Domain: Natural Science — Physics
Target concept: Gradient Descent Curve

Video generation prompt: Within the same vertical plane, two fixed tracks are set up: one is a straight line, and the other is a cycloid-shaped curve. The starting and ending heights of both tracks are the same. Two identical small balls are released simultaneously from the starting point of the tracks, and the one that reaches the endpoint first is observed.

Evaluation guide:
(i) Target concept: Brachistochrone principle. Among all possible curves connecting two points at different heights in a vertical plane, the cycloid minimizes descent time under gravity.
Minimum mechanism: Uniform gravitational field acting downward; frictionless contact between ball and track; rigid, fixed, and stationary tracks; balls behave as point masses sliding without rolling resistance or air drag; no external forces beyond gravity.
(ii)Storyline: [Frame 0] Static wide shot: two parallel tracks (straight + cycloid) fixed vertically, identical balls resting at topmost points, aligned horizontally at start height. [Frames 1–N] Simultaneous release → continuous downward motion along respective paths → cycloid ball maintains visible lead → [Final frame] cycloid ball fully settled at endpoint while straight ball is still descending and has not yet reached endpoint. Perspective: fixed frontal view, full-track visibility, no camera movement, no zoom, no cutaways.

Manual:
Experimental Procedure
1. Two fixed tracks are placed side-by-side in same vertical plane: left track is straight, right track is cycloid (inverted single-arch curve). Both share identical start height and identical end height.
2. Two identical small balls are placed simultaneously at the topmost point of each track.
3. Both balls are released from rest at the same instant.
Observation of Experimental Phenomena
The ball on the cycloid track reaches the endpoint visibly before the ball on the straight track.
Summary of Experimental Principles
The cycloid is the brachistochrone curve — the path of fastest descent under uniform gravity between two points not directly below each other. Its shape optimizes the trade-off between early acceleration and path length.

Prompt Grounding rubric:
level_1: Neither track is visible, or only one track appears; no balls appear on either track; the two tracks are not shown together in one frame; no release moment is depicted; the starting or ending points of the tracks cannot be identified.
level_2: Both tracks appear, but one is not clearly straight or the other is not clearly a smooth curve; only one ball is visible instead of two; the tracks are stacked one above the other, or angled apart, instead of standing next to each other in the same vertical plane; the balls are not released together or the release moment is unclear.
level_3: Both tracks are visible next to each other in the same vertical plane, one unmistakably straight and one unmistakably a smooth curved (cycloid-shaped) ramp; two visually identical balls sit at the same starting height on the two tracks; both balls are released at the same moment; the lower endpoint of each track is visible and both endpoints sit at the same height.
level_4: The straight/curved track pairing, matching balls, synchronized release, and shared endpoint height described above are all present; in addition, both balls stay visible for the whole descent without being hidden behind a track or each other; neither track bends, wobbles, or changes shape mid-scene; the two balls keep the same color, size, and shape throughout and never merge or split; and the release is a simple drop with no visible push or initial speed.
level_5: Everything above holds, and further: the cycloid track shows one smooth, symmetric arch with no kinks, loops, or flat spots, while the straight track is perfectly straight with no bow in it; both balls start exactly at the top of their own track, and both tracks end at exactly the same lower height; nothing about the balls' or tracks' appearance looks glitched, doubled, or spatially wrong at any point.

Scientific and Causal Correctness rubric:
level_1: There is no observable timing difference between the balls (they behave identically or move arbitrarily), and nothing about their motion suggests the curved track produces a shorter travel time than the straight one.
level_2: One ball clearly finishes before the other, but it is the straight-track ball that wins instead of the cycloid-track ball; or the two balls reach their endpoints at essentially the same moment despite the tracks having different shapes; or a ball's motion violates gravity, such as drifting upward, floating, or speeding up without cause partway down.
level_3: The ball on the cycloid track reaches its endpoint before the ball on the straight track; both balls move continuously downward from start to end without pausing, reversing direction, or lifting off the track; both endpoints sit lower than the starting point.
level_4: The cycloid ball's win over the straight-track ball is shown with smooth, steady downward motion for both balls: no sudden jerks, mid-descent stops, or bounces; there are no visible external pushes (no strings, magnets, or blown air); and both balls stay in contact with their track surfaces the whole way down instead of hopping or floating free of them.
level_5: The time gap between the two balls is unmistakable: the cycloid ball has clearly finished and come to rest at its endpoint while the straight-track ball is still visibly partway down its own track, not just slightly behind; there is no frame duplication, freeze, or stutter that would make the arrival order hard to judge; and the cycloid ball noticeably speeds up early in its fall, consistent with its track shape giving it a head start.

Spatiotemporal Consistency rubric:
level_1: A ball vanishes from one frame and appears somewhere else in the next; a section of track disappears or changes shape mid-scene; the overall brightness or color tone of the shot jumps sharply between frames with no visible cause; the camera angle suddenly shifts or spins; a ball or track flickers in and out or seems to dissolve.
level_2: One ball briefly disappears and then reappears in a new spot rather than moving there continuously; the lower ends of the tracks do not line up consistently from frame to frame; the shadows cast by a ball or track point in a different direction than the scene's lighting would suggest; a ball's position jumps by more than its own width between consecutive frames instead of sliding smoothly.
level_3: There is one small but noticeable flaw (for example a ball's position jitters slightly instead of tracing a smooth downward path, or a shadow flickers briefly, or a track edge briefly hides less than about a third of a ball's area), but otherwise the camera viewpoint never jumps and neither track nor ball structurally breaks apart.
level_4: Beyond a single minor flaw, no part of a ball is ever hidden behind a track edge or the other ball by more than about a quarter of its area; shadows keep pointing the same direction and stay proportionate to the balls' positions as they descend; both tracks stay rigid and unwarped throughout; each ball's motion is continuous, with no sudden jump in position or stutter in speed.
level_5: The balls' downward paths look perfectly smooth to the eye with no visible jitter at all; shadow length and direction change only gradually as the balls descend and never snap to a new angle; both track edges stay crisp and stable with no warping or shimmer; the overall brightness and color of the scene stay uniform across the entire sequence.