 cm/s, and constant force 7.859 N.
Claim: After 5 steps, object o0 ends at position[0] ≈ 1.001 (within 1%).
Answer with exactly YES or NO. |
T1_6612207e6e8c82f8 | train | T1 | {
"dim": 1,
"dt": 0.05,
"horizon": 4,
"objects": [
{
"id": "o0",
"mass": 8.6990517398,
"position": [
-4.0064537539
],
"velocity": [
3.7136053096
],
"force": [
1.7786344593
]
},
{
"id": "o1",
"mass": 9.8005827651,
... | {
"objects": [
{
"id": "o0",
"position": [
-3.2606657466
],
"velocity": [
3.7544979152
]
},
{
"id": "o1",
"position": [
-1.8396932002000002
],
"velocity": [
-2.2904095885
]
}
]
} | {
"horizon": 4,
"n_obj": 2,
"n_col": 0,
"ood_axis": "id",
"dim": 1
} | {} | 6612207e6e8c82f8 | Simulate the evolution of the system below.
Time step Δt = 0.05 s. Predict the state after 4 steps.
Object o0 has mass 8.699 kg, position -4.006 m, velocity 3.714 m/s, and constant force 1.779 N.
Object o1 has mass 9801 g, position -1.413 m, velocity -2.037 m/s, and constant force -12.41 N.
Walls at [-8.0, 8.0].
Object... |
T1_fd8fd33ce3a4ead7 | train | T1 | {
"dim": 1,
"dt": 0.05,
"horizon": 5,
"objects": [
{
"id": "o0",
"mass": 8.3174768301,
"position": [
-2.6700132095
],
"velocity": [
5.4873715561
],
"force": [
11.5457501711
]
}
],
"walls": null,
"collisions": false,
"gravity... | {
"objects": [
{
"id": "o0",
"position": [
-1.2634670372999999
],
"velocity": [
5.8344043885
]
}
]
} | {
"horizon": 5,
"n_obj": 1,
"n_col": 0,
"ood_axis": "id",
"dim": 1
} | {} | fd8fd33ce3a4ead7 | You are given this physics setup.
Time step Δt = 0.05 s. Predict the state after 5 steps.
Object o0 has mass 8.317 kg, position -2.67 m, velocity 548.7 cm/s, and constant force 11.55 N.
Return JSON with keys objects (list of {id, position, velocity}), using SI units (m, m/s). |
T1_cffde2db86f89f8f | train | T1 | {
"dim": 1,
"dt": 0.1,
"horizon": 1,
"objects": [
{
"id": "o0",
"mass": 8.1098619781,
"position": [
-2.6206839391
],
"velocity": [
-3.5245707608
],
"force": [
-13.0301519438
]
}
],
"walls": [
-8,
8
],
"collisions": f... | {
"objects": [
{
"id": "o0",
"position": [
-2.9731410152
],
"velocity": [
-3.6852412133
]
}
]
} | {
"horizon": 1,
"n_obj": 1,
"n_col": 0,
"ood_axis": "id",
"dim": 1
} | {} | cffde2db86f89f8f | Simulate the evolution of the system below.
Time step Δt = 0.1 s. Predict the state after 1 steps.
Object o0 has mass 8.11 kg, position -2.621 m, velocity -352.5 cm/s, and constant force -13.03 N.
Walls at [-8.0, 8.0].
Return JSON with keys objects (list of {id, position, velocity}), using SI units (m, m/s). |
T2_4a38b31ead8a4cdc | train | T2 | {
"dim": 1,
"dt": 0.2,
"horizon": 4,
"objects": [
{
"id": "o0",
"mass": 2.9939478078,
"position": [
1.1510683628
],
"velocity": [
4.5448599433
],
"force": [
16.3500675163
]
}
],
"walls": null,
"collisions": false,
"gravity":... | 2.9939478078 | {
"horizon": 4,
"n_obj": 1,
"n_col": 0,
"ood_axis": "id",
"dim": 1
} | {
"unknown": {
"object_id": "o0",
"field": "mass",
"value": 2.9939478078
},
"observation": {
"objects": [
{
"id": "o0",
"position": [
6.0976058197
],
"velocity": [
8.9136916173
]
}
]
}
} | 4a38b31ead8a4cdc | An unknown parameter must be recovered from the data below.
Time step Δt = 0.2 s, horizon = 4.
Object o0 has unknown mass, position 115.1 cm, velocity 4.545 m/s, constant force 16.35 N.
After 4 steps the observed state is: {'objects': [{'id': 'o0', 'position': [6.097605819678616], 'velocity': [8.913691617322998]}]}.
Wh... |
T3_c59768fb43633de9 | train | T3 | {
"dim": 1,
"dt": 0.1,
"horizon": 1,
"objects": [
{
"id": "o0",
"mass": 7.4116118341,
"position": [
-0.5643767064
],
"velocity": [
7.9853353025
],
"force": [
-7.1155272101
]
}
],
"walls": [
-8,
8
],
"collisions": fal... | "YES" | {
"horizon": 1,
"n_obj": 1,
"n_col": 0,
"ood_axis": "id",
"dim": 1
} | {
"claim": "After 1 steps, object o0 has position[0] > 0.",
"label": "YES",
"true_x0": 0.2341568239
} | c59768fb43633de9 | Answer yes or no: is this outcome physically feasible?
Object o0 has mass 7412 g, position -56.44 cm, velocity 798.5 cm/s, and constant force -7.116 N.
Claim: After 1 steps, object o0 has position[0] > 0.
Answer with exactly YES or NO. |
T1_50aaba5cfb9941bc | train | T1 | {
"dim": 1,
"dt": 0.2,
"horizon": 5,
"objects": [
{
"id": "o0",
"mass": 8.7894308413,
"position": [
-0.6993005833
],
"velocity": [
7.7618204398
],
"force": [
-3.4474571529
]
}
],
"walls": null,
"collisions": false,
"gravity"... | {
"objects": [
{
"id": "o0",
"position": [
6.9056288261
],
"velocity": [
7.3695928638
]
}
]
} | {
"horizon": 5,
"n_obj": 1,
"n_col": 0,
"ood_axis": "id",
"dim": 1
} | {} | 50aaba5cfb9941bc | Simulate the evolution of the system below.
Time step Δt = 0.2 s. Predict the state after 5 steps.
Object o0 has mass 8789 g, position -0.6993 m, velocity 776.2 cm/s, and constant force -3.447 N.
Return JSON with keys objects (list of {id, position, velocity}), using SI units (m, m/s). |
T1_d71f6e788d3e9040 | train | T1 | {
"dim": 1,
"dt": 0.05,
"horizon": 4,
"objects": [
{
"id": "o0",
"mass": 1.8210230953,
"position": [
-4.1463564267
],
"velocity": [
-1.362469629
],
"force": [
9.7835587677
]
}
],
"walls": null,
"collisions": false,
"gravity"... | {
"objects": [
{
"id": "o0",
"position": [
-4.3382619284
],
"velocity": [
-0.28795730750000004
]
}
]
} | {
"horizon": 4,
"n_obj": 1,
"n_col": 0,
"ood_axis": "id",
"dim": 1
} | {} | d71f6e788d3e9040 | Here is a Newtonian point-mass scene.
Time step Δt = 0.05 s. Predict the state after 4 steps.
Object o0 has mass 1.821 kg, position -414.6 cm, velocity -1.362 m/s, and constant force 9.784 N.
Return JSON with keys objects (list of {id, position, velocity}), using SI units (m, m/s). |
T1_b50bd1dbbff9da14 | train | T1 | {
"dim": 1,
"dt": 0.1,
"horizon": 1,
"objects": [
{
"id": "o0",
"mass": 6.403690821,
"position": [
-1.4835381431
],
"velocity": [
1.5583703678
],
"force": [
-11.4904477731
]
},
{
"id": "o1",
"mass": 6.9106267269,
... | {
"objects": [
{
"id": "o0",
"position": [
-1.3277011063
],
"velocity": [
1.3789355997000001
]
},
{
"id": "o1",
"position": [
-3.5411145451
],
"velocity": [
-7.6357237672
]
}
]
} | {
"horizon": 1,
"n_obj": 2,
"n_col": 0,
"ood_axis": "id",
"dim": 1
} | {} | b50bd1dbbff9da14 | You are given this physics setup.
Time step Δt = 0.1 s. Predict the state after 1 steps.
Object o0 has mass 6.404 kg, position -148.4 cm, velocity 1.558 m/s, and constant force -11.49 N.
Object o1 has mass 6.911 kg, position -2.758 m, velocity -783.6 cm/s, and constant force 13.81 N.
Objects collide elastically when th... |
T3_4388d1c11e72431b | train | T3 | {
"dim": 1,
"dt": 0.2,
"horizon": 2,
"objects": [
{
"id": "o0",
"mass": 6.9161017135,
"position": [
-4.3041457875
],
"velocity": [
4.8193811824
],
"force": [
18.8724127503
]
}
],
"walls": [
-8,
8
],
"collisions": fal... | "NO" | {
"horizon": 2,
"n_obj": 1,
"n_col": 0,
"ood_axis": "id",
"dim": 1
} | {
"claim": "After 2 steps, object o0 ends at position[0] = 2.733.",
"label": "NO",
"true_x0": -2.2672427351
} | 4388d1c11e72431b | Is the following claim consistent with Newtonian mechanics?
Object o0 has mass 6916 g, position -4.304 m, velocity 481.9 cm/s, and constant force 18.87 N.
Claim: After 2 steps, object o0 ends at position[0] = 2.733.
Answer with exactly YES or NO. |
T2_47a20883e3d4f5fb | train | T2 | {
"dim": 1,
"dt": 0.05,
"horizon": 1,
"objects": [
{
"id": "o0",
"mass": 2.416689074,
"position": [
1.1783818193
],
"velocity": [
3.4793742123
],
"force": [
-9.1158862582
]
}
],
"walls": null,
"collisions": false,
"gravity":... | 2.416689074 | {
"horizon": 1,
"n_obj": 1,
"n_col": 0,
"ood_axis": "id",
"dim": 1
} | {
"unknown": {
"object_id": "o0",
"field": "mass",
"value": 2.416689074
},
"observation": {
"objects": [
{
"id": "o0",
"position": [
1.3523505299
],
"velocity": [
3.2907714177000003
]
}
]
}
} | 47a20883e3d4f5fb | An unknown parameter must be recovered from the data below.
Time step Δt = 0.05 s, horizon = 1.
Object o0 has unknown mass, position 117.8 cm, velocity 347.9 cm/s, constant force -9.116 N.
After 1 steps the observed state is: {'objects': [{'id': 'o0', 'position': [1.3523505298734189], 'velocity': [3.2907714177124974]}]... |
T1_ddf11d778de351a0 | train | T1 | {
"dim": 1,
"dt": 0.05,
"horizon": 4,
"objects": [
{
"id": "o0",
"mass": 3.5492182307,
"position": [
1.7848625476
],
"velocity": [
-0.2673449327
],
"force": [
6.6853023495
]
},
{
"id": "o1",
"mass": 1.4087562634,
... | {
"objects": [
{
"id": "o0",
"position": [
1.7596475395
],
"velocity": [
0.1093747793
]
},
{
"id": "o1",
"position": [
-0.8597460233
],
"velocity": [
-0.8092316877
]
}
]
} | {
"horizon": 4,
"n_obj": 2,
"n_col": 0,
"ood_axis": "id",
"dim": 1
} | {} | ddf11d778de351a0 | Here is a Newtonian point-mass scene.
Time step Δt = 0.05 s. Predict the state after 4 steps.
Object o0 has mass 3.549 kg, position 178.5 cm, velocity -26.73 cm/s, and constant force 6.685 N.
Object o1 has mass 1.409 kg, position -1.047 m, velocity 198.6 cm/s, and constant force -19.69 N.
Walls at [-8.0, 8.0].
Objects ... |
T1_a34f57301a4c2419 | train | T1 | {
"dim": 1,
"dt": 0.2,
"horizon": 5,
"objects": [
{
"id": "o0",
"mass": 8.5001878218,
"position": [
3.0620018657
],
"velocity": [
-8.5584900682
],
"force": [
14.4705744809
]
}
],
"walls": [
-8,
8
],
"collisions": fal... | {
"objects": [
{
"id": "o0",
"position": [
-4.8155350384
],
"velocity": [
-6.856107158
]
}
]
} | {
"horizon": 5,
"n_obj": 1,
"n_col": 0,
"ood_axis": "id",
"dim": 1
} | {} | a34f57301a4c2419 | Consider the following physical system.
Time step Δt = 0.2 s. Predict the state after 5 steps.
Object o0 has mass 8500 g, position 3.062 m, velocity -855.8 cm/s, and constant force 14.47 N.
Walls at [-8.0, 8.0].
Return JSON with keys objects (list of {id, position, velocity}), using SI units (m, m/s). |
T1_89198468649d925a | train | T1 | {
"dim": 1,
"dt": 0.05,
"horizon": 3,
"objects": [
{
"id": "o0",
"mass": 4.6452907636,
"position": [
4.6619969103
],
"velocity": [
-6.5625363884
],
"force": [
17.9045723731
]
},
{
"id": "o1",
"mass": 5.140872117,
... | {
"objects": [
{
"id": "o0",
"position": [
3.7065240705
],
"velocity": [
-5.9843840202
]
},
{
"id": "o1",
"position": [
1.4779652461000001
],
"velocity": [
-2.8368109426
]
}
]
} | {
"horizon": 3,
"n_obj": 2,
"n_col": 0,
"ood_axis": "id",
"dim": 1
} | {} | 89198468649d925a | Simulate the evolution of the system below.
Time step Δt = 0.05 s. Predict the state after 3 steps.
Object o0 has mass 4645 g, position 4.662 m, velocity -656.3 cm/s, and constant force 17.9 N.
Object o1 has mass 5141 g, position 1.896 m, velocity -276.3 cm/s, and constant force -2.532 N.
Walls at [-8.0, 8.0].
Objects ... |
T1_045c2f076ac44ac6 | train | T1 | {
"dim": 1,
"dt": 0.1,
"horizon": 3,
"objects": [
{
"id": "o0",
"mass": 7.5464119511,
"position": [
3.1894860152
],
"velocity": [
6.300740115
],
"force": [
-10.5492460421
]
}
],
"walls": [
-8,
8
],
"collisions": fals... | {
"objects": [
{
"id": "o0",
"position": [
5.0377705855
],
"velocity": [
5.8813654727
]
}
]
} | {
"horizon": 3,
"n_obj": 1,
"n_col": 0,
"ood_axis": "id",
"dim": 1
} | {} | 045c2f076ac44ac6 | Here is a Newtonian point-mass scene.
Time step Δt = 0.1 s. Predict the state after 3 steps.
Object o0 has mass 7.546 kg, position 3.189 m, velocity 6.301 m/s, and constant force -10.55 N.
Walls at [-8.0, 8.0].
Return JSON with keys objects (list of {id, position, velocity}), using SI units (m, m/s). |
T3_80d420171f8325ce | train | T3 | {
"dim": 1,
"dt": 0.2,
"horizon": 5,
"objects": [
{
"id": "o0",
"mass": 5.040147313,
"position": [
4.2415425839
],
"velocity": [
1.2898356681
],
"force": [
5.4119327624
]
}
],
"walls": null,
"collisions": false,
"gravity": n... | "YES" | {
"horizon": 5,
"n_obj": 1,
"n_col": 0,
"ood_axis": "id",
"dim": 1
} | {
"claim": "After 5 steps, object o0 ends at position[0] ≈ 5.961 (within 1%).",
"label": "YES",
"true_x0": 5.9608841712
} | 80d420171f8325ce | Decide whether the proposed outcome is physically possible.
Object o0 has mass 5040 g, position 4.242 m, velocity 129 cm/s, and constant force 5.412 N.
Claim: After 5 steps, object o0 ends at position[0] ≈ 5.961 (within 1%).
Answer with exactly YES or NO. |
T1_4e91c9ae6ad30560 | train | T1 | {
"dim": 1,
"dt": 0.2,
"horizon": 3,
"objects": [
{
"id": "o0",
"mass": 1.6677159056,
"position": [
-0.3825751355
],
"velocity": [
-9.2478550886
],
"force": [
-5.2504960204
]
}
],
"walls": [
-8,
8
],
"collisions": fa... | {
"objects": [
{
"id": "o0",
"position": [
-6.309086062
],
"velocity": [
-11.1368444553
]
}
]
} | {
"horizon": 3,
"n_obj": 1,
"n_col": 0,
"ood_axis": "id",
"dim": 1
} | {} | 4e91c9ae6ad30560 | Consider the following physical system.
Time step Δt = 0.2 s. Predict the state after 3 steps.
Object o0 has mass 1668 g, position -38.26 cm, velocity -9.248 m/s, and constant force -5.25 N.
Walls at [-8.0, 8.0].
Return JSON with keys objects (list of {id, position, velocity}), using SI units (m, m/s). |
T3_964f229029ef0d97 | train | T3 | {
"dim": 1,
"dt": 0.2,
"horizon": 3,
"objects": [
{
"id": "o0",
"mass": 5.2806612515,
"position": [
-3.491389233
],
"velocity": [
-8.762525998
],
"force": [
-15.8599249092
]
}
],
"walls": null,
"collisions": false,
"gravity"... | "NO" | {
"horizon": 3,
"n_obj": 1,
"n_col": 0,
"ood_axis": "id",
"dim": 1
} | {
"claim": "After 3 steps, object o0 has position[0] > 0.",
"label": "NO",
"true_x0": -9.1093125343
} | 964f229029ef0d97 | Answer yes or no: is this outcome physically feasible?
Object o0 has mass 5.281 kg, position -3.491 m, velocity -8.763 m/s, and constant force -15.86 N.
Claim: After 3 steps, object o0 has position[0] > 0.
Answer with exactly YES or NO. |
T2_8f7b479f4ea4ecb8 | train | T2 | {
"dim": 1,
"dt": 0.1,
"horizon": 3,
"objects": [
{
"id": "o0",
"mass": 9.2614311021,
"position": [
-1.1258344048
],
"velocity": [
5.4892957715
],
"force": [
7.1559088224
]
}
],
"walls": null,
"collisions": false,
"gravity":... | 9.2614311021 | {
"horizon": 3,
"n_obj": 1,
"n_col": 0,
"ood_axis": "id",
"dim": 1
} | {
"unknown": {
"object_id": "o0",
"field": "mass",
"value": 9.2614311021
},
"observation": {
"objects": [
{
"id": "o0",
"position": [
0.5441340342000001
],
"velocity": [
5.7210928471999996
]
}
]
}
} | 8f7b479f4ea4ecb8 | Use the observed motion to find the missing value.
Time step Δt = 0.1 s, horizon = 3.
Object o0 has unknown mass, position -112.6 cm, velocity 5.489 m/s, constant force 7.156 N.
After 3 steps the observed state is: {'objects': [{'id': 'o0', 'position': [0.5441340342485615], 'velocity': [5.721092847224607]}]}.
What is t... |
T1_d3fc275cff4f85f9 | train | T1 | {
"dim": 1,
"dt": 0.2,
"horizon": 3,
"objects": [
{
"id": "o0",
"mass": 8.6640963399,
"position": [
4.6441002865
],
"velocity": [
2.0540162732
],
"force": [
-13.9850669106
]
},
{
"id": "o1",
"mass": 1.733517887,
... | {
"objects": [
{
"id": "o0",
"position": [
5.8337942139
],
"velocity": [
2.7209551323000003
]
},
{
"id": "o1",
"position": [
5.2326184913
],
"velocity": [
-2.4661714316
]
}
]
} | {
"horizon": 3,
"n_obj": 2,
"n_col": 1,
"ood_axis": "id",
"dim": 1
} | {} | d3fc275cff4f85f9 | Simulate the evolution of the system below.
Time step Δt = 0.2 s. Predict the state after 3 steps.
Object o0 has mass 8.664 kg, position 4.644 m, velocity 205.4 cm/s, and constant force -13.99 N.
Object o1 has mass 1734 g, position 1.636 m, velocity 8.335 m/s, and constant force -7.591 N.
Objects collide elastically wh... |
T1_758d636a8ddbd913 | train | T1 | {
"dim": 2,
"dt": 0.05,
"horizon": 2,
"objects": [
{
"id": "o0",
"mass": 4.0755911062,
"position": [
2.6615620767,
-3.0799476634
],
"velocity": [
9.9995324221,
-6.9010965411
],
"force": [
-8.1683159338,
11.5248069469
... | {
"objects": [
{
"id": "o0",
"position": [
3.6565048089000003,
-3.7629879092
],
"velocity": [
9.7991120236,
-6.6183202113
]
},
{
"id": "o1",
"position": [
0.4575293053,
2.7124178632
],
"velocity": [
... | {
"horizon": 2,
"n_obj": 2,
"n_col": 0,
"ood_axis": "id",
"dim": 2
} | {} | 758d636a8ddbd913 | Here is a Newtonian point-mass scene.
Time step Δt = 0.05 s. Predict the state after 2 steps.
Object o0 has mass 4.076 kg, position [2.662, -3.08] m, velocity [10, -6.901] m/s, and force [-8.168, 11.52] N.
Object o1 has mass 5.569 kg, position [0.3977, 2.386] m, velocity [0.5306, 3.239] m/s, and force [15.06, 4.721] N.... |
T2_4214ddea448ac54e | train | T2 | {
"dim": 1,
"dt": 0.05,
"horizon": 4,
"objects": [
{
"id": "o0",
"mass": 4.6977275035,
"position": [
1.7636292219
],
"velocity": [
-5.2493959711
],
"force": [
-2.2320516078
]
}
],
"walls": null,
"collisions": false,
"gravity... | 4.6977275035 | {
"horizon": 4,
"n_obj": 1,
"n_col": 0,
"ood_axis": "id",
"dim": 1
} | {
"unknown": {
"object_id": "o0",
"field": "mass",
"value": 4.6977275035
},
"observation": {
"objects": [
{
"id": "o0",
"position": [
0.7066230127
],
"velocity": [
-5.344422837
]
}
]
}
} | 4214ddea448ac54e | Use the observed motion to find the missing value.
Time step Δt = 0.05 s, horizon = 4.
Object o0 has unknown mass, position 176.4 cm, velocity -5.249 m/s, constant force -2.232 N.
After 4 steps the observed state is: {'objects': [{'id': 'o0', 'position': [0.7066230127297155], 'velocity': [-5.344422836972338]}]}.
What i... |
T1_3d36f4913be310f0 | train | T1 | {
"dim": 1,
"dt": 0.1,
"horizon": 2,
"objects": [
{
"id": "o0",
"mass": 7.1047614256,
"position": [
0.7041939336
],
"velocity": [
-1.1880519298
],
"force": [
10.777542079
]
},
{
"id": "o1",
"mass": 8.0031163352,
... | {
"objects": [
{
"id": "o0",
"position": [
0.48175301140000004
],
"velocity": [
-0.8846626551000001
]
},
{
"id": "o1",
"position": [
-0.31318029000000003
],
"velocity": [
-1.9645937009
]
}
]
} | {
"horizon": 2,
"n_obj": 2,
"n_col": 0,
"ood_axis": "id",
"dim": 1
} | {} | 3d36f4913be310f0 | Here is a Newtonian point-mass scene.
Time step Δt = 0.1 s. Predict the state after 2 steps.
Object o0 has mass 7105 g, position 0.7042 m, velocity -118.8 cm/s, and constant force 10.78 N.
Object o1 has mass 8.003 kg, position 0.02907 m, velocity -162.7 cm/s, and constant force -13.52 N.
Walls at [-8.0, 8.0].
Objects c... |
T2_2956274a186ff03b | train | T2 | {
"dim": 1,
"dt": 0.05,
"horizon": 4,
"objects": [
{
"id": "o0",
"mass": 9.5177193671,
"position": [
-2.7796199309
],
"velocity": [
-0.9774401956
],
"force": [
-6.0165968745
]
}
],
"walls": null,
"collisions": false,
"gravit... | 9.5177193671 | {
"horizon": 4,
"n_obj": 1,
"n_col": 0,
"ood_axis": "id",
"dim": 1
} | {
"unknown": {
"object_id": "o0",
"field": "mass",
"value": 9.5177193671
},
"observation": {
"objects": [
{
"id": "o0",
"position": [
-2.9845901737
],
"velocity": [
-1.1038695773
]
}
]
}
} | 2956274a186ff03b | Infer the unknown quantity from the observed trajectory.
Time step Δt = 0.05 s, horizon = 4.
Object o0 has unknown mass, position -278 cm, velocity -97.74 cm/s, constant force -6.017 N.
After 4 steps the observed state is: {'objects': [{'id': 'o0', 'position': [-2.9845901736757523], 'velocity': [-1.103869577297746]}]}.... |
T1_0159c500a753a195 | train | T1 | {
"dim": 2,
"dt": 0.1,
"horizon": 1,
"objects": [
{
"id": "o0",
"mass": 9.3774331427,
"position": [
3.3917628761,
1.4996068429
],
"velocity": [
5.8276127496,
-7.2480082455
],
"force": [
-8.5248241075,
13.1904633261
... | {
"objects": [
{
"id": "o0",
"position": [
3.9745241511,
0.7748060184000001
],
"velocity": [
5.7367048863,
-7.1073464767
]
}
]
} | {
"horizon": 1,
"n_obj": 1,
"n_col": 0,
"ood_axis": "id",
"dim": 2
} | {} | 0159c500a753a195 | Here is a Newtonian point-mass scene.
Time step Δt = 0.1 s. Predict the state after 1 steps.
Object o0 has mass 9377 g, position [3.392, 1.5] m, velocity [5.828, -7.248] m/s, and force [-8.525, 13.19] N.
Return JSON with keys objects (list of {id, position, velocity}), using SI units (m, m/s). |
T1_3e15ea1df1ad350b | train | T1 | {
"dim": 2,
"dt": 0.1,
"horizon": 1,
"objects": [
{
"id": "o0",
"mass": 2.9408927002,
"position": [
-3.5048038104,
4.4022594934
],
"velocity": [
2.1776019823,
-1.534904821
],
"force": [
11.0469053054,
-10.4943909344
... | {
"objects": [
{
"id": "o0",
"position": [
-3.2870436121,
4.2487690113
],
"velocity": [
2.5532330043,
-1.8917485418000002
]
}
]
} | {
"horizon": 1,
"n_obj": 1,
"n_col": 0,
"ood_axis": "id",
"dim": 2
} | {} | 3e15ea1df1ad350b | Here is a Newtonian point-mass scene.
Time step Δt = 0.1 s. Predict the state after 1 steps.
Object o0 has mass 2941 g, position [-3.505, 4.402] m, velocity [2.178, -1.535] m/s, and force [11.05, -10.49] N.
Walls at [-8.0, 8.0, -8.0, 8.0].
Return JSON with keys objects (list of {id, position, velocity}), using SI units... |
T1_cbbbd607d6477cb1 | train | T1 | {
"dim": 1,
"dt": 0.1,
"horizon": 1,
"objects": [
{
"id": "o0",
"mass": 6.3706513854,
"position": [
-4.8356464779
],
"velocity": [
0.3075146042
],
"force": [
-10.3224746232
]
}
],
"walls": [
-8,
8
],
"collisions": fa... | {
"objects": [
{
"id": "o0",
"position": [
-4.8048950175
],
"velocity": [
0.14548290600000002
]
}
]
} | {
"horizon": 1,
"n_obj": 1,
"n_col": 0,
"ood_axis": "id",
"dim": 1
} | {} | cbbbd607d6477cb1 | Simulate the evolution of the system below.
Time step Δt = 0.1 s. Predict the state after 1 steps.
Object o0 has mass 6.371 kg, position -483.6 cm, velocity 0.3075 m/s, and constant force -10.32 N.
Walls at [-8.0, 8.0].
Return JSON with keys objects (list of {id, position, velocity}), using SI units (m, m/s). |
T1_b1d33f867608a229 | train | T1 | {
"dim": 1,
"dt": 0.2,
"horizon": 1,
"objects": [
{
"id": "o0",
"mass": 5.8967376394,
"position": [
2.8641233585
],
"velocity": [
0.1524517766
],
"force": [
-19.1866277485
]
},
{
"id": "o1",
"mass": 8.8599829467,
... | {
"objects": [
{
"id": "o0",
"position": [
2.8946137138
],
"velocity": [
-0.4983022139
]
},
{
"id": "o1",
"position": [
-5.0171304622
],
"velocity": [
-2.3767734401
]
}
]
} | {
"horizon": 1,
"n_obj": 2,
"n_col": 0,
"ood_axis": "id",
"dim": 1
} | {} | b1d33f867608a229 | You are given this physics setup.
Time step Δt = 0.2 s. Predict the state after 1 steps.
Object o0 has mass 5.897 kg, position 286.4 cm, velocity 0.1525 m/s, and constant force -19.19 N.
Object o1 has mass 8860 g, position -4.565 m, velocity -2.262 m/s, and constant force -5.068 N.
Objects collide elastically when they... |
T1_06725147af43e44a | train | T1 | {
"dim": 1,
"dt": 0.2,
"horizon": 4,
"objects": [
{
"id": "o0",
"mass": 5.3067805446,
"position": [
-3.1772200159
],
"velocity": [
-7.3029483761
],
"force": [
8.6418023038
]
}
],
"walls": null,
"collisions": false,
"gravity"... | {
"objects": [
{
"id": "o0",
"position": [
-8.6287518236
],
"velocity": [
-6.0001920655
]
}
]
} | {
"horizon": 4,
"n_obj": 1,
"n_col": 0,
"ood_axis": "id",
"dim": 1
} | {} | 06725147af43e44a | Consider the following physical system.
Time step Δt = 0.2 s. Predict the state after 4 steps.
Object o0 has mass 5307 g, position -3.177 m, velocity -7.303 m/s, and constant force 8.642 N.
Return JSON with keys objects (list of {id, position, velocity}), using SI units (m, m/s). |
T3_23cfc93bb9cf3820 | train | T3 | {
"dim": 1,
"dt": 0.1,
"horizon": 5,
"objects": [
{
"id": "o0",
"mass": 9.9021043207,
"position": [
0.4303069765
],
"velocity": [
-4.9337246959
],
"force": [
10.1316367528
]
}
],
"walls": [
-8,
8
],
"collisions": fal... | "NO" | {
"horizon": 5,
"n_obj": 1,
"n_col": 0,
"ood_axis": "id",
"dim": 1
} | {
"claim": "After 5 steps, object o0 has position[0] > 0.",
"label": "NO",
"true_x0": -1.9342373547
} | 23cfc93bb9cf3820 | Decide whether the proposed outcome is physically possible.
Object o0 has mass 9902 g, position 43.03 cm, velocity -4.934 m/s, and constant force 10.13 N.
Claim: After 5 steps, object o0 has position[0] > 0.
Answer with exactly YES or NO. |
T1_b1e8bb168c121273 | train | T1 | {
"dim": 1,
"dt": 0.1,
"horizon": 4,
"objects": [
{
"id": "o0",
"mass": 9.7635122588,
"position": [
-0.0379677346
],
"velocity": [
-0.0495321501
],
"force": [
16.9724186651
]
},
{
"id": "o1",
"mass": 5.6734826818,
... | {
"objects": [
{
"id": "o0",
"position": [
0.0465205106
],
"velocity": [
0.6458085517000001
]
},
{
"id": "o1",
"position": [
4.6500089218
],
"velocity": [
3.3541428403999998
]
}
]
} | {
"horizon": 4,
"n_obj": 2,
"n_col": 0,
"ood_axis": "id",
"dim": 1
} | {} | b1e8bb168c121273 | Here is a Newtonian point-mass scene.
Time step Δt = 0.1 s. Predict the state after 4 steps.
Object o0 has mass 9764 g, position -3.797 cm, velocity -0.04953 m/s, and constant force 16.97 N.
Object o1 has mass 5673 g, position 301.1 cm, velocity 454.2 cm/s, and constant force -16.84 N.
Objects collide elastically when ... |
T1_91eb06d8e804114b | train | T1 | {
"dim": 1,
"dt": 0.1,
"horizon": 3,
"objects": [
{
"id": "o0",
"mass": 1.3811964657,
"position": [
3.7003717506
],
"velocity": [
-2.9488137938
],
"force": [
19.9260239109
]
},
{
"id": "o1",
"mass": 3.4709982407,
... | {
"objects": [
{
"id": "o0",
"position": [
3.2485268066
],
"velocity": [
1.3791781479
]
},
{
"id": "o1",
"position": [
7.3407815008
],
"velocity": [
7.488911944
]
}
]
} | {
"horizon": 3,
"n_obj": 2,
"n_col": 0,
"ood_axis": "id",
"dim": 1
} | {} | 91eb06d8e804114b | You are given this physics setup.
Time step Δt = 0.1 s. Predict the state after 3 steps.
Object o0 has mass 1.381 kg, position 3.7 m, velocity -2.949 m/s, and constant force 19.93 N.
Object o1 has mass 3.471 kg, position 4.8 m, velocity 8.958 m/s, and constant force -17 N.
Objects collide elastically when they meet.
Re... |
T2_84cac6ebec5b84f9 | train | T2 | {
"dim": 1,
"dt": 0.05,
"horizon": 5,
"objects": [
{
"id": "o0",
"mass": 6.4458534597,
"position": [
1.7906205691
],
"velocity": [
8.9764705853
],
"force": [
-5.1194648612
]
}
],
"walls": null,
"collisions": false,
"gravity"... | 6.4458534597 | {
"horizon": 5,
"n_obj": 1,
"n_col": 0,
"ood_axis": "id",
"dim": 1
} | {
"unknown": {
"object_id": "o0",
"field": "mass",
"value": 6.4458534597
},
"observation": {
"objects": [
{
"id": "o0",
"position": [
4.0148825637
],
"velocity": [
8.7779140678
]
}
]
}
} | 84cac6ebec5b84f9 | Use the observed motion to find the missing value.
Time step Δt = 0.05 s, horizon = 5.
Object o0 has unknown mass, position 1.791 m, velocity 897.6 cm/s, constant force -5.119 N.
After 5 steps the observed state is: {'objects': [{'id': 'o0', 'position': [4.014882563711404], 'velocity': [8.77791406780784]}]}.
What is th... |
T1_6865ba96c170dc92 | train | T1 | {
"dim": 1,
"dt": 0.2,
"horizon": 1,
"objects": [
{
"id": "o0",
"mass": 2.6744324453,
"position": [
0.1774527421
],
"velocity": [
8.2708501163
],
"force": [
-15.2895601804
]
}
],
"walls": null,
"collisions": false,
"gravity"... | {
"objects": [
{
"id": "o0",
"position": [
1.8316227653000001
],
"velocity": [
7.1274628374
]
}
]
} | {
"horizon": 1,
"n_obj": 1,
"n_col": 0,
"ood_axis": "id",
"dim": 1
} | {} | 6865ba96c170dc92 | Simulate the evolution of the system below.
Time step Δt = 0.2 s. Predict the state after 1 steps.
Object o0 has mass 2.674 kg, position 17.75 cm, velocity 827.1 cm/s, and constant force -15.29 N.
Return JSON with keys objects (list of {id, position, velocity}), using SI units (m, m/s). |
T1_d14a53fe5c5d1328 | train | T1 | {
"dim": 1,
"dt": 0.2,
"horizon": 2,
"objects": [
{
"id": "o0",
"mass": 5.0060007347,
"position": [
-4.122092589
],
"velocity": [
3.638585205
],
"force": [
13.820848759
]
},
{
"id": "o1",
"mass": 3.8762899489,
... | {
"objects": [
{
"id": "o0",
"position": [
-4.7663931599
],
"velocity": [
-6.4378920109
]
},
{
"id": "o1",
"position": [
-2.1327702383
],
"velocity": [
5.9122223501
]
}
]
} | {
"horizon": 2,
"n_obj": 2,
"n_col": 1,
"ood_axis": "id",
"dim": 1
} | {} | d14a53fe5c5d1328 | Here is a Newtonian point-mass scene.
Time step Δt = 0.2 s. Predict the state after 2 steps.
Object o0 has mass 5.006 kg, position -412.2 cm, velocity 3.639 m/s, and constant force 13.82 N.
Object o1 has mass 3.876 kg, position -1.526 m, velocity -8.701 m/s, and constant force 1.687 N.
Objects collide elastically when ... |
T1_99cf816ff6c02c19 | train | T1 | {
"dim": 1,
"dt": 0.2,
"horizon": 4,
"objects": [
{
"id": "o0",
"mass": 2.1679410674,
"position": [
3.8424644683
],
"velocity": [
-8.6850378947
],
"force": [
-4.0736007692
]
},
{
"id": "o1",
"mass": 7.4524023866,
... | {
"objects": [
{
"id": "o0",
"position": [
-0.6323927869
],
"velocity": [
1.6963787935
]
},
{
"id": "o1",
"position": [
-2.615385004
],
"velocity": [
-5.630281116
]
}
]
} | {
"horizon": 4,
"n_obj": 2,
"n_col": 1,
"ood_axis": "id",
"dim": 1
} | {} | 99cf816ff6c02c19 | Here is a Newtonian point-mass scene.
Time step Δt = 0.2 s. Predict the state after 4 steps.
Object o0 has mass 2168 g, position 3.842 m, velocity -868.5 cm/s, and constant force -4.074 N.
Object o1 has mass 7452 g, position -0.2133 m, velocity -1.784 m/s, and constant force -3.623 N.
Objects collide elastically when t... |
T1_ef2979434d894094 | train | T1 | {
"dim": 1,
"dt": 0.2,
"horizon": 1,
"objects": [
{
"id": "o0",
"mass": 2.3771392013,
"position": [
-3.3534292011
],
"velocity": [
-3.5467849769
],
"force": [
8.3732853012
]
}
],
"walls": [
-8,
8
],
"collisions": fal... | {
"objects": [
{
"id": "o0",
"position": [
-4.0627861965
],
"velocity": [
-2.8423007552
]
}
]
} | {
"horizon": 1,
"n_obj": 1,
"n_col": 0,
"ood_axis": "id",
"dim": 1
} | {} | ef2979434d894094 | You are given this physics setup.
Time step Δt = 0.2 s. Predict the state after 1 steps.
Object o0 has mass 2.377 kg, position -335.3 cm, velocity -3.547 m/s, and constant force 8.373 N.
Walls at [-8.0, 8.0].
Return JSON with keys objects (list of {id, position, velocity}), using SI units (m, m/s). |
T1_834222da3f9e455b | train | T1 | {
"dim": 1,
"dt": 0.2,
"horizon": 5,
"objects": [
{
"id": "o0",
"mass": 2.5177231157,
"position": [
4.4160698787
],
"velocity": [
-6.9161146624
],
"force": [
6.3493149354
]
}
],
"walls": null,
"collisions": false,
"gravity":... | {
"objects": [
{
"id": "o0",
"position": [
-1.4913055946
],
"velocity": [
-4.3942666897
]
}
]
} | {
"horizon": 5,
"n_obj": 1,
"n_col": 0,
"ood_axis": "id",
"dim": 1
} | {} | 834222da3f9e455b | You are given this physics setup.
Time step Δt = 0.2 s. Predict the state after 5 steps.
Object o0 has mass 2.518 kg, position 4.416 m, velocity -6.916 m/s, and constant force 6.349 N.
Return JSON with keys objects (list of {id, position, velocity}), using SI units (m, m/s). |
T3_1e2d9cf62ee6ea5d | train | T3 | {
"dim": 1,
"dt": 0.2,
"horizon": 2,
"objects": [
{
"id": "o0",
"mass": 4.749281053,
"position": [
1.3899119221
],
"velocity": [
-0.0392387973
],
"force": [
5.0865604119
]
}
],
"walls": [
-8,
8
],
"collisions": false... | "NO" | {
"horizon": 2,
"n_obj": 1,
"n_col": 0,
"ood_axis": "id",
"dim": 1
} | {
"claim": "After 2 steps, object o0 ends at position[0] = 6.417.",
"label": "NO",
"true_x0": 1.4170570804
} | 1e2d9cf62ee6ea5d | Answer yes or no: is this outcome physically feasible?
Object o0 has mass 4749 g, position 139 cm, velocity -3.924 cm/s, and constant force 5.087 N.
Claim: After 2 steps, object o0 ends at position[0] = 6.417.
Answer with exactly YES or NO. |
T1_fcf7a4f2ba4aed0e | train | T1 | {
"dim": 2,
"dt": 0.1,
"horizon": 4,
"objects": [
{
"id": "o0",
"mass": 2.8362071221,
"position": [
1.0666026282,
-1.8741750075
],
"velocity": [
4.3672577022,
4.6839950961
],
"force": [
14.4310946302,
19.0149651166
... | {
"objects": [
{
"id": "o0",
"position": [
3.118795711,
0.4016848749
],
"velocity": [
6.4025243819,
7.365740723
]
},
{
"id": "o1",
"position": [
-2.9980305083000003,
0.07037640440000001
],
"velocity": [
... | {
"horizon": 4,
"n_obj": 2,
"n_col": 0,
"ood_axis": "id",
"dim": 2
} | {} | fcf7a4f2ba4aed0e | You are given this physics setup.
Time step Δt = 0.1 s. Predict the state after 4 steps.
Object o0 has mass 2836 g, position [1.067, -1.874] m, velocity [4.367, 4.684] m/s, and force [14.43, 19.01] N.
Object o1 has mass 2177 g, position [-1.295, 0.6165] m, velocity [-3.618, -0.6705] m/s, and force [-9.301, -10.08] N.
W... |
T1_a427568db62559e0 | train | T1 | {
"dim": 1,
"dt": 0.2,
"horizon": 3,
"objects": [
{
"id": "o0",
"mass": 7.4901558594,
"position": [
-3.1016589878
],
"velocity": [
-6.8131517621
],
"force": [
19.8387764438
]
}
],
"walls": null,
"collisions": false,
"gravity... | {
"objects": [
{
"id": "o0",
"position": [
-6.8717124435
],
"velocity": [
-5.2239637546
]
}
]
} | {
"horizon": 3,
"n_obj": 1,
"n_col": 0,
"ood_axis": "id",
"dim": 1
} | {} | a427568db62559e0 | You are given this physics setup.
Time step Δt = 0.2 s. Predict the state after 3 steps.
Object o0 has mass 7490 g, position -3.102 m, velocity -6.813 m/s, and constant force 19.84 N.
Return JSON with keys objects (list of {id, position, velocity}), using SI units (m, m/s). |
T1_f27a00db7a752525 | train | T1 | {
"dim": 1,
"dt": 0.1,
"horizon": 5,
"objects": [
{
"id": "o0",
"mass": 1.4379231964,
"position": [
-2.1864366163
],
"velocity": [
1.9503754202
],
"force": [
13.7139858765
]
}
],
"walls": null,
"collisions": false,
"gravity"... | {
"objects": [
{
"id": "o0",
"position": [
-0.2575132747
],
"velocity": [
6.7190535774
]
}
]
} | {
"horizon": 5,
"n_obj": 1,
"n_col": 0,
"ood_axis": "id",
"dim": 1
} | {} | f27a00db7a752525 | You are given this physics setup.
Time step Δt = 0.1 s. Predict the state after 5 steps.
Object o0 has mass 1.438 kg, position -2.186 m, velocity 195 cm/s, and constant force 13.71 N.
Return JSON with keys objects (list of {id, position, velocity}), using SI units (m, m/s). |
T3_defee96fb1bffaa5 | train | T3 | {
"dim": 1,
"dt": 0.05,
"horizon": 3,
"objects": [
{
"id": "o0",
"mass": 4.6052345891,
"position": [
0.7028164388
],
"velocity": [
-6.1068939622
],
"force": [
2.1289170648
]
}
],
"walls": [
-8,
8
],
"collisions": fal... | "YES" | {
"horizon": 3,
"n_obj": 1,
"n_col": 0,
"ood_axis": "id",
"dim": 1
} | {
"claim": "After 3 steps, object o0 ends at position[0] ≈ -0.2098 (within 1%).",
"label": "YES",
"true_x0": -0.2097505405
} | defee96fb1bffaa5 | Is the following claim consistent with Newtonian mechanics?
Object o0 has mass 4.605 kg, position 0.7028 m, velocity -6.107 m/s, and constant force 2.129 N.
Claim: After 3 steps, object o0 ends at position[0] ≈ -0.2098 (within 1%).
Answer with exactly YES or NO. |
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PhiLLM data
Synthetic Newtonian point-mass problems with exact simulator ground truth.
Splits
| File | N | Description |
|---|---|---|
train.jsonl |
50,000 | ID training |
dev.jsonl |
1,000 | ID development (checkpoint selection) |
dlab.jsonl |
5,000 | ID call-labeling set |
test.jsonl |
2,000 | ID test |
ood_mag.jsonl |
2,000 | OOD magnitudes |
ood_hor.jsonl |
2,000 | OOD horizons |
ood_obj.jsonl |
2,000 | OOD #objects |
ood_col.jsonl |
2,000 | OOD multi-collision |
inspect_50.jsonl |
50 | Level-0 inspection set |
Each row: id, split, task_type (T1/T2/T3), text, gold_spec, gold_answer, tags, param_hash.
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