Domain: Engineering — Computer Science
Target concept: Union

Video generation prompt: Display two sets A={1,2,3,4} and B={3,4,5,6} on a white background, represented by blue and yellow boxes respectively, demonstrating the dynamic process of computing their union, with the resulting set displayed in a green box below.

Evaluation guide:
(i) Target concept: Set union operation in discrete mathematics, defined as A ∪ B = {x | x ∈ A or x ∈ B}.
Minimum mechanism: The video must support inference that the green output set is derived *exclusively* from the contents of the two input sets, with shared elements contributing once and uniquely sourced elements contributing from their respective origins, requiring visible co-presence of 3 and 4 in both A and B *prior* to union, and absence of any element in the green box that is missing from both inputs.
(ii)Storyline: Frame 0–2: Static phase: blue A and yellow B appear side-by-side, fully labeled and legible; 3 and 4 visibly present in both. Frame 3–4: Causal trigger: 3 and 4 simultaneously highlighted in both boxes, establishing commonality. Frame 5–6: Derivation phase: 1 and 2 animate from A into emerging green box; 5 and 6 animate from B into same box; motion originates *from source boxes*, not empty space. Frame 7–10: Resolution phase: green box stabilizes with complete, correct union label; all input boxes remain visible and unchanged until video end. Perspective: Fixed frontal orthographic view; no camera movement; all objects fully visible within frame at all times.

Manual:
Experimental Procedure
1. Display blue rectangular box labeled "A={1,2,3,4}" on left and yellow rectangular box labeled "B={3,4,5,6}" on right — both centered vertically on white background.
2. Simultaneously highlight shared elements "3" and "4" in both boxes (e.g., pulse or border glow).
3. Animate "1" and "2" sliding from A into a new green box appearing below center.
4. Animate "5" and "6" sliding from B into same green box.
5. Display final green box labeled "{1,2,3,4,5,6}".
Observation of Experimental Phenomena
- Two colored boxes (blue/yellow) appear side-by-side with correct numeric content.
- Elements 3 and 4 appear identically in both boxes before union.
- Green box appears below, containing exactly six unique numbers: 1,2,3,4,5,6 — no duplicates, no omissions.
Summary of Experimental Principles
- Union of two sets A and B is the set of all elements belonging to A or B or both.
- Shared elements appear only once in the union.
- Visual representation uses color-coding and spatial layout to distinguish inputs and output, with animation illustrating derivation.

Prompt Grounding rubric:
level_1: Neither the blue box labeled A={1,2,3,4} nor the yellow box labeled B={3,4,5,6} appears on the white background, or the green union-result box never appears at all.
level_2: Only one of the two input boxes appears with its correct color and label; the union box appears but shows the wrong color (not green) or is missing outright; or the boxes are not both shown on a white background.
level_3: The blue A={1,2,3,4} box and yellow B={3,4,5,6} box both appear side-by-side on the white background, and a green box appears below them; all labels are legible and match the numbers given in the prompt; however, the boxes appear only as a static end-state, with no visible transition, highlight, or motion connecting A and B to the green box.
level_4: All of score 3 holds, and some visible transition (motion, highlight, or fade) connects the input boxes to the green box rather than the green box simply appearing fully formed; the layout stays side-by-side (A, B) with the green box centered below; only a minor visual flaw is present, such as a brief flicker or slight misalignment during the transition, without affecting label legibility.
level_5: All of score 4 holds, and the whole sequence renders cleanly start to finish: the blue and yellow boxes are legible and stable before any transition begins, the transition into the green box shows no occlusion, distortion, flicker, or mislabeling at any point, and the final green box remains fully legible and unobstructed for the rest of the clip.

Scientific and Causal Correctness rubric:
level_1: The union shown is mathematically wrong (for example {1,2,3,4,5}, {1,2,3,4,5,6,7}, {3,4}, or an empty box); or the color scheme contradicts the prompt (e.g., A drawn yellow, B drawn blue, union drawn red); or the shared numbers 3 and 4 are dropped from the union or listed twice with no explanation.
level_2: The union set has exactly one numeric error (e.g., 1 is missing, or an extra 7 is included); or A and B have their colors swapped (A yellow, B blue); or 3 and 4 are drawn as if they belonged to only one set instead of both; or the green union box shows up before A and B are both fully drawn.
level_3: The union set {1,2,3,4,5,6} is numerically correct; A and B keep their correct colors (blue, yellow) and correct number lists; the union box is green, but the causal link is missing: the union appears with no visual cue for how it came from A and B, or 3 and 4 are shown only in the union without first appearing in both input boxes.
level_4: The union is numerically correct, the colors are correct, and 3 and 4 appear identically in both A and B before the union forms, but either 3 and 4 are shown moving into the union from only one of the two boxes instead of both, or 1/2 or 5/6 show up in the union before their source box has fully appeared, breaking the expected cause-then-effect order.
level_5: The union {1,2,3,4,5,6} is exact; blue A and yellow B each show their complete, correct numbers before anything moves; 3 and 4 clearly appear in both A and B first; during the union, 3 and 4 are visibly tied to both source boxes (e.g., highlighted in both, then landing once in the union); 1 and 2 visibly come only from A, and 5 and 6 only from B; no number appears in the union without first appearing in an input box, no extra number appears anywhere, and the whole input-to-output sequence is easy to follow without gaps.

Spatiotemporal Consistency rubric:
level_1: A or B box appears to jump from one location to another between frames rather than moving continuously; the blue or yellow box changes shape (e.g., turns trapezoidal) mid-clip; the green union box blinks in and out of existence rather than entering once; or the white background changes color or texture partway through.
level_2: A box jumps abruptly from small to large with no visible growth in between; the number labels pop onto the boxes with no fade-in or entrance motion; the green box appears fully formed with no slide-in, fade-in, or build-up motion; or A and B shift their horizontal alignment relative to each other partway through the clip.
level_3: The blue, yellow, and green boxes keep a consistent rectangular shape, solid color, and upright orientation throughout; no box jumps position or breaks apart; the white background stays uniform; any motion present is continuous rather than jumpy, except for one small flaw, such as the green box briefly overlapping A or B as it enters, the A/B boxes trembling slightly while sitting still, or a number's position shifting mid-animation.
level_4: All of score 3 holds, with no trembling, overlap, or size/shape drift in any box at any point; motion (numbers sliding into the green box, etc.) moves steadily in one direction without reversing or pausing; A and B stay side-by-side with an unchanging gap between them; the green box builds in from below with steady growth or fade, except for one brief hiccup, such as a short noticeable freeze during the transition or one number blinking off and back on during the animation.
level_5: A and B sit still, rigid, and identically sized throughout their static phase; the green box grows in smoothly from below with continuous upward motion or fade; the numbers 1, 2, 3, 4, 5, 6 animate in without reversing, pausing, or stuttering; no box changes size, rotation, tilt, or transparency except as part of the intended smooth motion; no box is ever clipped, hidden, or rendered with a visible glitch.