bench_ablation/videogen.json

[
  {
    "case": "at_rest/0",
    "track": "perception_graphic",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\n\nGenerate a video where the background, ground, sky, and all annotations (coordinate axes, velocity arrows) gradually fade to pure white, while the subject physical objects remain still and unchanged. Static camera, no zoom, no rotation. The final frame should show only the objects with labeled physical properties on white — remove supporting structures (ramps, tracks, rails, platforms). Do not transform, resize, or replace any object. Each object must retain its exact position, size, shape, color, and texture.",
    "image": "firstframe/at_rest/0/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "at_rest/0",
    "track": "comprehension_text",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\n\nBelow are 4 candidate formulas. Exactly ONE is correct:\n  A) ΣF = m·Δv / (Δt·cosθ)\n  B) ΣF_ext = 0\n  C) T = 2π·√(m/k)\n  D) F_drag = (1/2)·C_d·ρ·A·v²\n\nGenerate a video ending on a white background with THREE lines of large, clearly readable, centered text:\n  Line 1: the correct option letter (A/B/C/D).\n  Line 2: the correct formula exactly as written above.\n  Line 3: the formula with annotated values substituted in from the parameters above.\n\nWhen substituting: if multiple objects exist, pick one consistent set.",
    "image": "firstframe/at_rest/0/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "at_rest/0",
    "track": "comprehension_graphic",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\n\nPredict the physical state at t = 1.0 s. Generate a video where the original annotations (coordinate axes and any initial velocity arrows) gradually fade out and cleanly disappear, while the background, ground, sky, and all scene lighting remain completely unchanged throughout. Objects move smoothly to their correct positions at t = 1.0 s — each object must retain its exact texture, material, size, and shape. For each moving object, draw a borderless orange arrow starting from the object's center pointing in its velocity direction, with a label \"v = X.XX\" (speed value, no unit). If at rest, show \"v = 0\" with no arrow. Static camera, no zoom, no rotation.",
    "image": "firstframe/at_rest/0/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "at_rest/0",
    "track": "generation",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\n\nGenerate 4 seconds of physically accurate motion strictly following these parameters. Every object AND the ground surface are perfectly rigid — nothing breaks, cracks, deforms, or creates craters. Each object maintains its exact material, color, and texture throughout. The coordinate axes and any initial velocity arrows must cleanly disappear after the first frame. Static camera, fixed background. Smooth, continuous motion.",
    "image": "firstframe/at_rest/0/rgb_0000.png",
    "duration": 4,
    "size": "1280x720"
  },
  {
    "case": "at_rest/2",
    "track": "perception_graphic",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\n\nGenerate a video where the background, ground, sky, and all annotations (coordinate axes, velocity arrows) gradually fade to pure white, while the subject physical objects remain still and unchanged. Static camera, no zoom, no rotation. The final frame should show only the objects with labeled physical properties on white — remove supporting structures (ramps, tracks, rails, platforms). Do not transform, resize, or replace any object. Each object must retain its exact position, size, shape, color, and texture.",
    "image": "firstframe/at_rest/2/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "at_rest/2",
    "track": "comprehension_text",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\n\nBelow are 4 candidate formulas. Exactly ONE is correct:\n  A) n_1·sinθ_1 = n_2·sinθ_2\n  B) ΣF_ext = 0\n  C) G = m·g\n  D) τ_net = Σ(F_i·r_i·sinθ_i) · e^(-μ·t)\n\nGenerate a video ending on a white background with THREE lines of large, clearly readable, centered text:\n  Line 1: the correct option letter (A/B/C/D).\n  Line 2: the correct formula exactly as written above.\n  Line 3: the formula with annotated values substituted in from the parameters above.\n\nWhen substituting: if multiple objects exist, pick one consistent set.",
    "image": "firstframe/at_rest/2/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "at_rest/2",
    "track": "comprehension_graphic",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\n\nPredict the physical state at t = 1.0 s. Generate a video where the original annotations (coordinate axes and any initial velocity arrows) gradually fade out and cleanly disappear, while the background, ground, sky, and all scene lighting remain completely unchanged throughout. Objects move smoothly to their correct positions at t = 1.0 s — each object must retain its exact texture, material, size, and shape. For each moving object, draw a borderless orange arrow starting from the object's center pointing in its velocity direction, with a label \"v = X.XX\" (speed value, no unit). If at rest, show \"v = 0\" with no arrow. Static camera, no zoom, no rotation.",
    "image": "firstframe/at_rest/2/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "at_rest/2",
    "track": "generation",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\n\nGenerate 4 seconds of physically accurate motion strictly following these parameters. Every object AND the ground surface are perfectly rigid — nothing breaks, cracks, deforms, or creates craters. Each object maintains its exact material, color, and texture throughout. The coordinate axes and any initial velocity arrows must cleanly disappear after the first frame. Static camera, fixed background. Smooth, continuous motion.",
    "image": "firstframe/at_rest/2/rgb_0000.png",
    "duration": 4,
    "size": "1280x720"
  },
  {
    "case": "at_rest/3",
    "track": "perception_graphic",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\n\nGenerate a video where the background, ground, sky, and all annotations (coordinate axes, velocity arrows) gradually fade to pure white, while the subject physical objects remain still and unchanged. Static camera, no zoom, no rotation. The final frame should show only the objects with labeled physical properties on white — remove supporting structures (ramps, tracks, rails, platforms). Do not transform, resize, or replace any object. Each object must retain its exact position, size, shape, color, and texture.",
    "image": "firstframe/at_rest/3/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "at_rest/3",
    "track": "comprehension_text",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\n\nBelow are 4 candidate formulas. Exactly ONE is correct:\n  A) G = m·g\n  B) ΣF = m·Δv / (Δt·cosθ)\n  C) ΣF_ext = 0\n  D) U = -G·m_1·m_2 / r\n\nGenerate a video ending on a white background with THREE lines of large, clearly readable, centered text:\n  Line 1: the correct option letter (A/B/C/D).\n  Line 2: the correct formula exactly as written above.\n  Line 3: the formula with annotated values substituted in from the parameters above.\n\nWhen substituting: if multiple objects exist, pick one consistent set.",
    "image": "firstframe/at_rest/3/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "at_rest/3",
    "track": "comprehension_graphic",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\n\nPredict the physical state at t = 1.0 s. Generate a video where the original annotations (coordinate axes and any initial velocity arrows) gradually fade out and cleanly disappear, while the background, ground, sky, and all scene lighting remain completely unchanged throughout. Objects move smoothly to their correct positions at t = 1.0 s — each object must retain its exact texture, material, size, and shape. For each moving object, draw a borderless orange arrow starting from the object's center pointing in its velocity direction, with a label \"v = X.XX\" (speed value, no unit). If at rest, show \"v = 0\" with no arrow. Static camera, no zoom, no rotation.",
    "image": "firstframe/at_rest/3/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "at_rest/3",
    "track": "generation",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\n\nGenerate 4 seconds of physically accurate motion strictly following these parameters. Every object AND the ground surface are perfectly rigid — nothing breaks, cracks, deforms, or creates craters. Each object maintains its exact material, color, and texture throughout. The coordinate axes and any initial velocity arrows must cleanly disappear after the first frame. Static camera, fixed background. Smooth, continuous motion.",
    "image": "firstframe/at_rest/3/rgb_0000.png",
    "duration": 4,
    "size": "1280x720"
  },
  {
    "case": "at_rest/7",
    "track": "perception_graphic",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\n\nGenerate a video where the background, ground, sky, and all annotations (coordinate axes, velocity arrows) gradually fade to pure white, while the subject physical objects remain still and unchanged. Static camera, no zoom, no rotation. The final frame should show only the objects with labeled physical properties on white — remove supporting structures (ramps, tracks, rails, platforms). Do not transform, resize, or replace any object. Each object must retain its exact position, size, shape, color, and texture.",
    "image": "firstframe/at_rest/7/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "at_rest/7",
    "track": "comprehension_text",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\n\nBelow are 4 candidate formulas. Exactly ONE is correct:\n  A) ΣF_ext = 0\n  B) τ_net = Σ(F_i·r_i·sinθ_i) · e^(-μ·t)\n  C) T = 2π·√(m/k)\n  D) G = m·g\n\nGenerate a video ending on a white background with THREE lines of large, clearly readable, centered text:\n  Line 1: the correct option letter (A/B/C/D).\n  Line 2: the correct formula exactly as written above.\n  Line 3: the formula with annotated values substituted in from the parameters above.\n\nWhen substituting: if multiple objects exist, pick one consistent set.",
    "image": "firstframe/at_rest/7/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "at_rest/7",
    "track": "comprehension_graphic",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\n\nPredict the physical state at t = 0.5 s. Generate a video where the original annotations (coordinate axes and any initial velocity arrows) gradually fade out and cleanly disappear, while the background, ground, sky, and all scene lighting remain completely unchanged throughout. Objects move smoothly to their correct positions at t = 0.5 s — each object must retain its exact texture, material, size, and shape. For each moving object, draw a borderless orange arrow starting from the object's center pointing in its velocity direction, with a label \"v = X.XX\" (speed value, no unit). If at rest, show \"v = 0\" with no arrow. Static camera, no zoom, no rotation.",
    "image": "firstframe/at_rest/7/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "at_rest/7",
    "track": "generation",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\n\nGenerate 4 seconds of physically accurate motion strictly following these parameters. Every object AND the ground surface are perfectly rigid — nothing breaks, cracks, deforms, or creates craters. Each object maintains its exact material, color, and texture throughout. The coordinate axes and any initial velocity arrows must cleanly disappear after the first frame. Static camera, fixed background. Smooth, continuous motion.",
    "image": "firstframe/at_rest/7/rgb_0000.png",
    "duration": 4,
    "size": "1280x720"
  },
  {
    "case": "at_rest/8",
    "track": "perception_graphic",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\n\nGenerate a video where the background, ground, sky, and all annotations (coordinate axes, velocity arrows) gradually fade to pure white, while the subject physical objects remain still and unchanged. Static camera, no zoom, no rotation. The final frame should show only the objects with labeled physical properties on white — remove supporting structures (ramps, tracks, rails, platforms). Do not transform, resize, or replace any object. Each object must retain its exact position, size, shape, color, and texture.",
    "image": "firstframe/at_rest/8/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "at_rest/8",
    "track": "comprehension_text",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\n\nBelow are 4 candidate formulas. Exactly ONE is correct:\n  A) W = ΔE_k = (1/2)·m·v_t² - (1/2)·m·v_0²\n  B) I = V / R\n  C) ΣF = m·Δv / (Δt·cosθ)\n  D) ΣM_ext = 0\n\nGenerate a video ending on a white background with THREE lines of large, clearly readable, centered text:\n  Line 1: the correct option letter (A/B/C/D).\n  Line 2: the correct formula exactly as written above.\n  Line 3: the formula with annotated values substituted in from the parameters above.\n\nWhen substituting: if multiple objects exist, pick one consistent set.",
    "image": "firstframe/at_rest/8/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "at_rest/8",
    "track": "comprehension_graphic",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\n\nPredict the physical state at t = 1.0 s. Generate a video where the original annotations (coordinate axes and any initial velocity arrows) gradually fade out and cleanly disappear, while the background, ground, sky, and all scene lighting remain completely unchanged throughout. Objects move smoothly to their correct positions at t = 1.0 s — each object must retain its exact texture, material, size, and shape. For each moving object, draw a borderless orange arrow starting from the object's center pointing in its velocity direction, with a label \"v = X.XX\" (speed value, no unit). If at rest, show \"v = 0\" with no arrow. Static camera, no zoom, no rotation.",
    "image": "firstframe/at_rest/8/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "at_rest/8",
    "track": "generation",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\n\nGenerate 4 seconds of physically accurate motion strictly following these parameters. Every object AND the ground surface are perfectly rigid — nothing breaks, cracks, deforms, or creates craters. Each object maintains its exact material, color, and texture throughout. The coordinate axes and any initial velocity arrows must cleanly disappear after the first frame. Static camera, fixed background. Smooth, continuous motion.",
    "image": "firstframe/at_rest/8/rgb_0000.png",
    "duration": 4,
    "size": "1280x720"
  },
  {
    "case": "circular/0",
    "track": "perception_graphic",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.7, mu_k=0.6\nTireSphere: d = 1.0, e = 0.6, theta_start = 0°, v_0 = 4.0\nTrack_0: R = 2.0, e = 0.3, theta_min = 0°, theta_max = 360°, mu_s = 0.0, mu_k = 0.0\n\nGenerate a video where the background, ground, sky, and all annotations (coordinate axes, velocity arrows) gradually fade to pure white, while the subject physical objects remain still and unchanged. Static camera, no zoom, no rotation. The final frame should show only the objects with labeled physical properties on white — remove supporting structures (ramps, tracks, rails, platforms). Do not transform, resize, or replace any object. Each object must retain its exact position, size, shape, color, and texture.",
    "image": "firstframe/circular/0/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "circular/0",
    "track": "comprehension_text",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.7, mu_k=0.6\nTireSphere: d = 1.0, e = 0.6, theta_start = 0°, v_0 = 4.0\nTrack_0: R = 2.0, e = 0.3, theta_min = 0°, theta_max = 360°, mu_s = 0.0, mu_k = 0.0\n\nBelow are 4 candidate formulas. Exactly ONE is correct:\n  A) a_c = v²·cosθ / (R·sinθ)\n  B) PV = nRT\n  C) F = (3/4)·E*·√(R·d³)\n  D) (1/2)·m·v_0² + m·g·R·(1-cosθ_start) = (1/2)·m·v² + m·g·R·(1-cosθ)\n\nGenerate a video ending on a white background with THREE lines of large, clearly readable, centered text:\n  Line 1: the correct option letter (A/B/C/D).\n  Line 2: the correct formula exactly as written above.\n  Line 3: the formula with annotated values substituted in from the parameters above.\n\nWhen substituting: if multiple objects exist, pick one consistent set.",
    "image": "firstframe/circular/0/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "circular/0",
    "track": "comprehension_graphic",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.7, mu_k=0.6\nTireSphere: d = 1.0, e = 0.6, theta_start = 0°, v_0 = 4.0\nTrack_0: R = 2.0, e = 0.3, theta_min = 0°, theta_max = 360°, mu_s = 0.0, mu_k = 0.0\n\nPredict the physical state at t = 2.0 s. Generate a video where the original annotations (coordinate axes and any initial velocity arrows) gradually fade out and cleanly disappear, while the background, ground, sky, and all scene lighting remain completely unchanged throughout. Objects move smoothly to their correct positions at t = 2.0 s — each object must retain its exact texture, material, size, and shape. For each moving object, draw a borderless orange arrow starting from the object's center pointing in its velocity direction, with a label \"v = X.XX\" (speed value, no unit). If at rest, show \"v = 0\" with no arrow. Static camera, no zoom, no rotation.",
    "image": "firstframe/circular/0/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "circular/0",
    "track": "generation",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.7, mu_k=0.6\nTireSphere: d = 1.0, e = 0.6, theta_start = 0°, v_0 = 4.0\nTrack_0: R = 2.0, e = 0.3, theta_min = 0°, theta_max = 360°, mu_s = 0.0, mu_k = 0.0\n\nGenerate 4 seconds of physically accurate motion strictly following these parameters. Every object AND the ground surface are perfectly rigid — nothing breaks, cracks, deforms, or creates craters. Each object maintains its exact material, color, and texture throughout. The coordinate axes and any initial velocity arrows must cleanly disappear after the first frame. Static camera, fixed background. Smooth, continuous motion.",
    "image": "firstframe/circular/0/rgb_0000.png",
    "duration": 4,
    "size": "1280x720"
  },
  {
    "case": "circular/2",
    "track": "perception_graphic",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.7, mu_k=0.6\nTireSphere: d = 1.0, e = 0.6, theta_start = 0°, v_0 = 14.0\nTrack_0: R = 2.5, e = 0.3, theta_min = 0°, theta_max = 360°, mu_s = 0.0, mu_k = 0.0\n\nGenerate a video where the background, ground, sky, and all annotations (coordinate axes, velocity arrows) gradually fade to pure white, while the subject physical objects remain still and unchanged. Static camera, no zoom, no rotation. The final frame should show only the objects with labeled physical properties on white — remove supporting structures (ramps, tracks, rails, platforms). Do not transform, resize, or replace any object. Each object must retain its exact position, size, shape, color, and texture.",
    "image": "firstframe/circular/2/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "circular/2",
    "track": "comprehension_text",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.7, mu_k=0.6\nTireSphere: d = 1.0, e = 0.6, theta_start = 0°, v_0 = 14.0\nTrack_0: R = 2.5, e = 0.3, theta_min = 0°, theta_max = 360°, mu_s = 0.0, mu_k = 0.0\n\nBelow are 4 candidate formulas. Exactly ONE is correct:\n  A) C = Q / V\n  B) (1/2)·m·v_0² + m·g·R·(1-cosθ_start) = (1/2)·m·v² + m·g·R·(1-cosθ)\n  C) e = (v_2f - v_1f) / (v_1i - v_2i)\n  D) F_N = m·g·(cosθ - 2) + m·v²/R\n\nGenerate a video ending on a white background with THREE lines of large, clearly readable, centered text:\n  Line 1: the correct option letter (A/B/C/D).\n  Line 2: the correct formula exactly as written above.\n  Line 3: the formula with annotated values substituted in from the parameters above.\n\nWhen substituting: if multiple objects exist, pick one consistent set.",
    "image": "firstframe/circular/2/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "circular/2",
    "track": "comprehension_graphic",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.7, mu_k=0.6\nTireSphere: d = 1.0, e = 0.6, theta_start = 0°, v_0 = 14.0\nTrack_0: R = 2.5, e = 0.3, theta_min = 0°, theta_max = 360°, mu_s = 0.0, mu_k = 0.0\n\nPredict the physical state at t = 1.5 s. Generate a video where the original annotations (coordinate axes and any initial velocity arrows) gradually fade out and cleanly disappear, while the background, ground, sky, and all scene lighting remain completely unchanged throughout. Objects move smoothly to their correct positions at t = 1.5 s — each object must retain its exact texture, material, size, and shape. For each moving object, draw a borderless orange arrow starting from the object's center pointing in its velocity direction, with a label \"v = X.XX\" (speed value, no unit). If at rest, show \"v = 0\" with no arrow. Static camera, no zoom, no rotation.",
    "image": "firstframe/circular/2/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "circular/2",
    "track": "generation",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.7, mu_k=0.6\nTireSphere: d = 1.0, e = 0.6, theta_start = 0°, v_0 = 14.0\nTrack_0: R = 2.5, e = 0.3, theta_min = 0°, theta_max = 360°, mu_s = 0.0, mu_k = 0.0\n\nGenerate 4 seconds of physically accurate motion strictly following these parameters. Every object AND the ground surface are perfectly rigid — nothing breaks, cracks, deforms, or creates craters. Each object maintains its exact material, color, and texture throughout. The coordinate axes and any initial velocity arrows must cleanly disappear after the first frame. Static camera, fixed background. Smooth, continuous motion.",
    "image": "firstframe/circular/2/rgb_0000.png",
    "duration": 4,
    "size": "1280x720"
  },
  {
    "case": "circular/6",
    "track": "perception_graphic",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.0, mu_k=0.0\nTireSphere: d = 1.0, e = 0.6, theta_start = 270°, v_0 = 0.0\nStyrofoamSphere: d = 1.0, e = 0.15, theta_start = 270°, v_0 = 0.0\nTrack_0: R = 2.0, e = 0.3, theta_min = 270°, theta_max = 360°, mu_s = 0.0, mu_k = 0.0\n\nGenerate a video where the background, ground, sky, and all annotations (coordinate axes, velocity arrows) gradually fade to pure white, while the subject physical objects remain still and unchanged. Static camera, no zoom, no rotation. The final frame should show only the objects with labeled physical properties on white — remove supporting structures (ramps, tracks, rails, platforms). Do not transform, resize, or replace any object. Each object must retain its exact position, size, shape, color, and texture.",
    "image": "firstframe/circular/6/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "circular/6",
    "track": "comprehension_text",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.0, mu_k=0.0\nTireSphere: d = 1.0, e = 0.6, theta_start = 270°, v_0 = 0.0\nStyrofoamSphere: d = 1.0, e = 0.15, theta_start = 270°, v_0 = 0.0\nTrack_0: R = 2.0, e = 0.3, theta_min = 270°, theta_max = 360°, mu_s = 0.0, mu_k = 0.0\n\nBelow are 4 candidate formulas. Exactly ONE is correct:\n  A) PV = nRT\n  B) e = (v_2f - v_1f) / (v_1i - v_2i)\n  C) F_N = m·g·(cosθ - 2) + m·v²/R\n  D) F_N - m·g·cosθ = m·v²/R\n\nGenerate a video ending on a white background with THREE lines of large, clearly readable, centered text:\n  Line 1: the correct option letter (A/B/C/D).\n  Line 2: the correct formula exactly as written above.\n  Line 3: the formula with annotated values substituted in from the parameters above.\n\nWhen substituting: if multiple objects exist, pick one consistent set.",
    "image": "firstframe/circular/6/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "circular/6",
    "track": "comprehension_graphic",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.0, mu_k=0.0\nTireSphere: d = 1.0, e = 0.6, theta_start = 270°, v_0 = 0.0\nStyrofoamSphere: d = 1.0, e = 0.15, theta_start = 270°, v_0 = 0.0\nTrack_0: R = 2.0, e = 0.3, theta_min = 270°, theta_max = 360°, mu_s = 0.0, mu_k = 0.0\n\nPredict the physical state at t = 1.0 s. Generate a video where the original annotations (coordinate axes and any initial velocity arrows) gradually fade out and cleanly disappear, while the background, ground, sky, and all scene lighting remain completely unchanged throughout. Objects move smoothly to their correct positions at t = 1.0 s — each object must retain its exact texture, material, size, and shape. For each moving object, draw a borderless orange arrow starting from the object's center pointing in its velocity direction, with a label \"v = X.XX\" (speed value, no unit). If at rest, show \"v = 0\" with no arrow. Static camera, no zoom, no rotation.",
    "image": "firstframe/circular/6/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "circular/6",
    "track": "generation",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.0, mu_k=0.0\nTireSphere: d = 1.0, e = 0.6, theta_start = 270°, v_0 = 0.0\nStyrofoamSphere: d = 1.0, e = 0.15, theta_start = 270°, v_0 = 0.0\nTrack_0: R = 2.0, e = 0.3, theta_min = 270°, theta_max = 360°, mu_s = 0.0, mu_k = 0.0\n\nGenerate 4 seconds of physically accurate motion strictly following these parameters. Every object AND the ground surface are perfectly rigid — nothing breaks, cracks, deforms, or creates craters. Each object maintains its exact material, color, and texture throughout. The coordinate axes and any initial velocity arrows must cleanly disappear after the first frame. Static camera, fixed background. Smooth, continuous motion.",
    "image": "firstframe/circular/6/rgb_0000.png",
    "duration": 4,
    "size": "1280x720"
  },
  {
    "case": "circular/7",
    "track": "perception_graphic",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.0, mu_k=0.0\nTireSphere: d = 1.0, e = 0.6, theta_start = 270°, v_0 = 2.0\nStyrofoamSphere: d = 1.0, e = 0.15, theta_start = 270°, v_0 = 5.0\nTrack_0: R = 2.0, e = 0.3, theta_min = 270°, theta_max = 360°, mu_s = 0.0, mu_k = 0.0\n\nGenerate a video where the background, ground, sky, and all annotations (coordinate axes, velocity arrows) gradually fade to pure white, while the subject physical objects remain still and unchanged. Static camera, no zoom, no rotation. The final frame should show only the objects with labeled physical properties on white — remove supporting structures (ramps, tracks, rails, platforms). Do not transform, resize, or replace any object. Each object must retain its exact position, size, shape, color, and texture.",
    "image": "firstframe/circular/7/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "circular/7",
    "track": "comprehension_text",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.0, mu_k=0.0\nTireSphere: d = 1.0, e = 0.6, theta_start = 270°, v_0 = 2.0\nStyrofoamSphere: d = 1.0, e = 0.15, theta_start = 270°, v_0 = 5.0\nTrack_0: R = 2.0, e = 0.3, theta_min = 270°, theta_max = 360°, mu_s = 0.0, mu_k = 0.0\n\nBelow are 4 candidate formulas. Exactly ONE is correct:\n  A) (1/2)·m·v_0² + m·g·R·(1-cosθ_start) = (1/2)·m·v² + m·g·R·(1-cosθ)\n  B) F = (3/4)·E*·√(R·d³)\n  C) F_N = m·g·(cosθ - 2) + m·v²/R\n  D) v = f·λ\n\nGenerate a video ending on a white background with THREE lines of large, clearly readable, centered text:\n  Line 1: the correct option letter (A/B/C/D).\n  Line 2: the correct formula exactly as written above.\n  Line 3: the formula with annotated values substituted in from the parameters above.\n\nWhen substituting: if multiple objects exist, pick one consistent set.",
    "image": "firstframe/circular/7/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "circular/7",
    "track": "comprehension_graphic",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.0, mu_k=0.0\nTireSphere: d = 1.0, e = 0.6, theta_start = 270°, v_0 = 2.0\nStyrofoamSphere: d = 1.0, e = 0.15, theta_start = 270°, v_0 = 5.0\nTrack_0: R = 2.0, e = 0.3, theta_min = 270°, theta_max = 360°, mu_s = 0.0, mu_k = 0.0\n\nPredict the physical state at t = 1.0 s. Generate a video where the original annotations (coordinate axes and any initial velocity arrows) gradually fade out and cleanly disappear, while the background, ground, sky, and all scene lighting remain completely unchanged throughout. Objects move smoothly to their correct positions at t = 1.0 s — each object must retain its exact texture, material, size, and shape. For each moving object, draw a borderless orange arrow starting from the object's center pointing in its velocity direction, with a label \"v = X.XX\" (speed value, no unit). If at rest, show \"v = 0\" with no arrow. Static camera, no zoom, no rotation.",
    "image": "firstframe/circular/7/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "circular/7",
    "track": "generation",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.0, mu_k=0.0\nTireSphere: d = 1.0, e = 0.6, theta_start = 270°, v_0 = 2.0\nStyrofoamSphere: d = 1.0, e = 0.15, theta_start = 270°, v_0 = 5.0\nTrack_0: R = 2.0, e = 0.3, theta_min = 270°, theta_max = 360°, mu_s = 0.0, mu_k = 0.0\n\nGenerate 4 seconds of physically accurate motion strictly following these parameters. Every object AND the ground surface are perfectly rigid — nothing breaks, cracks, deforms, or creates craters. Each object maintains its exact material, color, and texture throughout. The coordinate axes and any initial velocity arrows must cleanly disappear after the first frame. Static camera, fixed background. Smooth, continuous motion.",
    "image": "firstframe/circular/7/rgb_0000.png",
    "duration": 4,
    "size": "1280x720"
  },
  {
    "case": "circular_newbatch/14",
    "track": "perception_graphic",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.0, mu_k=0.0\nTireSphere: d = 1.0, e = 0.6, theta_start = 360°, v_0 = -4.0\nTrack_0: R = 2.5, e = 0.3, theta_min = 180°, theta_max = 360°, mu_s = 0.0, mu_k = 0.0\n\nGenerate a video where the background, ground, sky, and all annotations (coordinate axes, velocity arrows) gradually fade to pure white, while the subject physical objects remain still and unchanged. Static camera, no zoom, no rotation. The final frame should show only the objects with labeled physical properties on white — remove supporting structures (ramps, tracks, rails, platforms). Do not transform, resize, or replace any object. Each object must retain its exact position, size, shape, color, and texture.",
    "image": "firstframe/circular_newbatch/14/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "circular_newbatch/14",
    "track": "comprehension_text",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.0, mu_k=0.0\nTireSphere: d = 1.0, e = 0.6, theta_start = 360°, v_0 = -4.0\nTrack_0: R = 2.5, e = 0.3, theta_min = 180°, theta_max = 360°, mu_s = 0.0, mu_k = 0.0\n\nBelow are 4 candidate formulas. Exactly ONE is correct:\n  A) ΔS = Q_rev / T\n  B) F_N - m·g·cosθ = m·v²/R\n  C) f_s ≤ μ_s·F_N\n  D) a_c = v²·cosθ / (R·sinθ)\n\nGenerate a video ending on a white background with THREE lines of large, clearly readable, centered text:\n  Line 1: the correct option letter (A/B/C/D).\n  Line 2: the correct formula exactly as written above.\n  Line 3: the formula with annotated values substituted in from the parameters above.\n\nWhen substituting: if multiple objects exist, pick one consistent set.",
    "image": "firstframe/circular_newbatch/14/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "circular_newbatch/14",
    "track": "comprehension_graphic",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.0, mu_k=0.0\nTireSphere: d = 1.0, e = 0.6, theta_start = 360°, v_0 = -4.0\nTrack_0: R = 2.5, e = 0.3, theta_min = 180°, theta_max = 360°, mu_s = 0.0, mu_k = 0.0\n\nPredict the physical state at t = 0.5 s. Generate a video where the original annotations (coordinate axes and any initial velocity arrows) gradually fade out and cleanly disappear, while the background, ground, sky, and all scene lighting remain completely unchanged throughout. Objects move smoothly to their correct positions at t = 0.5 s — each object must retain its exact texture, material, size, and shape. For each moving object, draw a borderless orange arrow starting from the object's center pointing in its velocity direction, with a label \"v = X.XX\" (speed value, no unit). If at rest, show \"v = 0\" with no arrow. Static camera, no zoom, no rotation.",
    "image": "firstframe/circular_newbatch/14/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "circular_newbatch/14",
    "track": "generation",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.0, mu_k=0.0\nTireSphere: d = 1.0, e = 0.6, theta_start = 360°, v_0 = -4.0\nTrack_0: R = 2.5, e = 0.3, theta_min = 180°, theta_max = 360°, mu_s = 0.0, mu_k = 0.0\n\nGenerate 4 seconds of physically accurate motion strictly following these parameters. Every object AND the ground surface are perfectly rigid — nothing breaks, cracks, deforms, or creates craters. Each object maintains its exact material, color, and texture throughout. The coordinate axes and any initial velocity arrows must cleanly disappear after the first frame. Static camera, fixed background. Smooth, continuous motion.",
    "image": "firstframe/circular_newbatch/14/rgb_0000.png",
    "duration": 4,
    "size": "1280x720"
  },
  {
    "case": "circular_newbatch/5",
    "track": "perception_graphic",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.0, mu_k=0.0\nTireSphere: d = 1.0, e = 0.6, theta_start = 0°, v_0 = 10.0\nTrack_0: R = 2.0, e = 0.3, theta_min = 0°, theta_max = 360°, mu_s = 0.0, mu_k = 0.0\n\nGenerate a video where the background, ground, sky, and all annotations (coordinate axes, velocity arrows) gradually fade to pure white, while the subject physical objects remain still and unchanged. Static camera, no zoom, no rotation. The final frame should show only the objects with labeled physical properties on white — remove supporting structures (ramps, tracks, rails, platforms). Do not transform, resize, or replace any object. Each object must retain its exact position, size, shape, color, and texture.",
    "image": "firstframe/circular_newbatch/5/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "circular_newbatch/5",
    "track": "comprehension_text",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.0, mu_k=0.0\nTireSphere: d = 1.0, e = 0.6, theta_start = 0°, v_0 = 10.0\nTrack_0: R = 2.0, e = 0.3, theta_min = 0°, theta_max = 360°, mu_s = 0.0, mu_k = 0.0\n\nBelow are 4 candidate formulas. Exactly ONE is correct:\n  A) ω = √(g·cosθ / R) · (1 + sinθ)\n  B) e = (v_2f - v_1f) / (v_1i - v_2i)\n  C) Q = m·c·ΔT\n  D) F_N - m·g·cosθ = m·v²/R\n\nGenerate a video ending on a white background with THREE lines of large, clearly readable, centered text:\n  Line 1: the correct option letter (A/B/C/D).\n  Line 2: the correct formula exactly as written above.\n  Line 3: the formula with annotated values substituted in from the parameters above.\n\nWhen substituting: if multiple objects exist, pick one consistent set.",
    "image": "firstframe/circular_newbatch/5/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "circular_newbatch/5",
    "track": "comprehension_graphic",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.0, mu_k=0.0\nTireSphere: d = 1.0, e = 0.6, theta_start = 0°, v_0 = 10.0\nTrack_0: R = 2.0, e = 0.3, theta_min = 0°, theta_max = 360°, mu_s = 0.0, mu_k = 0.0\n\nPredict the physical state at t = 0.25 s. Generate a video where the original annotations (coordinate axes and any initial velocity arrows) gradually fade out and cleanly disappear, while the background, ground, sky, and all scene lighting remain completely unchanged throughout. Objects move smoothly to their correct positions at t = 0.25 s — each object must retain its exact texture, material, size, and shape. For each moving object, draw a borderless orange arrow starting from the object's center pointing in its velocity direction, with a label \"v = X.XX\" (speed value, no unit). If at rest, show \"v = 0\" with no arrow. Static camera, no zoom, no rotation.",
    "image": "firstframe/circular_newbatch/5/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "circular_newbatch/5",
    "track": "generation",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.0, mu_k=0.0\nTireSphere: d = 1.0, e = 0.6, theta_start = 0°, v_0 = 10.0\nTrack_0: R = 2.0, e = 0.3, theta_min = 0°, theta_max = 360°, mu_s = 0.0, mu_k = 0.0\n\nGenerate 4 seconds of physically accurate motion strictly following these parameters. Every object AND the ground surface are perfectly rigid — nothing breaks, cracks, deforms, or creates craters. Each object maintains its exact material, color, and texture throughout. The coordinate axes and any initial velocity arrows must cleanly disappear after the first frame. Static camera, fixed background. Smooth, continuous motion.",
    "image": "firstframe/circular_newbatch/5/rgb_0000.png",
    "duration": 4,
    "size": "1280x720"
  },
  {
    "case": "freefall/0",
    "track": "perception_graphic",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: e = 0.4\nClaySphere: d = 1.0, e = 0.2, h = 6.0, v_0 = 0.0\n\nGenerate a video where the background, ground, sky, and all annotations (coordinate axes, velocity arrows) gradually fade to pure white, while the subject physical objects remain still and unchanged. Static camera, no zoom, no rotation. The final frame should show only the objects with labeled physical properties on white — remove supporting structures (ramps, tracks, rails, platforms). Do not transform, resize, or replace any object. Each object must retain its exact position, size, shape, color, and texture.",
    "image": "firstframe/freefall/0/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "freefall/0",
    "track": "comprehension_text",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: e = 0.4\nClaySphere: d = 1.0, e = 0.2, h = 6.0, v_0 = 0.0\n\nBelow are 4 candidate formulas. Exactly ONE is correct:\n  A) n_1·sinθ_1 = n_2·sinθ_2\n  B) y(t) = h + v_0·t + (1/2)·g·t²\n  C) F_fall = m·g·(1 + v/c) / √(1 - v²/c²)\n  D) P + (1/2)·ρ·v² + ρ·g·h = constant\n\nGenerate a video ending on a white background with THREE lines of large, clearly readable, centered text:\n  Line 1: the correct option letter (A/B/C/D).\n  Line 2: the correct formula exactly as written above.\n  Line 3: the formula with annotated values substituted in from the parameters above.\n\nWhen substituting: if multiple objects exist, pick one consistent set.",
    "image": "firstframe/freefall/0/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "freefall/0",
    "track": "comprehension_graphic",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: e = 0.4\nClaySphere: d = 1.0, e = 0.2, h = 6.0, v_0 = 0.0\n\nPredict the physical state at t = 0.5 s. Generate a video where the original annotations (coordinate axes and any initial velocity arrows) gradually fade out and cleanly disappear, while the background, ground, sky, and all scene lighting remain completely unchanged throughout. Objects move smoothly to their correct positions at t = 0.5 s — each object must retain its exact texture, material, size, and shape. For each moving object, draw a borderless orange arrow starting from the object's center pointing in its velocity direction, with a label \"v = X.XX\" (speed value, no unit). If at rest, show \"v = 0\" with no arrow. Static camera, no zoom, no rotation.",
    "image": "firstframe/freefall/0/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "freefall/0",
    "track": "generation",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: e = 0.4\nClaySphere: d = 1.0, e = 0.2, h = 6.0, v_0 = 0.0\n\nGenerate 4 seconds of physically accurate motion strictly following these parameters. Every object AND the ground surface are perfectly rigid — nothing breaks, cracks, deforms, or creates craters. Each object maintains its exact material, color, and texture throughout. The coordinate axes and any initial velocity arrows must cleanly disappear after the first frame. Static camera, fixed background. Smooth, continuous motion.",
    "image": "firstframe/freefall/0/rgb_0000.png",
    "duration": 4,
    "size": "1280x720"
  },
  {
    "case": "freefall/4",
    "track": "perception_graphic",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.8, F_drag=0.0\nGround: e = 0.4\nBronzeAntiqueSphere: d = 2.0, e = 0.45, h = 15.0, v_0 = 0.0\nAgingCopperSphere: d = 2.0, e = 0.5, h = 15.0, v_0 = 0.0\n\nGenerate a video where the background, ground, sky, and all annotations (coordinate axes, velocity arrows) gradually fade to pure white, while the subject physical objects remain still and unchanged. Static camera, no zoom, no rotation. The final frame should show only the objects with labeled physical properties on white — remove supporting structures (ramps, tracks, rails, platforms). Do not transform, resize, or replace any object. Each object must retain its exact position, size, shape, color, and texture.",
    "image": "firstframe/freefall/4/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "freefall/4",
    "track": "comprehension_text",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.8, F_drag=0.0\nGround: e = 0.4\nBronzeAntiqueSphere: d = 2.0, e = 0.45, h = 15.0, v_0 = 0.0\nAgingCopperSphere: d = 2.0, e = 0.5, h = 15.0, v_0 = 0.0\n\nBelow are 4 candidate formulas. Exactly ONE is correct:\n  A) Q = m·c·ΔT\n  B) I = (1/10)·m·d²\n  C) F_fall = m·g·(1 + v/c) / √(1 - v²/c²)\n  D) y(t) = h + v_0·t + (1/2)·g·t²\n\nGenerate a video ending on a white background with THREE lines of large, clearly readable, centered text:\n  Line 1: the correct option letter (A/B/C/D).\n  Line 2: the correct formula exactly as written above.\n  Line 3: the formula with annotated values substituted in from the parameters above.\n\nWhen substituting: if multiple objects exist, pick one consistent set.",
    "image": "firstframe/freefall/4/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "freefall/4",
    "track": "comprehension_graphic",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.8, F_drag=0.0\nGround: e = 0.4\nBronzeAntiqueSphere: d = 2.0, e = 0.45, h = 15.0, v_0 = 0.0\nAgingCopperSphere: d = 2.0, e = 0.5, h = 15.0, v_0 = 0.0\n\nPredict the physical state at t = 1.25 s. Generate a video where the original annotations (coordinate axes and any initial velocity arrows) gradually fade out and cleanly disappear, while the background, ground, sky, and all scene lighting remain completely unchanged throughout. Objects move smoothly to their correct positions at t = 1.25 s — each object must retain its exact texture, material, size, and shape. For each moving object, draw a borderless orange arrow starting from the object's center pointing in its velocity direction, with a label \"v = X.XX\" (speed value, no unit). If at rest, show \"v = 0\" with no arrow. Static camera, no zoom, no rotation.",
    "image": "firstframe/freefall/4/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "freefall/4",
    "track": "generation",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.8, F_drag=0.0\nGround: e = 0.4\nBronzeAntiqueSphere: d = 2.0, e = 0.45, h = 15.0, v_0 = 0.0\nAgingCopperSphere: d = 2.0, e = 0.5, h = 15.0, v_0 = 0.0\n\nGenerate 4 seconds of physically accurate motion strictly following these parameters. Every object AND the ground surface are perfectly rigid — nothing breaks, cracks, deforms, or creates craters. Each object maintains its exact material, color, and texture throughout. The coordinate axes and any initial velocity arrows must cleanly disappear after the first frame. Static camera, fixed background. Smooth, continuous motion.",
    "image": "firstframe/freefall/4/rgb_0000.png",
    "duration": 4,
    "size": "1280x720"
  },
  {
    "case": "freefall/5",
    "track": "perception_graphic",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.8, F_drag=0.0\nGround: e = 0.4\nBronzeAntiqueSphere: d = 2.0, e = 0.45, h = 15.0, v_0 = -0.5\nAgingCopperSphere: d = 2.0, e = 0.5, h = 15.0, v_0 = 0.0\n\nGenerate a video where the background, ground, sky, and all annotations (coordinate axes, velocity arrows) gradually fade to pure white, while the subject physical objects remain still and unchanged. Static camera, no zoom, no rotation. The final frame should show only the objects with labeled physical properties on white — remove supporting structures (ramps, tracks, rails, platforms). Do not transform, resize, or replace any object. Each object must retain its exact position, size, shape, color, and texture.",
    "image": "firstframe/freefall/5/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "freefall/5",
    "track": "comprehension_text",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.8, F_drag=0.0\nGround: e = 0.4\nBronzeAntiqueSphere: d = 2.0, e = 0.45, h = 15.0, v_0 = -0.5\nAgingCopperSphere: d = 2.0, e = 0.5, h = 15.0, v_0 = 0.0\n\nBelow are 4 candidate formulas. Exactly ONE is correct:\n  A) v = v_0·cos(g·t / v_0)\n  B) ΔS = Q_rev / T\n  C) I = (1/10)·m·d²\n  D) y(t) = h + v_0·t + (1/2)·g·t²\n\nGenerate a video ending on a white background with THREE lines of large, clearly readable, centered text:\n  Line 1: the correct option letter (A/B/C/D).\n  Line 2: the correct formula exactly as written above.\n  Line 3: the formula with annotated values substituted in from the parameters above.\n\nWhen substituting: if multiple objects exist, pick one consistent set.",
    "image": "firstframe/freefall/5/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "freefall/5",
    "track": "comprehension_graphic",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.8, F_drag=0.0\nGround: e = 0.4\nBronzeAntiqueSphere: d = 2.0, e = 0.45, h = 15.0, v_0 = -0.5\nAgingCopperSphere: d = 2.0, e = 0.5, h = 15.0, v_0 = 0.0\n\nPredict the physical state at t = 1.25 s. Generate a video where the original annotations (coordinate axes and any initial velocity arrows) gradually fade out and cleanly disappear, while the background, ground, sky, and all scene lighting remain completely unchanged throughout. Objects move smoothly to their correct positions at t = 1.25 s — each object must retain its exact texture, material, size, and shape. For each moving object, draw a borderless orange arrow starting from the object's center pointing in its velocity direction, with a label \"v = X.XX\" (speed value, no unit). If at rest, show \"v = 0\" with no arrow. Static camera, no zoom, no rotation.",
    "image": "firstframe/freefall/5/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "freefall/5",
    "track": "generation",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.8, F_drag=0.0\nGround: e = 0.4\nBronzeAntiqueSphere: d = 2.0, e = 0.45, h = 15.0, v_0 = -0.5\nAgingCopperSphere: d = 2.0, e = 0.5, h = 15.0, v_0 = 0.0\n\nGenerate 4 seconds of physically accurate motion strictly following these parameters. Every object AND the ground surface are perfectly rigid — nothing breaks, cracks, deforms, or creates craters. Each object maintains its exact material, color, and texture throughout. The coordinate axes and any initial velocity arrows must cleanly disappear after the first frame. Static camera, fixed background. Smooth, continuous motion.",
    "image": "firstframe/freefall/5/rgb_0000.png",
    "duration": 4,
    "size": "1280x720"
  },
  {
    "case": "freefall/6",
    "track": "perception_graphic",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.8, F_drag=0.0\nGround: e = 0.4\nBronzeAntiqueSphere: d = 2.0, e = 0.45, h = 13.0, v_0 = 0.0\nAgingCopperSphere: d = 2.0, e = 0.5, h = 16.0, v_0 = 0.0\n\nGenerate a video where the background, ground, sky, and all annotations (coordinate axes, velocity arrows) gradually fade to pure white, while the subject physical objects remain still and unchanged. Static camera, no zoom, no rotation. The final frame should show only the objects with labeled physical properties on white — remove supporting structures (ramps, tracks, rails, platforms). Do not transform, resize, or replace any object. Each object must retain its exact position, size, shape, color, and texture.",
    "image": "firstframe/freefall/6/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "freefall/6",
    "track": "comprehension_text",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.8, F_drag=0.0\nGround: e = 0.4\nBronzeAntiqueSphere: d = 2.0, e = 0.45, h = 13.0, v_0 = 0.0\nAgingCopperSphere: d = 2.0, e = 0.5, h = 16.0, v_0 = 0.0\n\nBelow are 4 candidate formulas. Exactly ONE is correct:\n  A) v_final = -e·v_impact\n  B) F_fall = m·g·(1 + v/c) / √(1 - v²/c²)\n  C) y(t) = h + v_0·t + (1/2)·g·t²\n  D) n_1·sinθ_1 = n_2·sinθ_2\n\nGenerate a video ending on a white background with THREE lines of large, clearly readable, centered text:\n  Line 1: the correct option letter (A/B/C/D).\n  Line 2: the correct formula exactly as written above.\n  Line 3: the formula with annotated values substituted in from the parameters above.\n\nWhen substituting: if multiple objects exist, pick one consistent set.",
    "image": "firstframe/freefall/6/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "freefall/6",
    "track": "comprehension_graphic",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.8, F_drag=0.0\nGround: e = 0.4\nBronzeAntiqueSphere: d = 2.0, e = 0.45, h = 13.0, v_0 = 0.0\nAgingCopperSphere: d = 2.0, e = 0.5, h = 16.0, v_0 = 0.0\n\nPredict the physical state at t = 1.5 s. Generate a video where the original annotations (coordinate axes and any initial velocity arrows) gradually fade out and cleanly disappear, while the background, ground, sky, and all scene lighting remain completely unchanged throughout. Objects move smoothly to their correct positions at t = 1.5 s — each object must retain its exact texture, material, size, and shape. For each moving object, draw a borderless orange arrow starting from the object's center pointing in its velocity direction, with a label \"v = X.XX\" (speed value, no unit). If at rest, show \"v = 0\" with no arrow. Static camera, no zoom, no rotation.",
    "image": "firstframe/freefall/6/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "freefall/6",
    "track": "generation",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.8, F_drag=0.0\nGround: e = 0.4\nBronzeAntiqueSphere: d = 2.0, e = 0.45, h = 13.0, v_0 = 0.0\nAgingCopperSphere: d = 2.0, e = 0.5, h = 16.0, v_0 = 0.0\n\nGenerate 4 seconds of physically accurate motion strictly following these parameters. Every object AND the ground surface are perfectly rigid — nothing breaks, cracks, deforms, or creates craters. Each object maintains its exact material, color, and texture throughout. The coordinate axes and any initial velocity arrows must cleanly disappear after the first frame. Static camera, fixed background. Smooth, continuous motion.",
    "image": "firstframe/freefall/6/rgb_0000.png",
    "duration": 4,
    "size": "1280x720"
  },
  {
    "case": "freefall/8",
    "track": "perception_graphic",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-3.8, F_drag=0.0\nGround: e = 0.25\nBronzeAntiqueSphere: d = 2.0, e = 0.45, h = 15.0, v_0 = 0.0\n\nGenerate a video where the background, ground, sky, and all annotations (coordinate axes, velocity arrows) gradually fade to pure white, while the subject physical objects remain still and unchanged. Static camera, no zoom, no rotation. The final frame should show only the objects with labeled physical properties on white — remove supporting structures (ramps, tracks, rails, platforms). Do not transform, resize, or replace any object. Each object must retain its exact position, size, shape, color, and texture.",
    "image": "firstframe/freefall/8/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "freefall/8",
    "track": "comprehension_text",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-3.8, F_drag=0.0\nGround: e = 0.25\nBronzeAntiqueSphere: d = 2.0, e = 0.45, h = 15.0, v_0 = 0.0\n\nBelow are 4 candidate formulas. Exactly ONE is correct:\n  A) F_fall = m·g·(1 + v/c) / √(1 - v²/c²)\n  B) v = v_0 + g·t\n  C) Q = m·c·ΔT\n  D) P + (1/2)·ρ·v² + ρ·g·h = constant\n\nGenerate a video ending on a white background with THREE lines of large, clearly readable, centered text:\n  Line 1: the correct option letter (A/B/C/D).\n  Line 2: the correct formula exactly as written above.\n  Line 3: the formula with annotated values substituted in from the parameters above.\n\nWhen substituting: if multiple objects exist, pick one consistent set.",
    "image": "firstframe/freefall/8/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "freefall/8",
    "track": "comprehension_graphic",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-3.8, F_drag=0.0\nGround: e = 0.25\nBronzeAntiqueSphere: d = 2.0, e = 0.45, h = 15.0, v_0 = 0.0\n\nPredict the physical state at t = 2.5 s. Generate a video where the original annotations (coordinate axes and any initial velocity arrows) gradually fade out and cleanly disappear, while the background, ground, sky, and all scene lighting remain completely unchanged throughout. Objects move smoothly to their correct positions at t = 2.5 s — each object must retain its exact texture, material, size, and shape. For each moving object, draw a borderless orange arrow starting from the object's center pointing in its velocity direction, with a label \"v = X.XX\" (speed value, no unit). If at rest, show \"v = 0\" with no arrow. Static camera, no zoom, no rotation.",
    "image": "firstframe/freefall/8/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "freefall/8",
    "track": "generation",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-3.8, F_drag=0.0\nGround: e = 0.25\nBronzeAntiqueSphere: d = 2.0, e = 0.45, h = 15.0, v_0 = 0.0\n\nGenerate 4 seconds of physically accurate motion strictly following these parameters. Every object AND the ground surface are perfectly rigid — nothing breaks, cracks, deforms, or creates craters. Each object maintains its exact material, color, and texture throughout. The coordinate axes and any initial velocity arrows must cleanly disappear after the first frame. Static camera, fixed background. Smooth, continuous motion.",
    "image": "firstframe/freefall/8/rgb_0000.png",
    "duration": 4,
    "size": "1280x720"
  },
  {
    "case": "freefall_newbatch/4",
    "track": "perception_graphic",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: e = 0.4\nOakCube: a = 2.0, e = 0.5, h = 15.0, v_0 = 0.0\n\nGenerate a video where the background, ground, sky, and all annotations (coordinate axes, velocity arrows) gradually fade to pure white, while the subject physical objects remain still and unchanged. Static camera, no zoom, no rotation. The final frame should show only the objects with labeled physical properties on white — remove supporting structures (ramps, tracks, rails, platforms). Do not transform, resize, or replace any object. Each object must retain its exact position, size, shape, color, and texture.",
    "image": "firstframe/freefall_newbatch/4/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "freefall_newbatch/4",
    "track": "comprehension_text",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: e = 0.4\nOakCube: a = 2.0, e = 0.5, h = 15.0, v_0 = 0.0\n\nBelow are 4 candidate formulas. Exactly ONE is correct:\n  A) y(t) = h·(1 - e^(-g·t²/2))\n  B) v = f·λ\n  C) v_final = -e·v_impact\n  D) y(t) = h + v_0·t + (1/2)·g·t²\n\nGenerate a video ending on a white background with THREE lines of large, clearly readable, centered text:\n  Line 1: the correct option letter (A/B/C/D).\n  Line 2: the correct formula exactly as written above.\n  Line 3: the formula with annotated values substituted in from the parameters above.\n\nWhen substituting: if multiple objects exist, pick one consistent set.",
    "image": "firstframe/freefall_newbatch/4/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "freefall_newbatch/4",
    "track": "comprehension_graphic",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: e = 0.4\nOakCube: a = 2.0, e = 0.5, h = 15.0, v_0 = 0.0\n\nPredict the physical state at t = 1.25 s. Generate a video where the original annotations (coordinate axes and any initial velocity arrows) gradually fade out and cleanly disappear, while the background, ground, sky, and all scene lighting remain completely unchanged throughout. Objects move smoothly to their correct positions at t = 1.25 s — each object must retain its exact texture, material, size, and shape. For each moving object, draw a borderless orange arrow starting from the object's center pointing in its velocity direction, with a label \"v = X.XX\" (speed value, no unit). If at rest, show \"v = 0\" with no arrow. Static camera, no zoom, no rotation.",
    "image": "firstframe/freefall_newbatch/4/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "freefall_newbatch/4",
    "track": "generation",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: e = 0.4\nOakCube: a = 2.0, e = 0.5, h = 15.0, v_0 = 0.0\n\nGenerate 4 seconds of physically accurate motion strictly following these parameters. Every object AND the ground surface are perfectly rigid — nothing breaks, cracks, deforms, or creates craters. Each object maintains its exact material, color, and texture throughout. The coordinate axes and any initial velocity arrows must cleanly disappear after the first frame. Static camera, fixed background. Smooth, continuous motion.",
    "image": "firstframe/freefall_newbatch/4/rgb_0000.png",
    "duration": 4,
    "size": "1280x720"
  },
  {
    "case": "inclined_plane/1",
    "track": "perception_graphic",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.7, mu_k=0.6\nWoodBeechCube: a = 1.0, h = 4.83, v_0 = 0.0\nRamp_0: theta = 60°, H = 5.0, mu_s = 0.0, mu_k = 0.0\n\nGenerate a video where the background, ground, sky, and all annotations (coordinate axes, velocity arrows) gradually fade to pure white, while the subject physical objects remain still and unchanged. Static camera, no zoom, no rotation. The final frame should show only the objects with labeled physical properties on white — remove supporting structures (ramps, tracks, rails, platforms). Do not transform, resize, or replace any object. Each object must retain its exact position, size, shape, color, and texture.",
    "image": "firstframe/inclined_plane/1/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "inclined_plane/1",
    "track": "comprehension_text",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.7, mu_k=0.6\nWoodBeechCube: a = 1.0, h = 4.83, v_0 = 0.0\nRamp_0: theta = 60°, H = 5.0, mu_s = 0.0, mu_k = 0.0\n\nBelow are 4 candidate formulas. Exactly ONE is correct:\n  A) v² = v_0² + 2·a_slope·s\n  B) ΔS = Q_rev / T\n  C) E_p = m·g·(H - h)\n  D) s = v_0·t·cosθ + (1/2)·g·sinθ·t²\n\nGenerate a video ending on a white background with THREE lines of large, clearly readable, centered text:\n  Line 1: the correct option letter (A/B/C/D).\n  Line 2: the correct formula exactly as written above.\n  Line 3: the formula with annotated values substituted in from the parameters above.\n\nWhen substituting: if multiple objects exist, pick one consistent set.",
    "image": "firstframe/inclined_plane/1/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "inclined_plane/1",
    "track": "comprehension_graphic",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.7, mu_k=0.6\nWoodBeechCube: a = 1.0, h = 4.83, v_0 = 0.0\nRamp_0: theta = 60°, H = 5.0, mu_s = 0.0, mu_k = 0.0\n\nPredict the physical state at t = 0.5 s. Generate a video where the original annotations (coordinate axes and any initial velocity arrows) gradually fade out and cleanly disappear, while the background, ground, sky, and all scene lighting remain completely unchanged throughout. Objects move smoothly to their correct positions at t = 0.5 s — each object must retain its exact texture, material, size, and shape. For each moving object, draw a borderless orange arrow starting from the object's center pointing in its velocity direction, with a label \"v = X.XX\" (speed value, no unit). If at rest, show \"v = 0\" with no arrow. Static camera, no zoom, no rotation.",
    "image": "firstframe/inclined_plane/1/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "inclined_plane/1",
    "track": "generation",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.7, mu_k=0.6\nWoodBeechCube: a = 1.0, h = 4.83, v_0 = 0.0\nRamp_0: theta = 60°, H = 5.0, mu_s = 0.0, mu_k = 0.0\n\nGenerate 4 seconds of physically accurate motion strictly following these parameters. Every object AND the ground surface are perfectly rigid — nothing breaks, cracks, deforms, or creates craters. Each object maintains its exact material, color, and texture throughout. The coordinate axes and any initial velocity arrows must cleanly disappear after the first frame. Static camera, fixed background. Smooth, continuous motion.",
    "image": "firstframe/inclined_plane/1/rgb_0000.png",
    "duration": 4,
    "size": "1280x720"
  },
  {
    "case": "inclined_plane/2",
    "track": "perception_graphic",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.7, mu_k=0.6\nWoodBeechCube: a = 1.0, h = 3.19, v_0 = 2.0\nRamp_0: theta = 30°, H = 3.0, mu_s = 0.0, mu_k = 0.0\n\nGenerate a video where the background, ground, sky, and all annotations (coordinate axes, velocity arrows) gradually fade to pure white, while the subject physical objects remain still and unchanged. Static camera, no zoom, no rotation. The final frame should show only the objects with labeled physical properties on white — remove supporting structures (ramps, tracks, rails, platforms). Do not transform, resize, or replace any object. Each object must retain its exact position, size, shape, color, and texture.",
    "image": "firstframe/inclined_plane/2/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "inclined_plane/2",
    "track": "comprehension_text",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.7, mu_k=0.6\nWoodBeechCube: a = 1.0, h = 3.19, v_0 = 2.0\nRamp_0: theta = 30°, H = 3.0, mu_s = 0.0, mu_k = 0.0\n\nBelow are 4 candidate formulas. Exactly ONE is correct:\n  A) N = m·g·(cosθ - μ_k·sinθ)²\n  B) Q = m·c·ΔT\n  C) E_p = m·g·(H - h)\n  D) v² = v_0² + 2·a_slope·s\n\nGenerate a video ending on a white background with THREE lines of large, clearly readable, centered text:\n  Line 1: the correct option letter (A/B/C/D).\n  Line 2: the correct formula exactly as written above.\n  Line 3: the formula with annotated values substituted in from the parameters above.\n\nWhen substituting: if multiple objects exist, pick one consistent set.",
    "image": "firstframe/inclined_plane/2/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "inclined_plane/2",
    "track": "comprehension_graphic",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.7, mu_k=0.6\nWoodBeechCube: a = 1.0, h = 3.19, v_0 = 2.0\nRamp_0: theta = 30°, H = 3.0, mu_s = 0.0, mu_k = 0.0\n\nPredict the physical state at t = 1.0 s. Generate a video where the original annotations (coordinate axes and any initial velocity arrows) gradually fade out and cleanly disappear, while the background, ground, sky, and all scene lighting remain completely unchanged throughout. Objects move smoothly to their correct positions at t = 1.0 s — each object must retain its exact texture, material, size, and shape. For each moving object, draw a borderless orange arrow starting from the object's center pointing in its velocity direction, with a label \"v = X.XX\" (speed value, no unit). If at rest, show \"v = 0\" with no arrow. Static camera, no zoom, no rotation.",
    "image": "firstframe/inclined_plane/2/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "inclined_plane/2",
    "track": "generation",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.7, mu_k=0.6\nWoodBeechCube: a = 1.0, h = 3.19, v_0 = 2.0\nRamp_0: theta = 30°, H = 3.0, mu_s = 0.0, mu_k = 0.0\n\nGenerate 4 seconds of physically accurate motion strictly following these parameters. Every object AND the ground surface are perfectly rigid — nothing breaks, cracks, deforms, or creates craters. Each object maintains its exact material, color, and texture throughout. The coordinate axes and any initial velocity arrows must cleanly disappear after the first frame. Static camera, fixed background. Smooth, continuous motion.",
    "image": "firstframe/inclined_plane/2/rgb_0000.png",
    "duration": 4,
    "size": "1280x720"
  },
  {
    "case": "inclined_plane/3",
    "track": "perception_graphic",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.7, mu_k=0.6\nWoodBeechCube: a = 1.0, h = 6.96, v_0 = -2.0\nRamp_0: theta = 60°, H = 8.0, mu_s = 0.0, mu_k = 0.0\n\nGenerate a video where the background, ground, sky, and all annotations (coordinate axes, velocity arrows) gradually fade to pure white, while the subject physical objects remain still and unchanged. Static camera, no zoom, no rotation. The final frame should show only the objects with labeled physical properties on white — remove supporting structures (ramps, tracks, rails, platforms). Do not transform, resize, or replace any object. Each object must retain its exact position, size, shape, color, and texture.",
    "image": "firstframe/inclined_plane/3/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "inclined_plane/3",
    "track": "comprehension_text",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.7, mu_k=0.6\nWoodBeechCube: a = 1.0, h = 6.96, v_0 = -2.0\nRamp_0: theta = 60°, H = 8.0, mu_s = 0.0, mu_k = 0.0\n\nBelow are 4 candidate formulas. Exactly ONE is correct:\n  A) U = -G·m_1·m_2 / r\n  B) a_slope = g·(sinθ - μ_k·cosθ)\n  C) E_p = m·g·(H - h)\n  D) F_net = m·g·(sin²θ - μ_k·cos²θ) / sinθ\n\nGenerate a video ending on a white background with THREE lines of large, clearly readable, centered text:\n  Line 1: the correct option letter (A/B/C/D).\n  Line 2: the correct formula exactly as written above.\n  Line 3: the formula with annotated values substituted in from the parameters above.\n\nWhen substituting: if multiple objects exist, pick one consistent set.",
    "image": "firstframe/inclined_plane/3/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "inclined_plane/3",
    "track": "comprehension_graphic",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.7, mu_k=0.6\nWoodBeechCube: a = 1.0, h = 6.96, v_0 = -2.0\nRamp_0: theta = 60°, H = 8.0, mu_s = 0.0, mu_k = 0.0\n\nPredict the physical state at t = 1.5 s. Generate a video where the original annotations (coordinate axes and any initial velocity arrows) gradually fade out and cleanly disappear, while the background, ground, sky, and all scene lighting remain completely unchanged throughout. Objects move smoothly to their correct positions at t = 1.5 s — each object must retain its exact texture, material, size, and shape. For each moving object, draw a borderless orange arrow starting from the object's center pointing in its velocity direction, with a label \"v = X.XX\" (speed value, no unit). If at rest, show \"v = 0\" with no arrow. Static camera, no zoom, no rotation.",
    "image": "firstframe/inclined_plane/3/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "inclined_plane/3",
    "track": "generation",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.7, mu_k=0.6\nWoodBeechCube: a = 1.0, h = 6.96, v_0 = -2.0\nRamp_0: theta = 60°, H = 8.0, mu_s = 0.0, mu_k = 0.0\n\nGenerate 4 seconds of physically accurate motion strictly following these parameters. Every object AND the ground surface are perfectly rigid — nothing breaks, cracks, deforms, or creates craters. Each object maintains its exact material, color, and texture throughout. The coordinate axes and any initial velocity arrows must cleanly disappear after the first frame. Static camera, fixed background. Smooth, continuous motion.",
    "image": "firstframe/inclined_plane/3/rgb_0000.png",
    "duration": 4,
    "size": "1280x720"
  },
  {
    "case": "inclined_plane/7",
    "track": "perception_graphic",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.7, mu_k=0.6\nWoodBeechCube: a = 1.0, h = 4.01, v_0 = 0.1\nStoneBlackCube: a = 1.0, h = 3.30, v_0 = 0.2\nRamp_0: theta = 45°, H = 4.0, mu_s = 0.0, mu_k = 0.0\n\nGenerate a video where the background, ground, sky, and all annotations (coordinate axes, velocity arrows) gradually fade to pure white, while the subject physical objects remain still and unchanged. Static camera, no zoom, no rotation. The final frame should show only the objects with labeled physical properties on white — remove supporting structures (ramps, tracks, rails, platforms). Do not transform, resize, or replace any object. Each object must retain its exact position, size, shape, color, and texture.",
    "image": "firstframe/inclined_plane/7/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "inclined_plane/7",
    "track": "comprehension_text",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.7, mu_k=0.6\nWoodBeechCube: a = 1.0, h = 4.01, v_0 = 0.1\nStoneBlackCube: a = 1.0, h = 3.30, v_0 = 0.2\nRamp_0: theta = 45°, H = 4.0, mu_s = 0.0, mu_k = 0.0\n\nBelow are 4 candidate formulas. Exactly ONE is correct:\n  A) T = 2π·√(L/g)\n  B) v² = v_0² + 2·a_slope·s\n  C) h_cm·sinθ > (a/2)·cosθ\n  D) N = m·g·(cosθ - μ_k·sinθ)²\n\nGenerate a video ending on a white background with THREE lines of large, clearly readable, centered text:\n  Line 1: the correct option letter (A/B/C/D).\n  Line 2: the correct formula exactly as written above.\n  Line 3: the formula with annotated values substituted in from the parameters above.\n\nWhen substituting: if multiple objects exist, pick one consistent set.",
    "image": "firstframe/inclined_plane/7/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "inclined_plane/7",
    "track": "comprehension_graphic",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.7, mu_k=0.6\nWoodBeechCube: a = 1.0, h = 4.01, v_0 = 0.1\nStoneBlackCube: a = 1.0, h = 3.30, v_0 = 0.2\nRamp_0: theta = 45°, H = 4.0, mu_s = 0.0, mu_k = 0.0\n\nPredict the physical state at t = 0.5 s. Generate a video where the original annotations (coordinate axes and any initial velocity arrows) gradually fade out and cleanly disappear, while the background, ground, sky, and all scene lighting remain completely unchanged throughout. Objects move smoothly to their correct positions at t = 0.5 s — each object must retain its exact texture, material, size, and shape. For each moving object, draw a borderless orange arrow starting from the object's center pointing in its velocity direction, with a label \"v = X.XX\" (speed value, no unit). If at rest, show \"v = 0\" with no arrow. Static camera, no zoom, no rotation.",
    "image": "firstframe/inclined_plane/7/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "inclined_plane/7",
    "track": "generation",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.7, mu_k=0.6\nWoodBeechCube: a = 1.0, h = 4.01, v_0 = 0.1\nStoneBlackCube: a = 1.0, h = 3.30, v_0 = 0.2\nRamp_0: theta = 45°, H = 4.0, mu_s = 0.0, mu_k = 0.0\n\nGenerate 4 seconds of physically accurate motion strictly following these parameters. Every object AND the ground surface are perfectly rigid — nothing breaks, cracks, deforms, or creates craters. Each object maintains its exact material, color, and texture throughout. The coordinate axes and any initial velocity arrows must cleanly disappear after the first frame. Static camera, fixed background. Smooth, continuous motion.",
    "image": "firstframe/inclined_plane/7/rgb_0000.png",
    "duration": 4,
    "size": "1280x720"
  },
  {
    "case": "inclined_plane_newbatch/1",
    "track": "perception_graphic",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.7, mu_k=0.6\nWoodBeechCube: a = 1.0, h = 3.30, v_0 = -0.5\nRamp_0: theta = 45°, H = 4.0, mu_s = 0.0, mu_k = 0.0\n\nGenerate a video where the background, ground, sky, and all annotations (coordinate axes, velocity arrows) gradually fade to pure white, while the subject physical objects remain still and unchanged. Static camera, no zoom, no rotation. The final frame should show only the objects with labeled physical properties on white — remove supporting structures (ramps, tracks, rails, platforms). Do not transform, resize, or replace any object. Each object must retain its exact position, size, shape, color, and texture.",
    "image": "firstframe/inclined_plane_newbatch/1/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "inclined_plane_newbatch/1",
    "track": "comprehension_text",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.7, mu_k=0.6\nWoodBeechCube: a = 1.0, h = 3.30, v_0 = -0.5\nRamp_0: theta = 45°, H = 4.0, mu_s = 0.0, mu_k = 0.0\n\nBelow are 4 candidate formulas. Exactly ONE is correct:\n  A) s = v_0·t·cosθ + (1/2)·g·sinθ·t²\n  B) f_k = μ_k·m·g\n  C) T = 2π·√(L/g)\n  D) v² = v_0² + 2·a_slope·s\n\nGenerate a video ending on a white background with THREE lines of large, clearly readable, centered text:\n  Line 1: the correct option letter (A/B/C/D).\n  Line 2: the correct formula exactly as written above.\n  Line 3: the formula with annotated values substituted in from the parameters above.\n\nWhen substituting: if multiple objects exist, pick one consistent set.",
    "image": "firstframe/inclined_plane_newbatch/1/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "inclined_plane_newbatch/1",
    "track": "comprehension_graphic",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.7, mu_k=0.6\nWoodBeechCube: a = 1.0, h = 3.30, v_0 = -0.5\nRamp_0: theta = 45°, H = 4.0, mu_s = 0.0, mu_k = 0.0\n\nPredict the physical state at t = 1.0 s. Generate a video where the original annotations (coordinate axes and any initial velocity arrows) gradually fade out and cleanly disappear, while the background, ground, sky, and all scene lighting remain completely unchanged throughout. Objects move smoothly to their correct positions at t = 1.0 s — each object must retain its exact texture, material, size, and shape. For each moving object, draw a borderless orange arrow starting from the object's center pointing in its velocity direction, with a label \"v = X.XX\" (speed value, no unit). If at rest, show \"v = 0\" with no arrow. Static camera, no zoom, no rotation.",
    "image": "firstframe/inclined_plane_newbatch/1/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "inclined_plane_newbatch/1",
    "track": "generation",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.7, mu_k=0.6\nWoodBeechCube: a = 1.0, h = 3.30, v_0 = -0.5\nRamp_0: theta = 45°, H = 4.0, mu_s = 0.0, mu_k = 0.0\n\nGenerate 4 seconds of physically accurate motion strictly following these parameters. Every object AND the ground surface are perfectly rigid — nothing breaks, cracks, deforms, or creates craters. Each object maintains its exact material, color, and texture throughout. The coordinate axes and any initial velocity arrows must cleanly disappear after the first frame. Static camera, fixed background. Smooth, continuous motion.",
    "image": "firstframe/inclined_plane_newbatch/1/rgb_0000.png",
    "duration": 4,
    "size": "1280x720"
  },
  {
    "case": "inclined_plane_newbatch/8",
    "track": "perception_graphic",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.7, mu_k=0.6\nWoodBeechCube: a = 1.0, h = 2.69, v_0 = 0.3\nStoneBlackCube: a = 1.0, h = 3.19, v_0 = -1.0\nRamp_0: theta = 30°, H = 3.0, mu_s = 0.0, mu_k = 0.0\n\nGenerate a video where the background, ground, sky, and all annotations (coordinate axes, velocity arrows) gradually fade to pure white, while the subject physical objects remain still and unchanged. Static camera, no zoom, no rotation. The final frame should show only the objects with labeled physical properties on white — remove supporting structures (ramps, tracks, rails, platforms). Do not transform, resize, or replace any object. Each object must retain its exact position, size, shape, color, and texture.",
    "image": "firstframe/inclined_plane_newbatch/8/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "inclined_plane_newbatch/8",
    "track": "comprehension_text",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.7, mu_k=0.6\nWoodBeechCube: a = 1.0, h = 2.69, v_0 = 0.3\nStoneBlackCube: a = 1.0, h = 3.19, v_0 = -1.0\nRamp_0: theta = 30°, H = 3.0, mu_s = 0.0, mu_k = 0.0\n\nBelow are 4 candidate formulas. Exactly ONE is correct:\n  A) N = m·g·(cosθ - μ_k·sinθ)²\n  B) v² = v_0² + 2·a_slope·s\n  C) U = -G·m_1·m_2 / r\n  D) h_cm·sinθ > (a/2)·cosθ\n\nGenerate a video ending on a white background with THREE lines of large, clearly readable, centered text:\n  Line 1: the correct option letter (A/B/C/D).\n  Line 2: the correct formula exactly as written above.\n  Line 3: the formula with annotated values substituted in from the parameters above.\n\nWhen substituting: if multiple objects exist, pick one consistent set.",
    "image": "firstframe/inclined_plane_newbatch/8/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "inclined_plane_newbatch/8",
    "track": "comprehension_graphic",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.7, mu_k=0.6\nWoodBeechCube: a = 1.0, h = 2.69, v_0 = 0.3\nStoneBlackCube: a = 1.0, h = 3.19, v_0 = -1.0\nRamp_0: theta = 30°, H = 3.0, mu_s = 0.0, mu_k = 0.0\n\nPredict the physical state at t = 1.0 s. Generate a video where the original annotations (coordinate axes and any initial velocity arrows) gradually fade out and cleanly disappear, while the background, ground, sky, and all scene lighting remain completely unchanged throughout. Objects move smoothly to their correct positions at t = 1.0 s — each object must retain its exact texture, material, size, and shape. For each moving object, draw a borderless orange arrow starting from the object's center pointing in its velocity direction, with a label \"v = X.XX\" (speed value, no unit). If at rest, show \"v = 0\" with no arrow. Static camera, no zoom, no rotation.",
    "image": "firstframe/inclined_plane_newbatch/8/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "inclined_plane_newbatch/8",
    "track": "generation",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.7, mu_k=0.6\nWoodBeechCube: a = 1.0, h = 2.69, v_0 = 0.3\nStoneBlackCube: a = 1.0, h = 3.19, v_0 = -1.0\nRamp_0: theta = 30°, H = 3.0, mu_s = 0.0, mu_k = 0.0\n\nGenerate 4 seconds of physically accurate motion strictly following these parameters. Every object AND the ground surface are perfectly rigid — nothing breaks, cracks, deforms, or creates craters. Each object maintains its exact material, color, and texture throughout. The coordinate axes and any initial velocity arrows must cleanly disappear after the first frame. Static camera, fixed background. Smooth, continuous motion.",
    "image": "firstframe/inclined_plane_newbatch/8/rgb_0000.png",
    "duration": 4,
    "size": "1280x720"
  },
  {
    "case": "inelastic_collision/1",
    "track": "perception_graphic",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.0, mu_k=0.0\nGrogFiredClayCube: a = 2.0, e = 0.2, m = 16000.0, v_0 = 2.5\nWalnutCube: a = 2.0, e = 0.5, m = 5120.0, v_0 = 0.0\n\nGenerate a video where the background, ground, sky, and all annotations (coordinate axes, velocity arrows) gradually fade to pure white, while the subject physical objects remain still and unchanged. Static camera, no zoom, no rotation. The final frame should show only the objects with labeled physical properties on white — remove supporting structures (ramps, tracks, rails, platforms). Do not transform, resize, or replace any object. Each object must retain its exact position, size, shape, color, and texture.",
    "image": "firstframe/inelastic_collision/1/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "inelastic_collision/1",
    "track": "comprehension_text",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.0, mu_k=0.0\nGrogFiredClayCube: a = 2.0, e = 0.2, m = 16000.0, v_0 = 2.5\nWalnutCube: a = 2.0, e = 0.5, m = 5120.0, v_0 = 0.0\n\nBelow are 4 candidate formulas. Exactly ONE is correct:\n  A) U = -G·m_1·m_2 / r\n  B) e = (v_2f - v_1f) / (v_1i - v_2i)\n  C) ΔE_loss = (1/2)·e²·(m_1·m_2)/(m_1+m_2)·(v_1i + v_2i)²\n  D) W_f = ∫ μ_k·m·g·ds = ΔE_k\n\nGenerate a video ending on a white background with THREE lines of large, clearly readable, centered text:\n  Line 1: the correct option letter (A/B/C/D).\n  Line 2: the correct formula exactly as written above.\n  Line 3: the formula with annotated values substituted in from the parameters above.\n\nWhen substituting: if multiple objects exist, pick one consistent set.",
    "image": "firstframe/inelastic_collision/1/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "inelastic_collision/1",
    "track": "comprehension_graphic",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.0, mu_k=0.0\nGrogFiredClayCube: a = 2.0, e = 0.2, m = 16000.0, v_0 = 2.5\nWalnutCube: a = 2.0, e = 0.5, m = 5120.0, v_0 = 0.0\n\nPredict the physical state at t = 2.25 s. Generate a video where the original annotations (coordinate axes and any initial velocity arrows) gradually fade out and cleanly disappear, while the background, ground, sky, and all scene lighting remain completely unchanged throughout. Objects move smoothly to their correct positions at t = 2.25 s — each object must retain its exact texture, material, size, and shape. For each moving object, draw a borderless orange arrow starting from the object's center pointing in its velocity direction, with a label \"v = X.XX\" (speed value, no unit). If at rest, show \"v = 0\" with no arrow. Static camera, no zoom, no rotation.",
    "image": "firstframe/inelastic_collision/1/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "inelastic_collision/1",
    "track": "generation",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.0, mu_k=0.0\nGrogFiredClayCube: a = 2.0, e = 0.2, m = 16000.0, v_0 = 2.5\nWalnutCube: a = 2.0, e = 0.5, m = 5120.0, v_0 = 0.0\n\nGenerate 4 seconds of physically accurate motion strictly following these parameters. Every object AND the ground surface are perfectly rigid — nothing breaks, cracks, deforms, or creates craters. Each object maintains its exact material, color, and texture throughout. The coordinate axes and any initial velocity arrows must cleanly disappear after the first frame. Static camera, fixed background. Smooth, continuous motion.",
    "image": "firstframe/inelastic_collision/1/rgb_0000.png",
    "duration": 4,
    "size": "1280x720"
  },
  {
    "case": "inelastic_collision/2",
    "track": "perception_graphic",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.0, mu_k=0.0\nWalnutCube: a = 2.0, e = 0.5, m = 5120.0, v_0 = 2.5\nGrogFiredClayCube: a = 2.0, e = 0.2, m = 16000.0, v_0 = 0.0\n\nGenerate a video where the background, ground, sky, and all annotations (coordinate axes, velocity arrows) gradually fade to pure white, while the subject physical objects remain still and unchanged. Static camera, no zoom, no rotation. The final frame should show only the objects with labeled physical properties on white — remove supporting structures (ramps, tracks, rails, platforms). Do not transform, resize, or replace any object. Each object must retain its exact position, size, shape, color, and texture.",
    "image": "firstframe/inelastic_collision/2/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "inelastic_collision/2",
    "track": "comprehension_text",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.0, mu_k=0.0\nWalnutCube: a = 2.0, e = 0.5, m = 5120.0, v_0 = 2.5\nGrogFiredClayCube: a = 2.0, e = 0.2, m = 16000.0, v_0 = 0.0\n\nBelow are 4 candidate formulas. Exactly ONE is correct:\n  A) ΔE = (1/2)·[(m_1·m_2) / (m_1 + m_2)]·(v_1i - v_2i)²\n  B) ΔE = (1/2)·m_1·m_2·e²·(v_1i - v_2i)² / (m_1 + m_2)\n  C) F = k·q_1·q_2 / r²\n  D) e = (v_2f - v_1f) / (v_1i - v_2i)\n\nGenerate a video ending on a white background with THREE lines of large, clearly readable, centered text:\n  Line 1: the correct option letter (A/B/C/D).\n  Line 2: the correct formula exactly as written above.\n  Line 3: the formula with annotated values substituted in from the parameters above.\n\nWhen substituting: if multiple objects exist, pick one consistent set.",
    "image": "firstframe/inelastic_collision/2/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "inelastic_collision/2",
    "track": "comprehension_graphic",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.0, mu_k=0.0\nWalnutCube: a = 2.0, e = 0.5, m = 5120.0, v_0 = 2.5\nGrogFiredClayCube: a = 2.0, e = 0.2, m = 16000.0, v_0 = 0.0\n\nPredict the physical state at t = 2.25 s. Generate a video where the original annotations (coordinate axes and any initial velocity arrows) gradually fade out and cleanly disappear, while the background, ground, sky, and all scene lighting remain completely unchanged throughout. Objects move smoothly to their correct positions at t = 2.25 s — each object must retain its exact texture, material, size, and shape. For each moving object, draw a borderless orange arrow starting from the object's center pointing in its velocity direction, with a label \"v = X.XX\" (speed value, no unit). If at rest, show \"v = 0\" with no arrow. Static camera, no zoom, no rotation.",
    "image": "firstframe/inelastic_collision/2/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "inelastic_collision/2",
    "track": "generation",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.0, mu_k=0.0\nWalnutCube: a = 2.0, e = 0.5, m = 5120.0, v_0 = 2.5\nGrogFiredClayCube: a = 2.0, e = 0.2, m = 16000.0, v_0 = 0.0\n\nGenerate 4 seconds of physically accurate motion strictly following these parameters. Every object AND the ground surface are perfectly rigid — nothing breaks, cracks, deforms, or creates craters. Each object maintains its exact material, color, and texture throughout. The coordinate axes and any initial velocity arrows must cleanly disappear after the first frame. Static camera, fixed background. Smooth, continuous motion.",
    "image": "firstframe/inelastic_collision/2/rgb_0000.png",
    "duration": 4,
    "size": "1280x720"
  },
  {
    "case": "inelastic_collision/3",
    "track": "perception_graphic",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.0, mu_k=0.0\nWalnutCube1: a = 2.0, e = 0.5, m = 5120.0, v_0 = 1.5\nOakCube: a = 2.0, e = 0.5, m = 6000.0, v_0 = -1.5\n\nGenerate a video where the background, ground, sky, and all annotations (coordinate axes, velocity arrows) gradually fade to pure white, while the subject physical objects remain still and unchanged. Static camera, no zoom, no rotation. The final frame should show only the objects with labeled physical properties on white — remove supporting structures (ramps, tracks, rails, platforms). Do not transform, resize, or replace any object. Each object must retain its exact position, size, shape, color, and texture.",
    "image": "firstframe/inelastic_collision/3/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "inelastic_collision/3",
    "track": "comprehension_text",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.0, mu_k=0.0\nWalnutCube1: a = 2.0, e = 0.5, m = 5120.0, v_0 = 1.5\nOakCube: a = 2.0, e = 0.5, m = 6000.0, v_0 = -1.5\n\nBelow are 4 candidate formulas. Exactly ONE is correct:\n  A) v_1f = (m_1 - e·m_2)·v_1i / (m_1 + m_2) + v_2i·cosθ\n  B) σ = F/a² = E·ε\n  C) E = h·f\n  D) e = (v_2f - v_1f) / (v_1i - v_2i)\n\nGenerate a video ending on a white background with THREE lines of large, clearly readable, centered text:\n  Line 1: the correct option letter (A/B/C/D).\n  Line 2: the correct formula exactly as written above.\n  Line 3: the formula with annotated values substituted in from the parameters above.\n\nWhen substituting: if multiple objects exist, pick one consistent set.",
    "image": "firstframe/inelastic_collision/3/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "inelastic_collision/3",
    "track": "comprehension_graphic",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.0, mu_k=0.0\nWalnutCube1: a = 2.0, e = 0.5, m = 5120.0, v_0 = 1.5\nOakCube: a = 2.0, e = 0.5, m = 6000.0, v_0 = -1.5\n\nPredict the physical state at t = 2.0 s. Generate a video where the original annotations (coordinate axes and any initial velocity arrows) gradually fade out and cleanly disappear, while the background, ground, sky, and all scene lighting remain completely unchanged throughout. Objects move smoothly to their correct positions at t = 2.0 s — each object must retain its exact texture, material, size, and shape. For each moving object, draw a borderless orange arrow starting from the object's center pointing in its velocity direction, with a label \"v = X.XX\" (speed value, no unit). If at rest, show \"v = 0\" with no arrow. Static camera, no zoom, no rotation.",
    "image": "firstframe/inelastic_collision/3/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "inelastic_collision/3",
    "track": "generation",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.0, mu_k=0.0\nWalnutCube1: a = 2.0, e = 0.5, m = 5120.0, v_0 = 1.5\nOakCube: a = 2.0, e = 0.5, m = 6000.0, v_0 = -1.5\n\nGenerate 4 seconds of physically accurate motion strictly following these parameters. Every object AND the ground surface are perfectly rigid — nothing breaks, cracks, deforms, or creates craters. Each object maintains its exact material, color, and texture throughout. The coordinate axes and any initial velocity arrows must cleanly disappear after the first frame. Static camera, fixed background. Smooth, continuous motion.",
    "image": "firstframe/inelastic_collision/3/rgb_0000.png",
    "duration": 4,
    "size": "1280x720"
  },
  {
    "case": "inelastic_collision/6",
    "track": "perception_graphic",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.0, mu_k=0.0\nGrogFiredClayCube: a = 2.0, e = 0.2, m = 16000.0, v_0 = 3.5\nWalnutCube: a = 2.0, e = 0.5, m = 5120.0, v_0 = 0.5\n\nGenerate a video where the background, ground, sky, and all annotations (coordinate axes, velocity arrows) gradually fade to pure white, while the subject physical objects remain still and unchanged. Static camera, no zoom, no rotation. The final frame should show only the objects with labeled physical properties on white — remove supporting structures (ramps, tracks, rails, platforms). Do not transform, resize, or replace any object. Each object must retain its exact position, size, shape, color, and texture.",
    "image": "firstframe/inelastic_collision/6/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "inelastic_collision/6",
    "track": "comprehension_text",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.0, mu_k=0.0\nGrogFiredClayCube: a = 2.0, e = 0.2, m = 16000.0, v_0 = 3.5\nWalnutCube: a = 2.0, e = 0.5, m = 5120.0, v_0 = 0.5\n\nBelow are 4 candidate formulas. Exactly ONE is correct:\n  A) m_1·v_1i + m_2·v_2i = m_1·v_1f + m_2·v_2f\n  B) v_cm = (m_1·v_1i² + m_2·v_2i²) / (m_1·v_1i + m_2·v_2i)\n  C) σ = F/a² = E·ε\n  D) T = 2π·√(m/k)\n\nGenerate a video ending on a white background with THREE lines of large, clearly readable, centered text:\n  Line 1: the correct option letter (A/B/C/D).\n  Line 2: the correct formula exactly as written above.\n  Line 3: the formula with annotated values substituted in from the parameters above.\n\nWhen substituting: if multiple objects exist, pick one consistent set.",
    "image": "firstframe/inelastic_collision/6/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "inelastic_collision/6",
    "track": "comprehension_graphic",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.0, mu_k=0.0\nGrogFiredClayCube: a = 2.0, e = 0.2, m = 16000.0, v_0 = 3.5\nWalnutCube: a = 2.0, e = 0.5, m = 5120.0, v_0 = 0.5\n\nPredict the physical state at t = 2.25 s. Generate a video where the original annotations (coordinate axes and any initial velocity arrows) gradually fade out and cleanly disappear, while the background, ground, sky, and all scene lighting remain completely unchanged throughout. Objects move smoothly to their correct positions at t = 2.25 s — each object must retain its exact texture, material, size, and shape. For each moving object, draw a borderless orange arrow starting from the object's center pointing in its velocity direction, with a label \"v = X.XX\" (speed value, no unit). If at rest, show \"v = 0\" with no arrow. Static camera, no zoom, no rotation.",
    "image": "firstframe/inelastic_collision/6/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "inelastic_collision/6",
    "track": "generation",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.0, mu_k=0.0\nGrogFiredClayCube: a = 2.0, e = 0.2, m = 16000.0, v_0 = 3.5\nWalnutCube: a = 2.0, e = 0.5, m = 5120.0, v_0 = 0.5\n\nGenerate 4 seconds of physically accurate motion strictly following these parameters. Every object AND the ground surface are perfectly rigid — nothing breaks, cracks, deforms, or creates craters. Each object maintains its exact material, color, and texture throughout. The coordinate axes and any initial velocity arrows must cleanly disappear after the first frame. Static camera, fixed background. Smooth, continuous motion.",
    "image": "firstframe/inelastic_collision/6/rgb_0000.png",
    "duration": 4,
    "size": "1280x720"
  },
  {
    "case": "inelastic_collision/9",
    "track": "perception_graphic",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.0, mu_k=0.0\nWalnutCube1: a = 2.0, e = 0.5, m = 5120.0, v_0 = 2.0\nOakCube: a = 2.0, e = 0.5, m = 6000.0, v_0 = 1.0\nCherryCube: a = 2.0, e = 0.5, m = 5040.0, v_0 = 0.0\n\nGenerate a video where the background, ground, sky, and all annotations (coordinate axes, velocity arrows) gradually fade to pure white, while the subject physical objects remain still and unchanged. Static camera, no zoom, no rotation. The final frame should show only the objects with labeled physical properties on white — remove supporting structures (ramps, tracks, rails, platforms). Do not transform, resize, or replace any object. Each object must retain its exact position, size, shape, color, and texture.",
    "image": "firstframe/inelastic_collision/9/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "inelastic_collision/9",
    "track": "comprehension_text",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.0, mu_k=0.0\nWalnutCube1: a = 2.0, e = 0.5, m = 5120.0, v_0 = 2.0\nOakCube: a = 2.0, e = 0.5, m = 6000.0, v_0 = 1.0\nCherryCube: a = 2.0, e = 0.5, m = 5040.0, v_0 = 0.0\n\nBelow are 4 candidate formulas. Exactly ONE is correct:\n  A) σ = F/a² = E·ε\n  B) e = (v_2f - v_1f) / (v_1i - v_2i)\n  C) J = m_1·m_2·(v_1i - v_2i)·(1+e) / (m_1 + m_2) · sinθ\n  D) v = f·λ\n\nGenerate a video ending on a white background with THREE lines of large, clearly readable, centered text:\n  Line 1: the correct option letter (A/B/C/D).\n  Line 2: the correct formula exactly as written above.\n  Line 3: the formula with annotated values substituted in from the parameters above.\n\nWhen substituting: if multiple objects exist, pick one consistent set.",
    "image": "firstframe/inelastic_collision/9/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "inelastic_collision/9",
    "track": "comprehension_graphic",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.0, mu_k=0.0\nWalnutCube1: a = 2.0, e = 0.5, m = 5120.0, v_0 = 2.0\nOakCube: a = 2.0, e = 0.5, m = 6000.0, v_0 = 1.0\nCherryCube: a = 2.0, e = 0.5, m = 5040.0, v_0 = 0.0\n\nPredict the physical state at t = 4.0 s. Generate a video where the original annotations (coordinate axes and any initial velocity arrows) gradually fade out and cleanly disappear, while the background, ground, sky, and all scene lighting remain completely unchanged throughout. Objects move smoothly to their correct positions at t = 4.0 s — each object must retain its exact texture, material, size, and shape. For each moving object, draw a borderless orange arrow starting from the object's center pointing in its velocity direction, with a label \"v = X.XX\" (speed value, no unit). If at rest, show \"v = 0\" with no arrow. Static camera, no zoom, no rotation.",
    "image": "firstframe/inelastic_collision/9/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "inelastic_collision/9",
    "track": "generation",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.0, mu_k=0.0\nWalnutCube1: a = 2.0, e = 0.5, m = 5120.0, v_0 = 2.0\nOakCube: a = 2.0, e = 0.5, m = 6000.0, v_0 = 1.0\nCherryCube: a = 2.0, e = 0.5, m = 5040.0, v_0 = 0.0\n\nGenerate 4 seconds of physically accurate motion strictly following these parameters. Every object AND the ground surface are perfectly rigid — nothing breaks, cracks, deforms, or creates craters. Each object maintains its exact material, color, and texture throughout. The coordinate axes and any initial velocity arrows must cleanly disappear after the first frame. Static camera, fixed background. Smooth, continuous motion.",
    "image": "firstframe/inelastic_collision/9/rgb_0000.png",
    "duration": 4,
    "size": "1280x720"
  },
  {
    "case": "inelastic_collision_newbatch/7",
    "track": "perception_graphic",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.0, mu_k=0.0\nLeftBronzeAntiqueCube: a = 2.0, e = 0.45, m = 70400.0, v_0 = 1.2\nRightBeechCube: a = 2.0, e = 0.4, m = 5760.0, v_0 = 2.5\n\nGenerate a video where the background, ground, sky, and all annotations (coordinate axes, velocity arrows) gradually fade to pure white, while the subject physical objects remain still and unchanged. Static camera, no zoom, no rotation. The final frame should show only the objects with labeled physical properties on white — remove supporting structures (ramps, tracks, rails, platforms). Do not transform, resize, or replace any object. Each object must retain its exact position, size, shape, color, and texture.",
    "image": "firstframe/inelastic_collision_newbatch/7/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "inelastic_collision_newbatch/7",
    "track": "comprehension_text",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.0, mu_k=0.0\nLeftBronzeAntiqueCube: a = 2.0, e = 0.45, m = 70400.0, v_0 = 1.2\nRightBeechCube: a = 2.0, e = 0.4, m = 5760.0, v_0 = 2.5\n\nBelow are 4 candidate formulas. Exactly ONE is correct:\n  A) λ = h/(m·v)\n  B) ΔE = (1/2)·[(m_1·m_2) / (m_1 + m_2)]·(v_1i - v_2i)²\n  C) m_1·v_1i + m_2·v_2i = m_1·v_1f + m_2·v_2f\n  D) J = m_1·m_2·(v_1i - v_2i)·(1+e) / (m_1 + m_2) · sinθ\n\nGenerate a video ending on a white background with THREE lines of large, clearly readable, centered text:\n  Line 1: the correct option letter (A/B/C/D).\n  Line 2: the correct formula exactly as written above.\n  Line 3: the formula with annotated values substituted in from the parameters above.\n\nWhen substituting: if multiple objects exist, pick one consistent set.",
    "image": "firstframe/inelastic_collision_newbatch/7/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "inelastic_collision_newbatch/7",
    "track": "comprehension_graphic",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.0, mu_k=0.0\nLeftBronzeAntiqueCube: a = 2.0, e = 0.45, m = 70400.0, v_0 = 1.2\nRightBeechCube: a = 2.0, e = 0.4, m = 5760.0, v_0 = 2.5\n\nPredict the physical state at t = 1.75 s. Generate a video where the original annotations (coordinate axes and any initial velocity arrows) gradually fade out and cleanly disappear, while the background, ground, sky, and all scene lighting remain completely unchanged throughout. Objects move smoothly to their correct positions at t = 1.75 s — each object must retain its exact texture, material, size, and shape. For each moving object, draw a borderless orange arrow starting from the object's center pointing in its velocity direction, with a label \"v = X.XX\" (speed value, no unit). If at rest, show \"v = 0\" with no arrow. Static camera, no zoom, no rotation.",
    "image": "firstframe/inelastic_collision_newbatch/7/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "inelastic_collision_newbatch/7",
    "track": "generation",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.0, mu_k=0.0\nLeftBronzeAntiqueCube: a = 2.0, e = 0.45, m = 70400.0, v_0 = 1.2\nRightBeechCube: a = 2.0, e = 0.4, m = 5760.0, v_0 = 2.5\n\nGenerate 4 seconds of physically accurate motion strictly following these parameters. Every object AND the ground surface are perfectly rigid — nothing breaks, cracks, deforms, or creates craters. Each object maintains its exact material, color, and texture throughout. The coordinate axes and any initial velocity arrows must cleanly disappear after the first frame. Static camera, fixed background. Smooth, continuous motion.",
    "image": "firstframe/inelastic_collision_newbatch/7/rgb_0000.png",
    "duration": 4,
    "size": "1280x720"
  },
  {
    "case": "perfectly_elastic_collision/2",
    "track": "perception_graphic",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.0, mu_k=0.0\nRedGlassCube: a = 2.0, e = 1.0, m = 20000.0, v_0 = 2.5\nStainlessSteelCube: a = 2.0, e = 1.0, m = 63200.0, v_0 = 0.0\n\nGenerate a video where the background, ground, sky, and all annotations (coordinate axes, velocity arrows) gradually fade to pure white, while the subject physical objects remain still and unchanged. Static camera, no zoom, no rotation. The final frame should show only the objects with labeled physical properties on white — remove supporting structures (ramps, tracks, rails, platforms). Do not transform, resize, or replace any object. Each object must retain its exact position, size, shape, color, and texture.",
    "image": "firstframe/perfectly_elastic_collision/2/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "perfectly_elastic_collision/2",
    "track": "comprehension_text",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.0, mu_k=0.0\nRedGlassCube: a = 2.0, e = 1.0, m = 20000.0, v_0 = 2.5\nStainlessSteelCube: a = 2.0, e = 1.0, m = 63200.0, v_0 = 0.0\n\nBelow are 4 candidate formulas. Exactly ONE is correct:\n  A) (1/2)·m_1·v_1i² + (1/2)·m_2·v_2i² = (1/2)·m_1·v_1f² + (1/2)·m_2·v_2f²\n  B) B = μ_0·I / (2π·r)\n  C) ΔE = μ_k·m·g·d\n  D) v_2f = 2·m_1·v_1i·cosθ / (m_1 + m_2)\n\nGenerate a video ending on a white background with THREE lines of large, clearly readable, centered text:\n  Line 1: the correct option letter (A/B/C/D).\n  Line 2: the correct formula exactly as written above.\n  Line 3: the formula with annotated values substituted in from the parameters above.\n\nWhen substituting: if multiple objects exist, pick one consistent set.",
    "image": "firstframe/perfectly_elastic_collision/2/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "perfectly_elastic_collision/2",
    "track": "comprehension_graphic",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.0, mu_k=0.0\nRedGlassCube: a = 2.0, e = 1.0, m = 20000.0, v_0 = 2.5\nStainlessSteelCube: a = 2.0, e = 1.0, m = 63200.0, v_0 = 0.0\n\nPredict the physical state at t = 2.25 s. Generate a video where the original annotations (coordinate axes and any initial velocity arrows) gradually fade out and cleanly disappear, while the background, ground, sky, and all scene lighting remain completely unchanged throughout. Objects move smoothly to their correct positions at t = 2.25 s — each object must retain its exact texture, material, size, and shape. For each moving object, draw a borderless orange arrow starting from the object's center pointing in its velocity direction, with a label \"v = X.XX\" (speed value, no unit). If at rest, show \"v = 0\" with no arrow. Static camera, no zoom, no rotation.",
    "image": "firstframe/perfectly_elastic_collision/2/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "perfectly_elastic_collision/2",
    "track": "generation",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.0, mu_k=0.0\nRedGlassCube: a = 2.0, e = 1.0, m = 20000.0, v_0 = 2.5\nStainlessSteelCube: a = 2.0, e = 1.0, m = 63200.0, v_0 = 0.0\n\nGenerate 4 seconds of physically accurate motion strictly following these parameters. Every object AND the ground surface are perfectly rigid — nothing breaks, cracks, deforms, or creates craters. Each object maintains its exact material, color, and texture throughout. The coordinate axes and any initial velocity arrows must cleanly disappear after the first frame. Static camera, fixed background. Smooth, continuous motion.",
    "image": "firstframe/perfectly_elastic_collision/2/rgb_0000.png",
    "duration": 4,
    "size": "1280x720"
  },
  {
    "case": "perfectly_elastic_collision/3",
    "track": "perception_graphic",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.0, mu_k=0.0\nStainlessSteelCube1: a = 2.0, e = 1.0, m = 63200.0, v_0 = 1.5\nRedGlassCube: a = 2.0, e = 1.0, m = 20000.0, v_0 = -0.6\n\nGenerate a video where the background, ground, sky, and all annotations (coordinate axes, velocity arrows) gradually fade to pure white, while the subject physical objects remain still and unchanged. Static camera, no zoom, no rotation. The final frame should show only the objects with labeled physical properties on white — remove supporting structures (ramps, tracks, rails, platforms). Do not transform, resize, or replace any object. Each object must retain its exact position, size, shape, color, and texture.",
    "image": "firstframe/perfectly_elastic_collision/3/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "perfectly_elastic_collision/3",
    "track": "comprehension_text",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.0, mu_k=0.0\nStainlessSteelCube1: a = 2.0, e = 1.0, m = 63200.0, v_0 = 1.5\nRedGlassCube: a = 2.0, e = 1.0, m = 20000.0, v_0 = -0.6\n\nBelow are 4 candidate formulas. Exactly ONE is correct:\n  A) m_1·v_1i + m_2·v_2i = m_1·v_1f + m_2·v_2f\n  B) v_1f = v_1i · e^(-m_2/m_1) + v_2i·(1 - e^(-m_2/m_1))\n  C) v_2f - v_1f = e·(v_1i - v_2i)\n  D) L = I·ω\n\nGenerate a video ending on a white background with THREE lines of large, clearly readable, centered text:\n  Line 1: the correct option letter (A/B/C/D).\n  Line 2: the correct formula exactly as written above.\n  Line 3: the formula with annotated values substituted in from the parameters above.\n\nWhen substituting: if multiple objects exist, pick one consistent set.",
    "image": "firstframe/perfectly_elastic_collision/3/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "perfectly_elastic_collision/3",
    "track": "comprehension_graphic",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.0, mu_k=0.0\nStainlessSteelCube1: a = 2.0, e = 1.0, m = 63200.0, v_0 = 1.5\nRedGlassCube: a = 2.0, e = 1.0, m = 20000.0, v_0 = -0.6\n\nPredict the physical state at t = 2.75 s. Generate a video where the original annotations (coordinate axes and any initial velocity arrows) gradually fade out and cleanly disappear, while the background, ground, sky, and all scene lighting remain completely unchanged throughout. Objects move smoothly to their correct positions at t = 2.75 s — each object must retain its exact texture, material, size, and shape. For each moving object, draw a borderless orange arrow starting from the object's center pointing in its velocity direction, with a label \"v = X.XX\" (speed value, no unit). If at rest, show \"v = 0\" with no arrow. Static camera, no zoom, no rotation.",
    "image": "firstframe/perfectly_elastic_collision/3/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "perfectly_elastic_collision/3",
    "track": "generation",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.0, mu_k=0.0\nStainlessSteelCube1: a = 2.0, e = 1.0, m = 63200.0, v_0 = 1.5\nRedGlassCube: a = 2.0, e = 1.0, m = 20000.0, v_0 = -0.6\n\nGenerate 4 seconds of physically accurate motion strictly following these parameters. Every object AND the ground surface are perfectly rigid — nothing breaks, cracks, deforms, or creates craters. Each object maintains its exact material, color, and texture throughout. The coordinate axes and any initial velocity arrows must cleanly disappear after the first frame. Static camera, fixed background. Smooth, continuous motion.",
    "image": "firstframe/perfectly_elastic_collision/3/rgb_0000.png",
    "duration": 4,
    "size": "1280x720"
  },
  {
    "case": "perfectly_elastic_collision/5",
    "track": "perception_graphic",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.0, mu_k=0.0\nRedGlassCube: a = 2.0, e = 1.0, m = 20000.0, v_0 = 0.6\nStainlessSteelCube: a = 2.0, e = 1.0, m = 63200.0, v_0 = -1.5\n\nGenerate a video where the background, ground, sky, and all annotations (coordinate axes, velocity arrows) gradually fade to pure white, while the subject physical objects remain still and unchanged. Static camera, no zoom, no rotation. The final frame should show only the objects with labeled physical properties on white — remove supporting structures (ramps, tracks, rails, platforms). Do not transform, resize, or replace any object. Each object must retain its exact position, size, shape, color, and texture.",
    "image": "firstframe/perfectly_elastic_collision/5/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "perfectly_elastic_collision/5",
    "track": "comprehension_text",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.0, mu_k=0.0\nRedGlassCube: a = 2.0, e = 1.0, m = 20000.0, v_0 = 0.6\nStainlessSteelCube: a = 2.0, e = 1.0, m = 63200.0, v_0 = -1.5\n\nBelow are 4 candidate formulas. Exactly ONE is correct:\n  A) ΔE = μ_k·m·g·d\n  B) (1/2)·m_1·v_1i² + (1/2)·m_2·v_2i² = (1/2)·m_1·v_1f² + (1/2)·m_2·v_2f²\n  C) λ = h/(m·v)\n  D) v_2f = 2·m_1·v_1i·cosθ / (m_1 + m_2)\n\nGenerate a video ending on a white background with THREE lines of large, clearly readable, centered text:\n  Line 1: the correct option letter (A/B/C/D).\n  Line 2: the correct formula exactly as written above.\n  Line 3: the formula with annotated values substituted in from the parameters above.\n\nWhen substituting: if multiple objects exist, pick one consistent set.",
    "image": "firstframe/perfectly_elastic_collision/5/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "perfectly_elastic_collision/5",
    "track": "comprehension_graphic",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.0, mu_k=0.0\nRedGlassCube: a = 2.0, e = 1.0, m = 20000.0, v_0 = 0.6\nStainlessSteelCube: a = 2.0, e = 1.0, m = 63200.0, v_0 = -1.5\n\nPredict the physical state at t = 2.75 s. Generate a video where the original annotations (coordinate axes and any initial velocity arrows) gradually fade out and cleanly disappear, while the background, ground, sky, and all scene lighting remain completely unchanged throughout. Objects move smoothly to their correct positions at t = 2.75 s — each object must retain its exact texture, material, size, and shape. For each moving object, draw a borderless orange arrow starting from the object's center pointing in its velocity direction, with a label \"v = X.XX\" (speed value, no unit). If at rest, show \"v = 0\" with no arrow. Static camera, no zoom, no rotation.",
    "image": "firstframe/perfectly_elastic_collision/5/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "perfectly_elastic_collision/5",
    "track": "generation",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.0, mu_k=0.0\nRedGlassCube: a = 2.0, e = 1.0, m = 20000.0, v_0 = 0.6\nStainlessSteelCube: a = 2.0, e = 1.0, m = 63200.0, v_0 = -1.5\n\nGenerate 4 seconds of physically accurate motion strictly following these parameters. Every object AND the ground surface are perfectly rigid — nothing breaks, cracks, deforms, or creates craters. Each object maintains its exact material, color, and texture throughout. The coordinate axes and any initial velocity arrows must cleanly disappear after the first frame. Static camera, fixed background. Smooth, continuous motion.",
    "image": "firstframe/perfectly_elastic_collision/5/rgb_0000.png",
    "duration": 4,
    "size": "1280x720"
  },
  {
    "case": "perfectly_elastic_collision/7",
    "track": "perception_graphic",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.0, mu_k=0.0\nStainlessSteelCube: a = 2.0, e = 1.0, m = 63200.0, v_0 = 2.4\nRedGlassCube: a = 2.0, e = 1.0, m = 20000.0, v_0 = 0.6\n\nGenerate a video where the background, ground, sky, and all annotations (coordinate axes, velocity arrows) gradually fade to pure white, while the subject physical objects remain still and unchanged. Static camera, no zoom, no rotation. The final frame should show only the objects with labeled physical properties on white — remove supporting structures (ramps, tracks, rails, platforms). Do not transform, resize, or replace any object. Each object must retain its exact position, size, shape, color, and texture.",
    "image": "firstframe/perfectly_elastic_collision/7/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "perfectly_elastic_collision/7",
    "track": "comprehension_text",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.0, mu_k=0.0\nStainlessSteelCube: a = 2.0, e = 1.0, m = 63200.0, v_0 = 2.4\nRedGlassCube: a = 2.0, e = 1.0, m = 20000.0, v_0 = 0.6\n\nBelow are 4 candidate formulas. Exactly ONE is correct:\n  A) ∫ F(t) dt = Δ(mv)\n  B) v_1f = v_1i·(m_1² - m_2²) / (m_1 + m_2)²\n  C) λ = h/(m·v)\n  D) (1/2)·m_1·v_1i² + (1/2)·m_2·v_2i² = (1/2)·m_1·v_1f² + (1/2)·m_2·v_2f²\n\nGenerate a video ending on a white background with THREE lines of large, clearly readable, centered text:\n  Line 1: the correct option letter (A/B/C/D).\n  Line 2: the correct formula exactly as written above.\n  Line 3: the formula with annotated values substituted in from the parameters above.\n\nWhen substituting: if multiple objects exist, pick one consistent set.",
    "image": "firstframe/perfectly_elastic_collision/7/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "perfectly_elastic_collision/7",
    "track": "comprehension_graphic",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.0, mu_k=0.0\nStainlessSteelCube: a = 2.0, e = 1.0, m = 63200.0, v_0 = 2.4\nRedGlassCube: a = 2.0, e = 1.0, m = 20000.0, v_0 = 0.6\n\nPredict the physical state at t = 3.5 s. Generate a video where the original annotations (coordinate axes and any initial velocity arrows) gradually fade out and cleanly disappear, while the background, ground, sky, and all scene lighting remain completely unchanged throughout. Objects move smoothly to their correct positions at t = 3.5 s — each object must retain its exact texture, material, size, and shape. For each moving object, draw a borderless orange arrow starting from the object's center pointing in its velocity direction, with a label \"v = X.XX\" (speed value, no unit). If at rest, show \"v = 0\" with no arrow. Static camera, no zoom, no rotation.",
    "image": "firstframe/perfectly_elastic_collision/7/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "perfectly_elastic_collision/7",
    "track": "generation",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.0, mu_k=0.0\nStainlessSteelCube: a = 2.0, e = 1.0, m = 63200.0, v_0 = 2.4\nRedGlassCube: a = 2.0, e = 1.0, m = 20000.0, v_0 = 0.6\n\nGenerate 4 seconds of physically accurate motion strictly following these parameters. Every object AND the ground surface are perfectly rigid — nothing breaks, cracks, deforms, or creates craters. Each object maintains its exact material, color, and texture throughout. The coordinate axes and any initial velocity arrows must cleanly disappear after the first frame. Static camera, fixed background. Smooth, continuous motion.",
    "image": "firstframe/perfectly_elastic_collision/7/rgb_0000.png",
    "duration": 4,
    "size": "1280x720"
  },
  {
    "case": "perfectly_elastic_collision/8",
    "track": "perception_graphic",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.0, mu_k=0.0\nRedGlassCube: a = 2.0, e = 1.0, m = 20000.0, v_0 = 2.4\nStainlessSteelCube: a = 2.0, e = 1.0, m = 63200.0, v_0 = 0.3\n\nGenerate a video where the background, ground, sky, and all annotations (coordinate axes, velocity arrows) gradually fade to pure white, while the subject physical objects remain still and unchanged. Static camera, no zoom, no rotation. The final frame should show only the objects with labeled physical properties on white — remove supporting structures (ramps, tracks, rails, platforms). Do not transform, resize, or replace any object. Each object must retain its exact position, size, shape, color, and texture.",
    "image": "firstframe/perfectly_elastic_collision/8/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "perfectly_elastic_collision/8",
    "track": "comprehension_text",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.0, mu_k=0.0\nRedGlassCube: a = 2.0, e = 1.0, m = 20000.0, v_0 = 2.4\nStainlessSteelCube: a = 2.0, e = 1.0, m = 63200.0, v_0 = 0.3\n\nBelow are 4 candidate formulas. Exactly ONE is correct:\n  A) I = I_cm + m·(a/2)²\n  B) v_2f = 2·m_1·v_1i·cosθ / (m_1 + m_2)\n  C) (1/2)·m_1·v_1i² + (1/2)·m_2·v_2i² = (1/2)·m_1·v_1f² + (1/2)·m_2·v_2f²\n  D) F = k·q_1·q_2 / r²\n\nGenerate a video ending on a white background with THREE lines of large, clearly readable, centered text:\n  Line 1: the correct option letter (A/B/C/D).\n  Line 2: the correct formula exactly as written above.\n  Line 3: the formula with annotated values substituted in from the parameters above.\n\nWhen substituting: if multiple objects exist, pick one consistent set.",
    "image": "firstframe/perfectly_elastic_collision/8/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "perfectly_elastic_collision/8",
    "track": "comprehension_graphic",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.0, mu_k=0.0\nRedGlassCube: a = 2.0, e = 1.0, m = 20000.0, v_0 = 2.4\nStainlessSteelCube: a = 2.0, e = 1.0, m = 63200.0, v_0 = 0.3\n\nPredict the physical state at t = 2.75 s. Generate a video where the original annotations (coordinate axes and any initial velocity arrows) gradually fade out and cleanly disappear, while the background, ground, sky, and all scene lighting remain completely unchanged throughout. Objects move smoothly to their correct positions at t = 2.75 s — each object must retain its exact texture, material, size, and shape. For each moving object, draw a borderless orange arrow starting from the object's center pointing in its velocity direction, with a label \"v = X.XX\" (speed value, no unit). If at rest, show \"v = 0\" with no arrow. Static camera, no zoom, no rotation.",
    "image": "firstframe/perfectly_elastic_collision/8/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "perfectly_elastic_collision/8",
    "track": "generation",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.0, mu_k=0.0\nRedGlassCube: a = 2.0, e = 1.0, m = 20000.0, v_0 = 2.4\nStainlessSteelCube: a = 2.0, e = 1.0, m = 63200.0, v_0 = 0.3\n\nGenerate 4 seconds of physically accurate motion strictly following these parameters. Every object AND the ground surface are perfectly rigid — nothing breaks, cracks, deforms, or creates craters. Each object maintains its exact material, color, and texture throughout. The coordinate axes and any initial velocity arrows must cleanly disappear after the first frame. Static camera, fixed background. Smooth, continuous motion.",
    "image": "firstframe/perfectly_elastic_collision/8/rgb_0000.png",
    "duration": 4,
    "size": "1280x720"
  },
  {
    "case": "perfectly_elastic_collision/9",
    "track": "perception_graphic",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.0, mu_k=0.0\nStainlessSteelCube1: a = 2.0, e = 1.0, m = 63200.0, v_0 = 2.4\nRedGlassCube: a = 2.0, e = 1.0, m = 20000.0, v_0 = 0.0\nBlueGlassCube: a = 2.0, e = 1.0, m = 20000.0, v_0 = 0.0\n\nGenerate a video where the background, ground, sky, and all annotations (coordinate axes, velocity arrows) gradually fade to pure white, while the subject physical objects remain still and unchanged. Static camera, no zoom, no rotation. The final frame should show only the objects with labeled physical properties on white — remove supporting structures (ramps, tracks, rails, platforms). Do not transform, resize, or replace any object. Each object must retain its exact position, size, shape, color, and texture.",
    "image": "firstframe/perfectly_elastic_collision/9/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "perfectly_elastic_collision/9",
    "track": "comprehension_text",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.0, mu_k=0.0\nStainlessSteelCube1: a = 2.0, e = 1.0, m = 63200.0, v_0 = 2.4\nRedGlassCube: a = 2.0, e = 1.0, m = 20000.0, v_0 = 0.0\nBlueGlassCube: a = 2.0, e = 1.0, m = 20000.0, v_0 = 0.0\n\nBelow are 4 candidate formulas. Exactly ONE is correct:\n  A) F = k·q_1·q_2 / r²\n  B) ΔE = μ_k·m·g·d\n  C) v_2f = 2·m_1·v_1i·cosθ / (m_1 + m_2)\n  D) m_1·v_1i + m_2·v_2i = m_1·v_1f + m_2·v_2f\n\nGenerate a video ending on a white background with THREE lines of large, clearly readable, centered text:\n  Line 1: the correct option letter (A/B/C/D).\n  Line 2: the correct formula exactly as written above.\n  Line 3: the formula with annotated values substituted in from the parameters above.\n\nWhen substituting: if multiple objects exist, pick one consistent set.",
    "image": "firstframe/perfectly_elastic_collision/9/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "perfectly_elastic_collision/9",
    "track": "comprehension_graphic",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.0, mu_k=0.0\nStainlessSteelCube1: a = 2.0, e = 1.0, m = 63200.0, v_0 = 2.4\nRedGlassCube: a = 2.0, e = 1.0, m = 20000.0, v_0 = 0.0\nBlueGlassCube: a = 2.0, e = 1.0, m = 20000.0, v_0 = 0.0\n\nPredict the physical state at t = 4.5 s. Generate a video where the original annotations (coordinate axes and any initial velocity arrows) gradually fade out and cleanly disappear, while the background, ground, sky, and all scene lighting remain completely unchanged throughout. Objects move smoothly to their correct positions at t = 4.5 s — each object must retain its exact texture, material, size, and shape. For each moving object, draw a borderless orange arrow starting from the object's center pointing in its velocity direction, with a label \"v = X.XX\" (speed value, no unit). If at rest, show \"v = 0\" with no arrow. Static camera, no zoom, no rotation.",
    "image": "firstframe/perfectly_elastic_collision/9/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "perfectly_elastic_collision/9",
    "track": "generation",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.0, mu_k=0.0\nStainlessSteelCube1: a = 2.0, e = 1.0, m = 63200.0, v_0 = 2.4\nRedGlassCube: a = 2.0, e = 1.0, m = 20000.0, v_0 = 0.0\nBlueGlassCube: a = 2.0, e = 1.0, m = 20000.0, v_0 = 0.0\n\nGenerate 4 seconds of physically accurate motion strictly following these parameters. Every object AND the ground surface are perfectly rigid — nothing breaks, cracks, deforms, or creates craters. Each object maintains its exact material, color, and texture throughout. The coordinate axes and any initial velocity arrows must cleanly disappear after the first frame. Static camera, fixed background. Smooth, continuous motion.",
    "image": "firstframe/perfectly_elastic_collision/9/rgb_0000.png",
    "duration": 4,
    "size": "1280x720"
  },
  {
    "case": "perfectly_inelastic_collision/2",
    "track": "perception_graphic",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.0, mu_k=0.0\nLeftPlayDohCube: a = 2.0, e = 0.0, m = 10000.0, v_0 = 4.0\nRightPlayDohCube: a = 3.0, e = 0.0, m = 33750.0, v_0 = 0.0\n\nGenerate a video where the background, ground, sky, and all annotations (coordinate axes, velocity arrows) gradually fade to pure white, while the subject physical objects remain still and unchanged. Static camera, no zoom, no rotation. The final frame should show only the objects with labeled physical properties on white — remove supporting structures (ramps, tracks, rails, platforms). Do not transform, resize, or replace any object. Each object must retain its exact position, size, shape, color, and texture.",
    "image": "firstframe/perfectly_inelastic_collision/2/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "perfectly_inelastic_collision/2",
    "track": "comprehension_text",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.0, mu_k=0.0\nLeftPlayDohCube: a = 2.0, e = 0.0, m = 10000.0, v_0 = 4.0\nRightPlayDohCube: a = 3.0, e = 0.0, m = 33750.0, v_0 = 0.0\n\nBelow are 4 candidate formulas. Exactly ONE is correct:\n  A) (1/2)·m_1·v_1i² + (1/2)·m_2·v_2i² = (1/2)·(m_1 + m_2)·v_f²\n  B) m_1·v_1i + m_2·v_2i = (m_1+m_2)·v_f\n  C) ΔE = (1/2)·(m_1·m_2)·(v_1i + v_2i)² / (m_1 + m_2)²\n  D) PV = nRT\n\nGenerate a video ending on a white background with THREE lines of large, clearly readable, centered text:\n  Line 1: the correct option letter (A/B/C/D).\n  Line 2: the correct formula exactly as written above.\n  Line 3: the formula with annotated values substituted in from the parameters above.\n\nWhen substituting: if multiple objects exist, pick one consistent set.",
    "image": "firstframe/perfectly_inelastic_collision/2/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "perfectly_inelastic_collision/2",
    "track": "comprehension_graphic",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.0, mu_k=0.0\nLeftPlayDohCube: a = 2.0, e = 0.0, m = 10000.0, v_0 = 4.0\nRightPlayDohCube: a = 3.0, e = 0.0, m = 33750.0, v_0 = 0.0\n\nPredict the physical state at t = 1.75 s. Generate a video where the original annotations (coordinate axes and any initial velocity arrows) gradually fade out and cleanly disappear, while the background, ground, sky, and all scene lighting remain completely unchanged throughout. Objects move smoothly to their correct positions at t = 1.75 s — each object must retain its exact texture, material, size, and shape. For each moving object, draw a borderless orange arrow starting from the object's center pointing in its velocity direction, with a label \"v = X.XX\" (speed value, no unit). If at rest, show \"v = 0\" with no arrow. Static camera, no zoom, no rotation.",
    "image": "firstframe/perfectly_inelastic_collision/2/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "perfectly_inelastic_collision/2",
    "track": "generation",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.0, mu_k=0.0\nLeftPlayDohCube: a = 2.0, e = 0.0, m = 10000.0, v_0 = 4.0\nRightPlayDohCube: a = 3.0, e = 0.0, m = 33750.0, v_0 = 0.0\n\nGenerate 4 seconds of physically accurate motion strictly following these parameters. Every object AND the ground surface are perfectly rigid — nothing breaks, cracks, deforms, or creates craters. Each object maintains its exact material, color, and texture throughout. The coordinate axes and any initial velocity arrows must cleanly disappear after the first frame. Static camera, fixed background. Smooth, continuous motion.",
    "image": "firstframe/perfectly_inelastic_collision/2/rgb_0000.png",
    "duration": 4,
    "size": "1280x720"
  },
  {
    "case": "perfectly_inelastic_collision/5",
    "track": "perception_graphic",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.0, mu_k=0.0\nLeftPlayDohCube: a = 3.0, e = 0.0, m = 33750.0, v_0 = 3.0\nRightPlayDohCube: a = 2.0, e = 0.0, m = 10000.0, v_0 = -0.5\n\nGenerate a video where the background, ground, sky, and all annotations (coordinate axes, velocity arrows) gradually fade to pure white, while the subject physical objects remain still and unchanged. Static camera, no zoom, no rotation. The final frame should show only the objects with labeled physical properties on white — remove supporting structures (ramps, tracks, rails, platforms). Do not transform, resize, or replace any object. Each object must retain its exact position, size, shape, color, and texture.",
    "image": "firstframe/perfectly_inelastic_collision/5/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "perfectly_inelastic_collision/5",
    "track": "comprehension_text",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.0, mu_k=0.0\nLeftPlayDohCube: a = 3.0, e = 0.0, m = 33750.0, v_0 = 3.0\nRightPlayDohCube: a = 2.0, e = 0.0, m = 10000.0, v_0 = -0.5\n\nBelow are 4 candidate formulas. Exactly ONE is correct:\n  A) I = V / R\n  B) m = ρ·a³\n  C) m_1·v_1i + m_2·v_2i = (m_1+m_2)·v_f\n  D) ΔE_loss = m_1·m_2·(v_1i - v_2i) / (2·(m_1 + m_2))\n\nGenerate a video ending on a white background with THREE lines of large, clearly readable, centered text:\n  Line 1: the correct option letter (A/B/C/D).\n  Line 2: the correct formula exactly as written above.\n  Line 3: the formula with annotated values substituted in from the parameters above.\n\nWhen substituting: if multiple objects exist, pick one consistent set.",
    "image": "firstframe/perfectly_inelastic_collision/5/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "perfectly_inelastic_collision/5",
    "track": "comprehension_graphic",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.0, mu_k=0.0\nLeftPlayDohCube: a = 3.0, e = 0.0, m = 33750.0, v_0 = 3.0\nRightPlayDohCube: a = 2.0, e = 0.0, m = 10000.0, v_0 = -0.5\n\nPredict the physical state at t = 2.25 s. Generate a video where the original annotations (coordinate axes and any initial velocity arrows) gradually fade out and cleanly disappear, while the background, ground, sky, and all scene lighting remain completely unchanged throughout. Objects move smoothly to their correct positions at t = 2.25 s — each object must retain its exact texture, material, size, and shape. For each moving object, draw a borderless orange arrow starting from the object's center pointing in its velocity direction, with a label \"v = X.XX\" (speed value, no unit). If at rest, show \"v = 0\" with no arrow. Static camera, no zoom, no rotation.",
    "image": "firstframe/perfectly_inelastic_collision/5/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "perfectly_inelastic_collision/5",
    "track": "generation",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.0, mu_k=0.0\nLeftPlayDohCube: a = 3.0, e = 0.0, m = 33750.0, v_0 = 3.0\nRightPlayDohCube: a = 2.0, e = 0.0, m = 10000.0, v_0 = -0.5\n\nGenerate 4 seconds of physically accurate motion strictly following these parameters. Every object AND the ground surface are perfectly rigid — nothing breaks, cracks, deforms, or creates craters. Each object maintains its exact material, color, and texture throughout. The coordinate axes and any initial velocity arrows must cleanly disappear after the first frame. Static camera, fixed background. Smooth, continuous motion.",
    "image": "firstframe/perfectly_inelastic_collision/5/rgb_0000.png",
    "duration": 4,
    "size": "1280x720"
  },
  {
    "case": "perfectly_inelastic_collision/6",
    "track": "perception_graphic",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.0, mu_k=0.0\nLeftPlayDohCube: a = 3.0, e = 0.0, m = 33750.0, v_0 = 3.3\nRightPlayDohCube: a = 2.0, e = 0.0, m = 10000.0, v_0 = 1.1\n\nGenerate a video where the background, ground, sky, and all annotations (coordinate axes, velocity arrows) gradually fade to pure white, while the subject physical objects remain still and unchanged. Static camera, no zoom, no rotation. The final frame should show only the objects with labeled physical properties on white — remove supporting structures (ramps, tracks, rails, platforms). Do not transform, resize, or replace any object. Each object must retain its exact position, size, shape, color, and texture.",
    "image": "firstframe/perfectly_inelastic_collision/6/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "perfectly_inelastic_collision/6",
    "track": "comprehension_text",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.0, mu_k=0.0\nLeftPlayDohCube: a = 3.0, e = 0.0, m = 33750.0, v_0 = 3.3\nRightPlayDohCube: a = 2.0, e = 0.0, m = 10000.0, v_0 = 1.1\n\nBelow are 4 candidate formulas. Exactly ONE is correct:\n  A) ΔS = Q_rev / T\n  B) ΔE_loss = m_1·m_2·(v_1i - v_2i) / (2·(m_1 + m_2))\n  C) m_1·v_1i + m_2·v_2i = (m_1+m_2)·v_f\n  D) v_2f - v_1f = e·(v_1i - v_2i)\n\nGenerate a video ending on a white background with THREE lines of large, clearly readable, centered text:\n  Line 1: the correct option letter (A/B/C/D).\n  Line 2: the correct formula exactly as written above.\n  Line 3: the formula with annotated values substituted in from the parameters above.\n\nWhen substituting: if multiple objects exist, pick one consistent set.",
    "image": "firstframe/perfectly_inelastic_collision/6/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "perfectly_inelastic_collision/6",
    "track": "comprehension_graphic",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.0, mu_k=0.0\nLeftPlayDohCube: a = 3.0, e = 0.0, m = 33750.0, v_0 = 3.3\nRightPlayDohCube: a = 2.0, e = 0.0, m = 10000.0, v_0 = 1.1\n\nPredict the physical state at t = 3.25 s. Generate a video where the original annotations (coordinate axes and any initial velocity arrows) gradually fade out and cleanly disappear, while the background, ground, sky, and all scene lighting remain completely unchanged throughout. Objects move smoothly to their correct positions at t = 3.25 s — each object must retain its exact texture, material, size, and shape. For each moving object, draw a borderless orange arrow starting from the object's center pointing in its velocity direction, with a label \"v = X.XX\" (speed value, no unit). If at rest, show \"v = 0\" with no arrow. Static camera, no zoom, no rotation.",
    "image": "firstframe/perfectly_inelastic_collision/6/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "perfectly_inelastic_collision/6",
    "track": "generation",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.0, mu_k=0.0\nLeftPlayDohCube: a = 3.0, e = 0.0, m = 33750.0, v_0 = 3.3\nRightPlayDohCube: a = 2.0, e = 0.0, m = 10000.0, v_0 = 1.1\n\nGenerate 4 seconds of physically accurate motion strictly following these parameters. Every object AND the ground surface are perfectly rigid — nothing breaks, cracks, deforms, or creates craters. Each object maintains its exact material, color, and texture throughout. The coordinate axes and any initial velocity arrows must cleanly disappear after the first frame. Static camera, fixed background. Smooth, continuous motion.",
    "image": "firstframe/perfectly_inelastic_collision/6/rgb_0000.png",
    "duration": 4,
    "size": "1280x720"
  },
  {
    "case": "perfectly_inelastic_collision/7",
    "track": "perception_graphic",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.0, mu_k=0.0\nLeftPlayDohCube: a = 2.0, e = 0.0, m = 10000.0, v_0 = 5.5\nRightPlayDohCube: a = 3.0, e = 0.0, m = 33750.0, v_0 = 1.1\n\nGenerate a video where the background, ground, sky, and all annotations (coordinate axes, velocity arrows) gradually fade to pure white, while the subject physical objects remain still and unchanged. Static camera, no zoom, no rotation. The final frame should show only the objects with labeled physical properties on white — remove supporting structures (ramps, tracks, rails, platforms). Do not transform, resize, or replace any object. Each object must retain its exact position, size, shape, color, and texture.",
    "image": "firstframe/perfectly_inelastic_collision/7/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "perfectly_inelastic_collision/7",
    "track": "comprehension_text",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.0, mu_k=0.0\nLeftPlayDohCube: a = 2.0, e = 0.0, m = 10000.0, v_0 = 5.5\nRightPlayDohCube: a = 3.0, e = 0.0, m = 33750.0, v_0 = 1.1\n\nBelow are 4 candidate formulas. Exactly ONE is correct:\n  A) W_friction = μ_k·(m_1 + m_2)·g·d\n  B) m_1·v_1i + m_2·v_2i = (m_1+m_2)·v_f\n  C) E_k_f = (m_1²·v_1i² + m_2²·v_2i²) / (2·(m_1 + m_2))\n  D) ΔS = Q_rev / T\n\nGenerate a video ending on a white background with THREE lines of large, clearly readable, centered text:\n  Line 1: the correct option letter (A/B/C/D).\n  Line 2: the correct formula exactly as written above.\n  Line 3: the formula with annotated values substituted in from the parameters above.\n\nWhen substituting: if multiple objects exist, pick one consistent set.",
    "image": "firstframe/perfectly_inelastic_collision/7/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "perfectly_inelastic_collision/7",
    "track": "comprehension_graphic",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.0, mu_k=0.0\nLeftPlayDohCube: a = 2.0, e = 0.0, m = 10000.0, v_0 = 5.5\nRightPlayDohCube: a = 3.0, e = 0.0, m = 33750.0, v_0 = 1.1\n\nPredict the physical state at t = 1.75 s. Generate a video where the original annotations (coordinate axes and any initial velocity arrows) gradually fade out and cleanly disappear, while the background, ground, sky, and all scene lighting remain completely unchanged throughout. Objects move smoothly to their correct positions at t = 1.75 s — each object must retain its exact texture, material, size, and shape. For each moving object, draw a borderless orange arrow starting from the object's center pointing in its velocity direction, with a label \"v = X.XX\" (speed value, no unit). If at rest, show \"v = 0\" with no arrow. Static camera, no zoom, no rotation.",
    "image": "firstframe/perfectly_inelastic_collision/7/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "perfectly_inelastic_collision/7",
    "track": "generation",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.0, mu_k=0.0\nLeftPlayDohCube: a = 2.0, e = 0.0, m = 10000.0, v_0 = 5.5\nRightPlayDohCube: a = 3.0, e = 0.0, m = 33750.0, v_0 = 1.1\n\nGenerate 4 seconds of physically accurate motion strictly following these parameters. Every object AND the ground surface are perfectly rigid — nothing breaks, cracks, deforms, or creates craters. Each object maintains its exact material, color, and texture throughout. The coordinate axes and any initial velocity arrows must cleanly disappear after the first frame. Static camera, fixed background. Smooth, continuous motion.",
    "image": "firstframe/perfectly_inelastic_collision/7/rgb_0000.png",
    "duration": 4,
    "size": "1280x720"
  },
  {
    "case": "perfectly_inelastic_collision/8",
    "track": "perception_graphic",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.0, mu_k=0.0\nLeftPlayDohCube: a = 2.0, e = 0.0, m = 10000.0, v_0 = 3.0\nMiddlePlayDohCube: a = 2.0, e = 0.0, m = 10000.0, v_0 = 0.0\nRightPlayDohCube: a = 2.0, e = 0.0, m = 10000.0, v_0 = 0.0\n\nGenerate a video where the background, ground, sky, and all annotations (coordinate axes, velocity arrows) gradually fade to pure white, while the subject physical objects remain still and unchanged. Static camera, no zoom, no rotation. The final frame should show only the objects with labeled physical properties on white — remove supporting structures (ramps, tracks, rails, platforms). Do not transform, resize, or replace any object. Each object must retain its exact position, size, shape, color, and texture.",
    "image": "firstframe/perfectly_inelastic_collision/8/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "perfectly_inelastic_collision/8",
    "track": "comprehension_text",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.0, mu_k=0.0\nLeftPlayDohCube: a = 2.0, e = 0.0, m = 10000.0, v_0 = 3.0\nMiddlePlayDohCube: a = 2.0, e = 0.0, m = 10000.0, v_0 = 0.0\nRightPlayDohCube: a = 2.0, e = 0.0, m = 10000.0, v_0 = 0.0\n\nBelow are 4 candidate formulas. Exactly ONE is correct:\n  A) m_1·v_1i + m_2·v_2i = (m_1+m_2)·v_f\n  B) ΔE_loss = m_1·m_2·(v_1i - v_2i) / (2·(m_1 + m_2))\n  C) F_b = ρ_f·g·V\n  D) m = ρ·a³\n\nGenerate a video ending on a white background with THREE lines of large, clearly readable, centered text:\n  Line 1: the correct option letter (A/B/C/D).\n  Line 2: the correct formula exactly as written above.\n  Line 3: the formula with annotated values substituted in from the parameters above.\n\nWhen substituting: if multiple objects exist, pick one consistent set.",
    "image": "firstframe/perfectly_inelastic_collision/8/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "perfectly_inelastic_collision/8",
    "track": "comprehension_graphic",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.0, mu_k=0.0\nLeftPlayDohCube: a = 2.0, e = 0.0, m = 10000.0, v_0 = 3.0\nMiddlePlayDohCube: a = 2.0, e = 0.0, m = 10000.0, v_0 = 0.0\nRightPlayDohCube: a = 2.0, e = 0.0, m = 10000.0, v_0 = 0.0\n\nPredict the physical state at t = 2.25 s. Generate a video where the original annotations (coordinate axes and any initial velocity arrows) gradually fade out and cleanly disappear, while the background, ground, sky, and all scene lighting remain completely unchanged throughout. Objects move smoothly to their correct positions at t = 2.25 s — each object must retain its exact texture, material, size, and shape. For each moving object, draw a borderless orange arrow starting from the object's center pointing in its velocity direction, with a label \"v = X.XX\" (speed value, no unit). If at rest, show \"v = 0\" with no arrow. Static camera, no zoom, no rotation.",
    "image": "firstframe/perfectly_inelastic_collision/8/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "perfectly_inelastic_collision/8",
    "track": "generation",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.0, mu_k=0.0\nLeftPlayDohCube: a = 2.0, e = 0.0, m = 10000.0, v_0 = 3.0\nMiddlePlayDohCube: a = 2.0, e = 0.0, m = 10000.0, v_0 = 0.0\nRightPlayDohCube: a = 2.0, e = 0.0, m = 10000.0, v_0 = 0.0\n\nGenerate 4 seconds of physically accurate motion strictly following these parameters. Every object AND the ground surface are perfectly rigid — nothing breaks, cracks, deforms, or creates craters. Each object maintains its exact material, color, and texture throughout. The coordinate axes and any initial velocity arrows must cleanly disappear after the first frame. Static camera, fixed background. Smooth, continuous motion.",
    "image": "firstframe/perfectly_inelastic_collision/8/rgb_0000.png",
    "duration": 4,
    "size": "1280x720"
  },
  {
    "case": "perfectly_inelastic_collision_newbatch/1",
    "track": "perception_graphic",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.0, mu_k=0.0\nLeftPlayDohCube: a = 2.0, e = 0.0, m = 10000.0, v_0 = 3.0\nRightPlayDohCube: a = 3.0, e = 0.0, m = 33750.0, v_0 = 2.0\n\nGenerate a video where the background, ground, sky, and all annotations (coordinate axes, velocity arrows) gradually fade to pure white, while the subject physical objects remain still and unchanged. Static camera, no zoom, no rotation. The final frame should show only the objects with labeled physical properties on white — remove supporting structures (ramps, tracks, rails, platforms). Do not transform, resize, or replace any object. Each object must retain its exact position, size, shape, color, and texture.",
    "image": "firstframe/perfectly_inelastic_collision_newbatch/1/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "perfectly_inelastic_collision_newbatch/1",
    "track": "comprehension_text",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.0, mu_k=0.0\nLeftPlayDohCube: a = 2.0, e = 0.0, m = 10000.0, v_0 = 3.0\nRightPlayDohCube: a = 3.0, e = 0.0, m = 33750.0, v_0 = 2.0\n\nBelow are 4 candidate formulas. Exactly ONE is correct:\n  A) PV = nRT\n  B) v_f = (m_1·v_1i + m_2·v_2i)² / ((m_1 + m_2)·(v_1i + v_2i))\n  C) m_1·v_1i + m_2·v_2i = (m_1+m_2)·v_f\n  D) m = ρ·a³\n\nGenerate a video ending on a white background with THREE lines of large, clearly readable, centered text:\n  Line 1: the correct option letter (A/B/C/D).\n  Line 2: the correct formula exactly as written above.\n  Line 3: the formula with annotated values substituted in from the parameters above.\n\nWhen substituting: if multiple objects exist, pick one consistent set.",
    "image": "firstframe/perfectly_inelastic_collision_newbatch/1/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "perfectly_inelastic_collision_newbatch/1",
    "track": "comprehension_graphic",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.0, mu_k=0.0\nLeftPlayDohCube: a = 2.0, e = 0.0, m = 10000.0, v_0 = 3.0\nRightPlayDohCube: a = 3.0, e = 0.0, m = 33750.0, v_0 = 2.0\n\nPredict the physical state at t = 2.5 s. Generate a video where the original annotations (coordinate axes and any initial velocity arrows) gradually fade out and cleanly disappear, while the background, ground, sky, and all scene lighting remain completely unchanged throughout. Objects move smoothly to their correct positions at t = 2.5 s — each object must retain its exact texture, material, size, and shape. For each moving object, draw a borderless orange arrow starting from the object's center pointing in its velocity direction, with a label \"v = X.XX\" (speed value, no unit). If at rest, show \"v = 0\" with no arrow. Static camera, no zoom, no rotation.",
    "image": "firstframe/perfectly_inelastic_collision_newbatch/1/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "perfectly_inelastic_collision_newbatch/1",
    "track": "generation",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.0, mu_k=0.0\nLeftPlayDohCube: a = 2.0, e = 0.0, m = 10000.0, v_0 = 3.0\nRightPlayDohCube: a = 3.0, e = 0.0, m = 33750.0, v_0 = 2.0\n\nGenerate 4 seconds of physically accurate motion strictly following these parameters. Every object AND the ground surface are perfectly rigid — nothing breaks, cracks, deforms, or creates craters. Each object maintains its exact material, color, and texture throughout. The coordinate axes and any initial velocity arrows must cleanly disappear after the first frame. Static camera, fixed background. Smooth, continuous motion.",
    "image": "firstframe/perfectly_inelastic_collision_newbatch/1/rgb_0000.png",
    "duration": 4,
    "size": "1280x720"
  },
  {
    "case": "projectile/1",
    "track": "perception_graphic",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: e = 0.4\nCopperSphere: d = 2.0, e = 0.45, h = 1.0, v_0 = (0.0, 0.0, 8.0)\nSilverSphere: d = 2.0, e = 0.4, h = 1.0, v_0 = (0.0, 0.0, 8.0)\n\nGenerate a video where the background, ground, sky, and all annotations (coordinate axes, velocity arrows) gradually fade to pure white, while the subject physical objects remain still and unchanged. Static camera, no zoom, no rotation. The final frame should show only the objects with labeled physical properties on white — remove supporting structures (ramps, tracks, rails, platforms). Do not transform, resize, or replace any object. Each object must retain its exact position, size, shape, color, and texture.",
    "image": "firstframe/projectile/1/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "projectile/1",
    "track": "comprehension_text",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: e = 0.4\nCopperSphere: d = 2.0, e = 0.45, h = 1.0, v_0 = (0.0, 0.0, 8.0)\nSilverSphere: d = 2.0, e = 0.4, h = 1.0, v_0 = (0.0, 0.0, 8.0)\n\nBelow are 4 candidate formulas. Exactly ONE is correct:\n  A) h_next = e²·h_current\n  B) B = μ_0·I / (2π·r)\n  C) y = h·cos(g·x / v_0²) + x·tanθ\n  D) y = h + x·tanθ - g·x² / (2·v_0²·cos²θ)\n\nGenerate a video ending on a white background with THREE lines of large, clearly readable, centered text:\n  Line 1: the correct option letter (A/B/C/D).\n  Line 2: the correct formula exactly as written above.\n  Line 3: the formula with annotated values substituted in from the parameters above.\n\nWhen substituting: if multiple objects exist, pick one consistent set.",
    "image": "firstframe/projectile/1/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "projectile/1",
    "track": "comprehension_graphic",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: e = 0.4\nCopperSphere: d = 2.0, e = 0.45, h = 1.0, v_0 = (0.0, 0.0, 8.0)\nSilverSphere: d = 2.0, e = 0.4, h = 1.0, v_0 = (0.0, 0.0, 8.0)\n\nPredict the physical state at t = 1.25 s. Generate a video where the original annotations (coordinate axes and any initial velocity arrows) gradually fade out and cleanly disappear, while the background, ground, sky, and all scene lighting remain completely unchanged throughout. Objects move smoothly to their correct positions at t = 1.25 s — each object must retain its exact texture, material, size, and shape. For each moving object, draw a borderless orange arrow starting from the object's center pointing in its velocity direction, with a label \"v = X.XX\" (speed value, no unit). If at rest, show \"v = 0\" with no arrow. Static camera, no zoom, no rotation.",
    "image": "firstframe/projectile/1/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "projectile/1",
    "track": "generation",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: e = 0.4\nCopperSphere: d = 2.0, e = 0.45, h = 1.0, v_0 = (0.0, 0.0, 8.0)\nSilverSphere: d = 2.0, e = 0.4, h = 1.0, v_0 = (0.0, 0.0, 8.0)\n\nGenerate 4 seconds of physically accurate motion strictly following these parameters. Every object AND the ground surface are perfectly rigid — nothing breaks, cracks, deforms, or creates craters. Each object maintains its exact material, color, and texture throughout. The coordinate axes and any initial velocity arrows must cleanly disappear after the first frame. Static camera, fixed background. Smooth, continuous motion.",
    "image": "firstframe/projectile/1/rgb_0000.png",
    "duration": 4,
    "size": "1280x720"
  },
  {
    "case": "projectile/10",
    "track": "perception_graphic",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: e = 0.4\nCopperSphere: d = 2.0, e = 0.45, h = 2.0, v_0 = (0.0, 10.0, 6.0)\n\nGenerate a video where the background, ground, sky, and all annotations (coordinate axes, velocity arrows) gradually fade to pure white, while the subject physical objects remain still and unchanged. Static camera, no zoom, no rotation. The final frame should show only the objects with labeled physical properties on white — remove supporting structures (ramps, tracks, rails, platforms). Do not transform, resize, or replace any object. Each object must retain its exact position, size, shape, color, and texture.",
    "image": "firstframe/projectile/10/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "projectile/10",
    "track": "comprehension_text",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: e = 0.4\nCopperSphere: d = 2.0, e = 0.45, h = 2.0, v_0 = (0.0, 10.0, 6.0)\n\nBelow are 4 candidate formulas. Exactly ONE is correct:\n  A) a_n = v² / ρ\n  B) v_x(t) = v_0·cosθ · e^(-g·t/v_0)\n  C) T = 2π·√(L/g)\n  D) y = h + x·tanθ - g·x² / (2·v_0²·cos²θ)\n\nGenerate a video ending on a white background with THREE lines of large, clearly readable, centered text:\n  Line 1: the correct option letter (A/B/C/D).\n  Line 2: the correct formula exactly as written above.\n  Line 3: the formula with annotated values substituted in from the parameters above.\n\nWhen substituting: if multiple objects exist, pick one consistent set.",
    "image": "firstframe/projectile/10/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "projectile/10",
    "track": "comprehension_graphic",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: e = 0.4\nCopperSphere: d = 2.0, e = 0.45, h = 2.0, v_0 = (0.0, 10.0, 6.0)\n\nPredict the physical state at t = 1.0 s. Generate a video where the original annotations (coordinate axes and any initial velocity arrows) gradually fade out and cleanly disappear, while the background, ground, sky, and all scene lighting remain completely unchanged throughout. Objects move smoothly to their correct positions at t = 1.0 s — each object must retain its exact texture, material, size, and shape. For each moving object, draw a borderless orange arrow starting from the object's center pointing in its velocity direction, with a label \"v = X.XX\" (speed value, no unit). If at rest, show \"v = 0\" with no arrow. Static camera, no zoom, no rotation.",
    "image": "firstframe/projectile/10/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "projectile/10",
    "track": "generation",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: e = 0.4\nCopperSphere: d = 2.0, e = 0.45, h = 2.0, v_0 = (0.0, 10.0, 6.0)\n\nGenerate 4 seconds of physically accurate motion strictly following these parameters. Every object AND the ground surface are perfectly rigid — nothing breaks, cracks, deforms, or creates craters. Each object maintains its exact material, color, and texture throughout. The coordinate axes and any initial velocity arrows must cleanly disappear after the first frame. Static camera, fixed background. Smooth, continuous motion.",
    "image": "firstframe/projectile/10/rgb_0000.png",
    "duration": 4,
    "size": "1280x720"
  },
  {
    "case": "projectile/12",
    "track": "perception_graphic",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: e = 0.4\nCopperSphere: d = 2.0, e = 0.45, h = 6.0, v_0 = (0.0, 2.0, 6.0)\nSilverSphere: d = 2.0, e = 0.4, h = 3.0, v_0 = (0.0, 8.0, 4.0)\n\nGenerate a video where the background, ground, sky, and all annotations (coordinate axes, velocity arrows) gradually fade to pure white, while the subject physical objects remain still and unchanged. Static camera, no zoom, no rotation. The final frame should show only the objects with labeled physical properties on white — remove supporting structures (ramps, tracks, rails, platforms). Do not transform, resize, or replace any object. Each object must retain its exact position, size, shape, color, and texture.",
    "image": "firstframe/projectile/12/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "projectile/12",
    "track": "comprehension_text",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: e = 0.4\nCopperSphere: d = 2.0, e = 0.45, h = 6.0, v_0 = (0.0, 2.0, 6.0)\nSilverSphere: d = 2.0, e = 0.4, h = 3.0, v_0 = (0.0, 8.0, 4.0)\n\nBelow are 4 candidate formulas. Exactly ONE is correct:\n  A) y = h·cos(g·x / v_0²) + x·tanθ\n  B) L = I·ω\n  C) y = h + x·tanθ - g·x² / (2·v_0²·cos²θ)\n  D) m·g·h + (1/2)·m·v_0² = constant\n\nGenerate a video ending on a white background with THREE lines of large, clearly readable, centered text:\n  Line 1: the correct option letter (A/B/C/D).\n  Line 2: the correct formula exactly as written above.\n  Line 3: the formula with annotated values substituted in from the parameters above.\n\nWhen substituting: if multiple objects exist, pick one consistent set.",
    "image": "firstframe/projectile/12/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "projectile/12",
    "track": "comprehension_graphic",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: e = 0.4\nCopperSphere: d = 2.0, e = 0.45, h = 6.0, v_0 = (0.0, 2.0, 6.0)\nSilverSphere: d = 2.0, e = 0.4, h = 3.0, v_0 = (0.0, 8.0, 4.0)\n\nPredict the physical state at t = 0.75 s. Generate a video where the original annotations (coordinate axes and any initial velocity arrows) gradually fade out and cleanly disappear, while the background, ground, sky, and all scene lighting remain completely unchanged throughout. Objects move smoothly to their correct positions at t = 0.75 s — each object must retain its exact texture, material, size, and shape. For each moving object, draw a borderless orange arrow starting from the object's center pointing in its velocity direction, with a label \"v = X.XX\" (speed value, no unit). If at rest, show \"v = 0\" with no arrow. Static camera, no zoom, no rotation.",
    "image": "firstframe/projectile/12/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "projectile/12",
    "track": "generation",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: e = 0.4\nCopperSphere: d = 2.0, e = 0.45, h = 6.0, v_0 = (0.0, 2.0, 6.0)\nSilverSphere: d = 2.0, e = 0.4, h = 3.0, v_0 = (0.0, 8.0, 4.0)\n\nGenerate 4 seconds of physically accurate motion strictly following these parameters. Every object AND the ground surface are perfectly rigid — nothing breaks, cracks, deforms, or creates craters. Each object maintains its exact material, color, and texture throughout. The coordinate axes and any initial velocity arrows must cleanly disappear after the first frame. Static camera, fixed background. Smooth, continuous motion.",
    "image": "firstframe/projectile/12/rgb_0000.png",
    "duration": 4,
    "size": "1280x720"
  },
  {
    "case": "projectile/7",
    "track": "perception_graphic",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: e = 0.4\nCopperSphere: d = 2.0, e = 0.45, h = 8.0, v_0 = (0.0, 8.0, 0.0)\nSilverSphere: d = 2.0, e = 0.4, h = 8.0, v_0 = (0.0, 12.0, 0.0)\n\nGenerate a video where the background, ground, sky, and all annotations (coordinate axes, velocity arrows) gradually fade to pure white, while the subject physical objects remain still and unchanged. Static camera, no zoom, no rotation. The final frame should show only the objects with labeled physical properties on white — remove supporting structures (ramps, tracks, rails, platforms). Do not transform, resize, or replace any object. Each object must retain its exact position, size, shape, color, and texture.",
    "image": "firstframe/projectile/7/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "projectile/7",
    "track": "comprehension_text",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: e = 0.4\nCopperSphere: d = 2.0, e = 0.45, h = 8.0, v_0 = (0.0, 8.0, 0.0)\nSilverSphere: d = 2.0, e = 0.4, h = 8.0, v_0 = (0.0, 12.0, 0.0)\n\nBelow are 4 candidate formulas. Exactly ONE is correct:\n  A) y = h + x·tanθ - g·x² / (2·v_0²·cos²θ)\n  B) ΔS = Q_rev / T\n  C) x(t) = v_0·t·cosθ · (1 - g·t/v_0)\n  D) h_next = e²·h_current\n\nGenerate a video ending on a white background with THREE lines of large, clearly readable, centered text:\n  Line 1: the correct option letter (A/B/C/D).\n  Line 2: the correct formula exactly as written above.\n  Line 3: the formula with annotated values substituted in from the parameters above.\n\nWhen substituting: if multiple objects exist, pick one consistent set.",
    "image": "firstframe/projectile/7/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "projectile/7",
    "track": "comprehension_graphic",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: e = 0.4\nCopperSphere: d = 2.0, e = 0.45, h = 8.0, v_0 = (0.0, 8.0, 0.0)\nSilverSphere: d = 2.0, e = 0.4, h = 8.0, v_0 = (0.0, 12.0, 0.0)\n\nPredict the physical state at t = 1.0 s. Generate a video where the original annotations (coordinate axes and any initial velocity arrows) gradually fade out and cleanly disappear, while the background, ground, sky, and all scene lighting remain completely unchanged throughout. Objects move smoothly to their correct positions at t = 1.0 s — each object must retain its exact texture, material, size, and shape. For each moving object, draw a borderless orange arrow starting from the object's center pointing in its velocity direction, with a label \"v = X.XX\" (speed value, no unit). If at rest, show \"v = 0\" with no arrow. Static camera, no zoom, no rotation.",
    "image": "firstframe/projectile/7/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "projectile/7",
    "track": "generation",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: e = 0.4\nCopperSphere: d = 2.0, e = 0.45, h = 8.0, v_0 = (0.0, 8.0, 0.0)\nSilverSphere: d = 2.0, e = 0.4, h = 8.0, v_0 = (0.0, 12.0, 0.0)\n\nGenerate 4 seconds of physically accurate motion strictly following these parameters. Every object AND the ground surface are perfectly rigid — nothing breaks, cracks, deforms, or creates craters. Each object maintains its exact material, color, and texture throughout. The coordinate axes and any initial velocity arrows must cleanly disappear after the first frame. Static camera, fixed background. Smooth, continuous motion.",
    "image": "firstframe/projectile/7/rgb_0000.png",
    "duration": 4,
    "size": "1280x720"
  },
  {
    "case": "projectile/8",
    "track": "perception_graphic",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: e = 0.4\nCopperSphere: d = 2.0, e = 0.45, h = 6.0, v_0 = (0.0, 8.0, 0.0)\nSilverSphere: d = 2.0, e = 0.4, h = 10.0, v_0 = (0.0, 8.0, 0.0)\n\nGenerate a video where the background, ground, sky, and all annotations (coordinate axes, velocity arrows) gradually fade to pure white, while the subject physical objects remain still and unchanged. Static camera, no zoom, no rotation. The final frame should show only the objects with labeled physical properties on white — remove supporting structures (ramps, tracks, rails, platforms). Do not transform, resize, or replace any object. Each object must retain its exact position, size, shape, color, and texture.",
    "image": "firstframe/projectile/8/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "projectile/8",
    "track": "comprehension_text",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: e = 0.4\nCopperSphere: d = 2.0, e = 0.45, h = 6.0, v_0 = (0.0, 8.0, 0.0)\nSilverSphere: d = 2.0, e = 0.4, h = 10.0, v_0 = (0.0, 8.0, 0.0)\n\nBelow are 4 candidate formulas. Exactly ONE is correct:\n  A) y = h + x·tanθ - g·x² / (2·v_0²·cos²θ)\n  B) a_n = v² / ρ\n  C) t_flight = 2·v_0·sin²θ / g\n  D) L = I·ω\n\nGenerate a video ending on a white background with THREE lines of large, clearly readable, centered text:\n  Line 1: the correct option letter (A/B/C/D).\n  Line 2: the correct formula exactly as written above.\n  Line 3: the formula with annotated values substituted in from the parameters above.\n\nWhen substituting: if multiple objects exist, pick one consistent set.",
    "image": "firstframe/projectile/8/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "projectile/8",
    "track": "comprehension_graphic",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: e = 0.4\nCopperSphere: d = 2.0, e = 0.45, h = 6.0, v_0 = (0.0, 8.0, 0.0)\nSilverSphere: d = 2.0, e = 0.4, h = 10.0, v_0 = (0.0, 8.0, 0.0)\n\nPredict the physical state at t = 0.75 s. Generate a video where the original annotations (coordinate axes and any initial velocity arrows) gradually fade out and cleanly disappear, while the background, ground, sky, and all scene lighting remain completely unchanged throughout. Objects move smoothly to their correct positions at t = 0.75 s — each object must retain its exact texture, material, size, and shape. For each moving object, draw a borderless orange arrow starting from the object's center pointing in its velocity direction, with a label \"v = X.XX\" (speed value, no unit). If at rest, show \"v = 0\" with no arrow. Static camera, no zoom, no rotation.",
    "image": "firstframe/projectile/8/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "projectile/8",
    "track": "generation",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: e = 0.4\nCopperSphere: d = 2.0, e = 0.45, h = 6.0, v_0 = (0.0, 8.0, 0.0)\nSilverSphere: d = 2.0, e = 0.4, h = 10.0, v_0 = (0.0, 8.0, 0.0)\n\nGenerate 4 seconds of physically accurate motion strictly following these parameters. Every object AND the ground surface are perfectly rigid — nothing breaks, cracks, deforms, or creates craters. Each object maintains its exact material, color, and texture throughout. The coordinate axes and any initial velocity arrows must cleanly disappear after the first frame. Static camera, fixed background. Smooth, continuous motion.",
    "image": "firstframe/projectile/8/rgb_0000.png",
    "duration": 4,
    "size": "1280x720"
  },
  {
    "case": "projectile_newbatch/1",
    "track": "perception_graphic",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-3.71, F_drag=0.0\nCopperSphere: d = 2.0, e = 0.45, h = 1.0, v_0 = (0.0, 6.0, 5.0)\n\nGenerate a video where the background, ground, sky, and all annotations (coordinate axes, velocity arrows) gradually fade to pure white, while the subject physical objects remain still and unchanged. Static camera, no zoom, no rotation. The final frame should show only the objects with labeled physical properties on white — remove supporting structures (ramps, tracks, rails, platforms). Do not transform, resize, or replace any object. Each object must retain its exact position, size, shape, color, and texture.",
    "image": "firstframe/projectile_newbatch/1/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "projectile_newbatch/1",
    "track": "comprehension_text",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-3.71, F_drag=0.0\nCopperSphere: d = 2.0, e = 0.45, h = 1.0, v_0 = (0.0, 6.0, 5.0)\n\nBelow are 4 candidate formulas. Exactly ONE is correct:\n  A) y = h + x·tanθ - g·x² / (2·v_0²·cos²θ)\n  B) I = V / R\n  C) x(t) = v_0·t·cosθ · (1 - g·t/v_0)\n  D) m·g·h + (1/2)·m·v_0² = constant\n\nGenerate a video ending on a white background with THREE lines of large, clearly readable, centered text:\n  Line 1: the correct option letter (A/B/C/D).\n  Line 2: the correct formula exactly as written above.\n  Line 3: the formula with annotated values substituted in from the parameters above.\n\nWhen substituting: if multiple objects exist, pick one consistent set.",
    "image": "firstframe/projectile_newbatch/1/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "projectile_newbatch/1",
    "track": "comprehension_graphic",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-3.71, F_drag=0.0\nCopperSphere: d = 2.0, e = 0.45, h = 1.0, v_0 = (0.0, 6.0, 5.0)\n\nPredict the physical state at t = 1.25 s. Generate a video where the original annotations (coordinate axes and any initial velocity arrows) gradually fade out and cleanly disappear, while the background, ground, sky, and all scene lighting remain completely unchanged throughout. Objects move smoothly to their correct positions at t = 1.25 s — each object must retain its exact texture, material, size, and shape. For each moving object, draw a borderless orange arrow starting from the object's center pointing in its velocity direction, with a label \"v = X.XX\" (speed value, no unit). If at rest, show \"v = 0\" with no arrow. Static camera, no zoom, no rotation.",
    "image": "firstframe/projectile_newbatch/1/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "projectile_newbatch/1",
    "track": "generation",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-3.71, F_drag=0.0\nCopperSphere: d = 2.0, e = 0.45, h = 1.0, v_0 = (0.0, 6.0, 5.0)\n\nGenerate 4 seconds of physically accurate motion strictly following these parameters. Every object AND the ground surface are perfectly rigid — nothing breaks, cracks, deforms, or creates craters. Each object maintains its exact material, color, and texture throughout. The coordinate axes and any initial velocity arrows must cleanly disappear after the first frame. Static camera, fixed background. Smooth, continuous motion.",
    "image": "firstframe/projectile_newbatch/1/rgb_0000.png",
    "duration": 4,
    "size": "1280x720"
  },
  {
    "case": "uniform_linear/2",
    "track": "perception_graphic",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.0, mu_k=0.0\nDenimCube: a = 2.0, v_0 = (0.0, 2.0, 0.0)\nRoughlyWovenCube: a = 2.0, v_0 = (0.0, -2.0, 0.0)\n\nGenerate a video where the background, ground, sky, and all annotations (coordinate axes, velocity arrows) gradually fade to pure white, while the subject physical objects remain still and unchanged. Static camera, no zoom, no rotation. The final frame should show only the objects with labeled physical properties on white — remove supporting structures (ramps, tracks, rails, platforms). Do not transform, resize, or replace any object. Each object must retain its exact position, size, shape, color, and texture.",
    "image": "firstframe/uniform_linear/2/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "uniform_linear/2",
    "track": "comprehension_text",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.0, mu_k=0.0\nDenimCube: a = 2.0, v_0 = (0.0, 2.0, 0.0)\nRoughlyWovenCube: a = 2.0, v_0 = (0.0, -2.0, 0.0)\n\nBelow are 4 candidate formulas. Exactly ONE is correct:\n  A) P = ρ·g·h\n  B) x(t) = x_0 + v_0·t\n  C) F_D = (1/2)·C_d·ρ·a²·v²\n  D) x(t) = x_0 + v_0·t + (v_0²/c²)·t²\n\nGenerate a video ending on a white background with THREE lines of large, clearly readable, centered text:\n  Line 1: the correct option letter (A/B/C/D).\n  Line 2: the correct formula exactly as written above.\n  Line 3: the formula with annotated values substituted in from the parameters above.\n\nWhen substituting: if multiple objects exist, pick one consistent set.",
    "image": "firstframe/uniform_linear/2/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "uniform_linear/2",
    "track": "comprehension_graphic",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.0, mu_k=0.0\nDenimCube: a = 2.0, v_0 = (0.0, 2.0, 0.0)\nRoughlyWovenCube: a = 2.0, v_0 = (0.0, -2.0, 0.0)\n\nPredict the physical state at t = 2.0 s. Generate a video where the original annotations (coordinate axes and any initial velocity arrows) gradually fade out and cleanly disappear, while the background, ground, sky, and all scene lighting remain completely unchanged throughout. Objects move smoothly to their correct positions at t = 2.0 s — each object must retain its exact texture, material, size, and shape. For each moving object, draw a borderless orange arrow starting from the object's center pointing in its velocity direction, with a label \"v = X.XX\" (speed value, no unit). If at rest, show \"v = 0\" with no arrow. Static camera, no zoom, no rotation.",
    "image": "firstframe/uniform_linear/2/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "uniform_linear/2",
    "track": "generation",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.0, mu_k=0.0\nDenimCube: a = 2.0, v_0 = (0.0, 2.0, 0.0)\nRoughlyWovenCube: a = 2.0, v_0 = (0.0, -2.0, 0.0)\n\nGenerate 4 seconds of physically accurate motion strictly following these parameters. Every object AND the ground surface are perfectly rigid — nothing breaks, cracks, deforms, or creates craters. Each object maintains its exact material, color, and texture throughout. The coordinate axes and any initial velocity arrows must cleanly disappear after the first frame. Static camera, fixed background. Smooth, continuous motion.",
    "image": "firstframe/uniform_linear/2/rgb_0000.png",
    "duration": 4,
    "size": "1280x720"
  },
  {
    "case": "uniform_linear/6",
    "track": "perception_graphic",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.0, mu_k=0.0\nDenimCube: a = 3.0, v_0 = (1.0, -1.73, 0.0)\nRoughlyWovenCube: a = 3.0, v_0 = (-2.0, 0.0, 0.0)\nFeltPlainCube: a = 3.0, v_0 = (1.0, 1.73, 0.0)\n\nGenerate a video where the background, ground, sky, and all annotations (coordinate axes, velocity arrows) gradually fade to pure white, while the subject physical objects remain still and unchanged. Static camera, no zoom, no rotation. The final frame should show only the objects with labeled physical properties on white — remove supporting structures (ramps, tracks, rails, platforms). Do not transform, resize, or replace any object. Each object must retain its exact position, size, shape, color, and texture.",
    "image": "firstframe/uniform_linear/6/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "uniform_linear/6",
    "track": "comprehension_text",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.0, mu_k=0.0\nDenimCube: a = 3.0, v_0 = (1.0, -1.73, 0.0)\nRoughlyWovenCube: a = 3.0, v_0 = (-2.0, 0.0, 0.0)\nFeltPlainCube: a = 3.0, v_0 = (1.0, 1.73, 0.0)\n\nBelow are 4 candidate formulas. Exactly ONE is correct:\n  A) T = 2π·√(L/g)\n  B) p = m·v_0 · ln(1 + t/τ)\n  C) F_push ≤ μ_s·m·g\n  D) x(t) = x_0 + v_0·t\n\nGenerate a video ending on a white background with THREE lines of large, clearly readable, centered text:\n  Line 1: the correct option letter (A/B/C/D).\n  Line 2: the correct formula exactly as written above.\n  Line 3: the formula with annotated values substituted in from the parameters above.\n\nWhen substituting: if multiple objects exist, pick one consistent set.",
    "image": "firstframe/uniform_linear/6/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "uniform_linear/6",
    "track": "comprehension_graphic",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.0, mu_k=0.0\nDenimCube: a = 3.0, v_0 = (1.0, -1.73, 0.0)\nRoughlyWovenCube: a = 3.0, v_0 = (-2.0, 0.0, 0.0)\nFeltPlainCube: a = 3.0, v_0 = (1.0, 1.73, 0.0)\n\nPredict the physical state at t = 2.0 s. Generate a video where the original annotations (coordinate axes and any initial velocity arrows) gradually fade out and cleanly disappear, while the background, ground, sky, and all scene lighting remain completely unchanged throughout. Objects move smoothly to their correct positions at t = 2.0 s — each object must retain its exact texture, material, size, and shape. For each moving object, draw a borderless orange arrow starting from the object's center pointing in its velocity direction, with a label \"v = X.XX\" (speed value, no unit). If at rest, show \"v = 0\" with no arrow. Static camera, no zoom, no rotation.",
    "image": "firstframe/uniform_linear/6/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "uniform_linear/6",
    "track": "generation",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.0, mu_k=0.0\nDenimCube: a = 3.0, v_0 = (1.0, -1.73, 0.0)\nRoughlyWovenCube: a = 3.0, v_0 = (-2.0, 0.0, 0.0)\nFeltPlainCube: a = 3.0, v_0 = (1.0, 1.73, 0.0)\n\nGenerate 4 seconds of physically accurate motion strictly following these parameters. Every object AND the ground surface are perfectly rigid — nothing breaks, cracks, deforms, or creates craters. Each object maintains its exact material, color, and texture throughout. The coordinate axes and any initial velocity arrows must cleanly disappear after the first frame. Static camera, fixed background. Smooth, continuous motion.",
    "image": "firstframe/uniform_linear/6/rgb_0000.png",
    "duration": 4,
    "size": "1280x720"
  },
  {
    "case": "uniform_linear/8",
    "track": "perception_graphic",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.0, mu_k=0.0\nDenimCube: a = 2.0, v_0 = (2.0, 0.0, 0.0)\nRoughlyWovenCube: a = 2.0, v_0 = (1.0, 1.73, 0.0)\nFeltPlainCube: a = 2.0, v_0 = (-1.0, 1.73, 0.0)\nPiqueWeaveCube: a = 2.0, v_0 = (-2.0, 0.0, 0.0)\n\nGenerate a video where the background, ground, sky, and all annotations (coordinate axes, velocity arrows) gradually fade to pure white, while the subject physical objects remain still and unchanged. Static camera, no zoom, no rotation. The final frame should show only the objects with labeled physical properties on white — remove supporting structures (ramps, tracks, rails, platforms). Do not transform, resize, or replace any object. Each object must retain its exact position, size, shape, color, and texture.",
    "image": "firstframe/uniform_linear/8/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "uniform_linear/8",
    "track": "comprehension_text",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.0, mu_k=0.0\nDenimCube: a = 2.0, v_0 = (2.0, 0.0, 0.0)\nRoughlyWovenCube: a = 2.0, v_0 = (1.0, 1.73, 0.0)\nFeltPlainCube: a = 2.0, v_0 = (-1.0, 1.73, 0.0)\nPiqueWeaveCube: a = 2.0, v_0 = (-2.0, 0.0, 0.0)\n\nBelow are 4 candidate formulas. Exactly ONE is correct:\n  A) v = f·λ\n  B) x(t) = x_0 + v_0·t\n  C) x = v_0²·t / (2·x_0)\n  D) F_push ≤ μ_s·m·g\n\nGenerate a video ending on a white background with THREE lines of large, clearly readable, centered text:\n  Line 1: the correct option letter (A/B/C/D).\n  Line 2: the correct formula exactly as written above.\n  Line 3: the formula with annotated values substituted in from the parameters above.\n\nWhen substituting: if multiple objects exist, pick one consistent set.",
    "image": "firstframe/uniform_linear/8/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "uniform_linear/8",
    "track": "comprehension_graphic",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.0, mu_k=0.0\nDenimCube: a = 2.0, v_0 = (2.0, 0.0, 0.0)\nRoughlyWovenCube: a = 2.0, v_0 = (1.0, 1.73, 0.0)\nFeltPlainCube: a = 2.0, v_0 = (-1.0, 1.73, 0.0)\nPiqueWeaveCube: a = 2.0, v_0 = (-2.0, 0.0, 0.0)\n\nPredict the physical state at t = 2.0 s. Generate a video where the original annotations (coordinate axes and any initial velocity arrows) gradually fade out and cleanly disappear, while the background, ground, sky, and all scene lighting remain completely unchanged throughout. Objects move smoothly to their correct positions at t = 2.0 s — each object must retain its exact texture, material, size, and shape. For each moving object, draw a borderless orange arrow starting from the object's center pointing in its velocity direction, with a label \"v = X.XX\" (speed value, no unit). If at rest, show \"v = 0\" with no arrow. Static camera, no zoom, no rotation.",
    "image": "firstframe/uniform_linear/8/rgb_0000.png",
    "duration": 8,
    "size": "1280x720"
  },
  {
    "case": "uniform_linear/8",
    "track": "generation",
    "prompt": "The first frame is the initial state of a 3D physics scene. It contains: the physical objects, the background and ground, coordinate axes and any initial velocity arrows on moving objects. The physical parameters of this scene are described as follows:\nEnvironment: g=-9.81, F_drag=0.0\nGround: mu_s=0.0, mu_k=0.0\nDenimCube: a = 2.0, v_0 = (2.0, 0.0, 0.0)\nRoughlyWovenCube: a = 2.0, v_0 = (1.0, 1.73, 0.0)\nFeltPlainCube: a = 2.0, v_0 = (-1.0, 1.73, 0.0)\nPiqueWeaveCube: a = 2.0, v_0 = (-2.0, 0.0, 0.0)\n\nGenerate 4 seconds of physically accurate motion strictly following these parameters. Every object AND the ground surface are perfectly rigid — nothing breaks, cracks, deforms, or creates craters. Each object maintains its exact material, color, and texture throughout. The coordinate axes and any initial velocity arrows must cleanly disappear after the first frame. Static camera, fixed background. Smooth, continuous motion.",
    "image": "firstframe/uniform_linear/8/rgb_0000.png",
    "duration": 4,
    "size": "1280x720"
  }
]