Domain: Natural Science — Statistics & Data Science
Target concept: The Galton board (bean machine) produces a bell-shaped distribution through falling balls.

Video generation prompt: From the frontal viewpoint, a transparent Galton board with evenly spaced nails, a number of identical metal balls fall from a single funnel at the top into vertical collection bins below.

Evaluation guide:
(i) Target concept: Emergence of normal distribution from repeated independent binary stochastic events.
Minimum mechanism: Each ball must experience ≥3 sequential nail contacts, with each contact producing a visible left/right deflection; deflection direction must vary across balls; final bin counts must be non-uniform and centrally peaked.
(ii)Storyline: [Phase 1: Setup] Frontal view reveals transparent board with centered funnel, staggered nail rows, and aligned bins, all static and fully visible. [Phase 2: Initiation] Identical metal balls rest in funnel; first ball begins downward motion. [Phase 3: Interaction] Ball contacts first nail → deflects left/right → contacts second nail → deflects again → repeats across ≥3 rows. [Phase 4: Termination] Ball settles into one bin; other balls repeat Phases 2–3 asynchronously; cumulative occupancy increases most in central bins. [Phase 5: Outcome] At clip end, bin column heights show unambiguous modal concentration in center, decreasing outward: no occlusion, no viewpoint shift, no post-processing overlay.

Manual:
Experimental Procedure
1. Position camera at frontal viewpoint aligned with Galton board center.
2. Load identical metal balls into the top funnel.
3. Release balls sequentially so they fall freely under gravity.
4. Observe ball trajectories as they strike staggered nails and deflect stochastically left/right.
5. Record final accumulation in vertical collection bins.
Observation of Experimental Phenomena
Metal balls descend through the funnel, strike nails in staggered rows, and undergo repeated left/right deflections; final distribution across bins forms a concentrated peak in the center bins, tapering symmetrically toward outer bins.
Summary of Experimental Principles
The Galton board demonstrates how random binary outcomes (left/right deflection at each nail) aggregate to produce a normal (bell-shaped) distribution via the Central Limit Theorem.

Prompt Grounding rubric:
level_1: No Galton board is visible anywhere in the frame: there is no funnel, no lattice of nails, no set of vertical collection bins, and no metal balls; the scene instead shows an unrelated apparatus (e.g., a pendulum, a circuit board, or a beaker of liquid) with no structural resemblance to a Galton board.
level_2: A board-like panel appears, but at least two of the three defining parts are missing or unrecognizable (the top funnel, the staggered rows of evenly spaced nails, or the vertical collection bins at the bottom), and/or metal balls are absent or cannot be identified as identical spheres; alternatively, the camera view is not frontal (e.g., a steep overhead or oblique angle that hides the nail lattice).
level_3: A frontal, transparent Galton board is shown with a top funnel, multiple rows of nails, and bottom collection bins, and metal balls are visible in the funnel or mid-fall among the nails, in the correct top-to-bottom order (funnel, then nails, then bins); however, nail spacing is visibly irregular, bin walls are not evenly aligned, or the balls differ from each other in size, shape, or color.
level_4: A frontal, transparent Galton board is fully rendered with a centered top funnel, evenly spaced nails arranged in staggered rows, and evenly spaced vertical bins at the bottom; identical metal balls are visible simultaneously at two or more of: resting in the funnel, falling among the nails, or settled in a bin; no part is missing, duplicated, or misplaced; only cosmetic imperfections are allowed (e.g., a faint lens flare or slight motion blur on a fast-moving ball).
level_5: The frontal, transparent Galton board is rendered with the funnel centered directly above the nail lattice; nails form a consistent staggered triangular pattern across every row; bins are equally spaced, vertically oriented, and reach from the base up to the lowest nail row; every metal ball is identical in size, shape, and metallic finish; balls are visible at rest in the funnel, in mid-fall against the nails, and settled in bins all within the same shot; there is no missing part, no substituted object, and no departure from the frontal camera angle.

Scientific and Causal Correctness rubric:
level_1: There is no causal link between a ball's release and where it ends up: balls fall straight down without deflecting off any nail, or they spread evenly across every bin regardless of position; nails appear but balls pass through them or ignore them entirely, showing no branching or random behavior at all.
level_2: Balls are released and clearly avoid passing through nails, but each ball's path is a fixed straight or slightly angled line with no left/right deviation at contact points; nearly all balls land in the same bin or in immediately adjacent bins; the final bin occupancy is flat across all bins or rises/falls monotonically from one side to the other rather than showing any central concentration.
level_3: Balls visibly bounce left or right on contact with nails across multiple rows, and different balls end up in different bins, giving a final occupancy that is not uniform; central bins hold more balls than outer bins; however, either the same ball always deflects in the same direction at a given nail (no apparent randomness across similar encounters), or the final occupancy pattern is lopsided to one side or shows two separate peaks rather than one clear central concentration.
level_4: Each ball undergoes a sequence of left/right deflections as it strikes successive nail rows, with the direction of each deflection appearing independent and unpredictable from ball to ball; several balls are visible at different stages at once (in the funnel, mid-deflection, and settled) as the clip progresses; the final bin occupancy is clearly highest in the central bin(s) and lower toward the edges; ball motion after each deflection is physically sensible (balls keep falling, never floating or reversing upward); at most one isolated exception is allowed (e.g., one ball grazing a nail without a visible deflection).
level_5: Every ball-nail contact produces a visible leftward or rightward deflection, with no ball passing through, sticking to, or bouncing upward off a nail; across the population of balls, deflection directions vary enough that the accumulated bins form a single central peak tapering off toward both outer edges, consistent with many independent random left/right choices combining into a bell-like shape; the causal chain from release, to each nail impact, to the resulting change in trajectory, to the ball's final bin is visible and unbroken for every ball shown, and no bin away from the center ever ends up with a noticeably higher count than the central bin(s).

Spatiotemporal Consistency rubric:
level_1: Severe spatiotemporal breaks occur: a ball vanishes from one location and reappears elsewhere without visibly traveling the distance between (e.g., disappearing from the funnel and appearing already resting in a bin); the nail lattice or bin walls flicker, jump in scale, or shift position between frames; the camera itself pans, tilts, or zooms at any point instead of holding a fixed frontal shot.
level_2: A ball's speed changes with no visible cause: instantly stopping, instantly starting, or reversing direction without having struck a nail; the nail lattice or bins visibly wobble, warp, or partially dissolve and reform; a ball appears to pass behind a nail it has just visibly struck, breaking the expected front-to-back layering; motion overall looks jerky, with several visible freezes or skips across the clip.
level_3: One ball briefly drifts or hangs in place without the downward acceleration expected under gravity, or a single nail momentarily disappears for a couple of frames before reappearing in the same spot; bin walls appear to change thickness or transparency partway through the clip; aside from this, the funnel stays centered above the nail lattice, the bins keep their spacing below it, and the camera holds its frontal framing throughout.
level_4: The funnel stays centered above the nail lattice and the bins keep their fixed spacing below it for the entire clip; every ball's fall accelerates smoothly under gravity and slows immediately upon striking a nail, with no floating, warping, or teleporting; at most one brief, isolated visual slip is allowed (e.g., a single ball's edge looking momentarily soft, or one instant where a bin wall's transparency looks slightly off).
level_5: Across the entire clip, every ball's motion is unbroken and physically continuous: each ball accelerates downward before reaching a nail, changes direction immediately at the moment of contact, and settles into a bin without skipping, freezing, or jumping between positions; the funnel, nail lattice, and bins hold the same fixed spacing and alignment to one another from first frame to last, and the camera keeps the same frontal framing throughout; no ball, nail, or bin ever flickers, changes shape, or disappears and reappears at any point in the sequence.