Domain: Natural Science — Physics
Target concept: Isochrone

Video generation prompt: A cycloid track is placed in a vertical plane. Two small balls are released from different heights (half of the track length, and the full length), and the order in which the balls reach the endpoint is observed.

Evaluation guide:
(i) Target concept: Tautochrone (isochrone) property of a cycloid curve under uniform gravity. A ball released from rest at any point on the curve takes the same time to reach the curve's lowest point, regardless of where along the curve it started. A valid demonstration therefore shows two balls, released from rest at different points on the same cycloid (the half-length position and the full-length/top position), reaching the shared bottom endpoint at essentially the same moment, not one ball arriving measurably ahead of the other.
Minimum mechanism: Rigid cycloid geometry; vertical orientation; motion governed by gravity alone (no friction dominance, no external push); both balls released from rest; a single shared endpoint at the lowest point of the curve.
(ii)Storyline: [Frame 0] Static shot: vertical cycloid track with two visibly distinct balls at rest, one at the half-length position, one at the top (full-length) position. [Frame sequence A] Simultaneous release: both balls begin moving downward along the track's contour with increasing speed. [Frame sequence B] Continuous descent: each ball follows the cycloid's own contour without leaving the track or contacting anything else. [Frame sequence C] Arrival event: both balls reach the shared endpoint at, or within an imperceptible instant of, the same time; no clearly resolvable ball arrives first, illustrating that descent time did not depend on release height. [Visibility constraint] Fixed frontal view, full track in frame, no occlusion, constant lighting; the near-simultaneous arrival must be legible without annotation or narration.

Manual:
Experimental Procedure
1. Mount a rigid cycloid-shaped track vertically.
2. Place one small ball at the position halfway along the track's arc length from the top.
3. Place a second small ball at the topmost point of the track (the full-length position).
4. Release both balls simultaneously from rest.
Observation of Experimental Phenomena
Despite starting from different points on the cycloid, the two balls reach the bottom endpoint at essentially the same moment, with no clearly resolvable difference in arrival order.
Summary of Experimental Principles
This demonstrates the tautochrone (isochrone) property of the cycloid: under gravity, the descent time from any point on the curve to its lowest point is independent of the starting height, so releasing balls from different points on the same cycloid and observing their near-simultaneous arrival confirms the underlying principle.

Prompt Grounding rubric:
level_1: No cycloid-shaped track is visible in a vertical plane; fewer than two balls appear, or no two release points at different heights (the half-length position and the full-length/top position) are shown; no shared bottom endpoint is visible.
level_2: A curved track appears but is not shown in a vertical plane (e.g., lying flat, tilted at a shallow angle, or its orientation is ambiguous); or only one ball is present; or both balls start from the same height with no visible height difference; or the bottom endpoint cannot be identified.
level_3: A single cycloid-shaped track is mounted in a vertical plane; two visibly distinct balls are shown at rest at two different points along the track, one at roughly the half-length position, one at the top (full-length) position; both balls are released and travel down the track to a common visible endpoint at the bottom.
level_4: All requirements of the 3-point level are met, AND both release points lie on the same continuous cycloid curve (not on two separate tracks or visually different curves); AND each ball begins from rest with no visible push, throw, or added velocity; AND the shared bottom endpoint is unambiguously the lowest point of the curve, common to both balls' paths.
level_5: All requirements of the 4-point level are met, AND both balls are released at the same visible instant (e.g., both released by the same visible action on the same frame); AND each ball's path stays exclusively on the cycloid track with no jumping off, branching, or shortcuts; AND the full track, from top to bottom endpoint, stays visible at a constant scale and viewing angle throughout.

Scientific and Causal Correctness rubric:
level_1: Neither ball moves under gravity (both stay in place, float, or are pulled by a visible external force); or the ball released from the top (full-length) position visibly reaches the endpoint before the ball released from the half-length position, reversing the relationship where the shorter path can at worst only tie, never trail.
level_2: The balls move but do not follow the cycloid's curvature (e.g., a straight-line or circular-arc path instead); or one ball never reaches the endpoint while the other does, making any timing comparison impossible; or the motion is not gravity-driven (e.g., constant speed throughout, or a visible push at release).
level_3: Both balls, released from rest at their respective start points, descend continuously along the cycloid's curve under apparent gravity and reach the shared bottom endpoint, with the half-length-release ball arriving no later than the top-release ball; a clearly visible gap between the two arrivals is still present (the two do not arrive together).
level_4: All requirements of the 3-point level are met, AND the gap between the two arrivals has narrowed enough that a viewer would hesitate to call a clear winner (the finish looks close, not a decisive head start); AND both balls show smooth, continuously increasing speed with no jerky starts or pauses; AND neither ball overshoots or bounces off the endpoint.
level_5: All requirements of the 4-point level are met, AND the two arrivals are visually indistinguishable in time (the balls reach the shared endpoint together, within a single perceptible moment, with no discernible winner), directly illustrating that descent time along the cycloid does not depend on release height; AND both balls come to rest at the identical endpoint location.

Spatiotemporal Consistency rubric:
level_1: The cycloid track or either ball vanishes and reappears between frames; a ball jumps from one position to another without visibly traversing the track in between; the track's curve changes shape from one frame to the next; the scene's lighting swings abruptly between bright and dark with no visible cause; or the camera cuts, pans, or zooms abruptly mid-descent.
level_2: The track shows a visible break, gap, or mismatch in its curve at some point; a ball flickers out of view for a moment during its descent and then reappears; the light source's apparent direction changes partway through the shot, causing shadows to jump to a new direction; background elements behind the track shift position relative to the track.
level_3: The cycloid track's shape stays continuous and unbroken across the whole shot; both balls stay visible within the frame for the entire descent; shadows cast by the track and balls point in one consistent direction throughout, matching a single unmoving light source; the camera does not cut, pan, tilt, or zoom during the sequence.
level_4: All requirements of the 3-point level are met, AND both balls keep the same apparent size throughout their descent (no sudden growing or shrinking); AND the cycloid curve's shape looks the same from the fixed camera angle in every frame (no warping, stretching, or perspective distortion of the track); AND the balls' motion shows no freezing, skipping, or repeated frames.
level_5: All requirements of the 4-point level are met, AND the balls' downward motion looks continuously fluid frame to frame, without stutter or sudden position jumps that would make their path hard to follow; AND the balls and track keep clean, stable outlines throughout with no flickering or shimmering edges; AND nothing in front of the track ever appears to pass through the track or balls in a way that breaks the depth ordering.