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How Does Geometry Enter Generated Motion?

Weihan Li, Junhao Wu, Yuhan Song, Xiaofeng Lin, Xinlei Chen

arXiv:2610.05135v1cs.CVcs.AI

TL;DR

The paper asks how visible geometry shapes generated motion when the physical law and initial state remain fixed. It compares videos from nine image-to-video models with simulator predictions under matched geometry changes and paired interventions. Geometry modulates local motion, but generated state evolution often diverges from physical dynamics, while prompts and clip length organize destination and timing.

  • Problem

    Prior evaluations measure physical plausibility and trajectory correctness, but leave open how visible geometry shapes generated dynamics when law and initial state are held fixed.

    Source: §1 · p. 1

  • Method

    The study holds law and initial state fixed, varies matched track and deflector geometries, and compares generated trajectories with simulator predictions across paired interventions.

    Source: §1 · pp. 1–2

  • Results

    Across nine models, track geometry modulates speed, but contacts, locality, and energy bounds often diverge from physical predictions; prompts shape destination and clip length paces timing.

    Source: §1 · p. 2, §4.2 · p. 5

  • Takeaways & Limitations

    Generated motion behaves as geometry-conditioned synthesis with local shape, prompt outcome, and clip length organizing different aspects of motion rather than a fixed physical law’s state evolution.

    Source: §1 · p. 2, §5 · p. 7

    The study covers one rigid ball in two planar geometry families, nine image-to-video models, and clips of 3 to 8 seconds.

    Source: §5 · p. 8

Abstract

from arXiv · show

Under a fixed physical law, the visible geometry of a scene determines how motion must change. We ask how video generators realize this relationship. We fix the law and the initial state and change only the geometry drawn in the first frame, within matched families of tracks and deflectors, and compare each generated trajectory with the simulator prediction for that geometry. Paired interventions change one thing at a time: a local bump, the height of a barrier, the words of the prompt, the length of the clip. Across nine image-to-video models, geometry is preserved and shapes the motion: the speed of the ball follows the drawn undulation of a track. A physical state would carry this response forward, and here the generated motion parts from the law. The mean slope barely accelerates the ball, successive contacts fail to compose through a consistent state, an edit ahead of the ball alters its motion before it arrives, and the ball climbs over barriers higher than its release point. Two global conditions organize the global trajectory: text strongly controls the destination, while clip length strongly controls timing in the open-weight models tested. The pattern persists with photographed first frames. Current video generation thus behaves as geometry-conditioned motion synthesis whose evolution of state differs systematically from that of a fixed physical law.

1. Introduction

The paper tests whether video generators change motion as a fixed physical law requires when only visible geometry changes. Across nine models, geometry modulates local motion, but generated trajectories often fail to follow the law’s state-dependent organization; text and clip length also shape global outcomes.

Study design

  • The study fixes the law and initial state, varies matched track and deflector geometries, and compares generated trajectories with simulator predictions.Paired interventions also change a local bump, barrier height, prompt wording, or clip length one at a time.Source: §1 · pp. 1–2

Main findings

  • Across nine models, track geometry is preserved and modulates ball speed with the drawn undulation, while mean slope contributes little acceleration.Undulation gain is 0.5 to 1.2 of the physical gain; in eight models, its phase leads the physical phase by 15 to 41 degrees.Source: §1 · p. 2
  • Generated motion often fails to compose through a physical state: contact order is rare, edits ahead of the ball can alter its path, and barriers above release height are crossed.The ball rises above its release height in 63 of 72 videos and crosses 43 of 49 physically impassable barriers.Source: Figure 1 · p. 1, §1 · p. 2
  • The named outcome in a prompt controls destination, while clip length controls event timing in the open-weight models tested.With a neutral prompt, tray arrival falls by 33 to 96 percentage points across all eight tested models.Source: §1 · p. 2

2. Related Work

Prior work has made physical correctness in generated video measurable through plausibility judgments, trajectory analysis, simulator comparisons, and controlled interventions. This paper focuses on the complementary question of how visible geometry shapes generated dynamics when law and initial state are fixed.

Physics in generated video

  • Evaluation has progressed from plausibility judgments [3] [19] to testing equations and conserved quantities [31], simulator rollouts [9], and scale- or time-independent relational readings [29].These approaches measure gaps from physical motion for individual scenes.Source: §2 · pp. 2–3

Controlled response and composition

  • Controlled studies vary prompt or frame parameters [10] [34], collision-chain length [5], counterfactual branches [16], or caption-video inputs.The present work instead varies track and deflector shape, testing whether responses compose across contacts, act where the ball is, and respect energy.Source: §2 · p. 3

What organizes generated motion

  • Prior work reports slower-than-physical falls [6], weak nonzero-frequency motion [22], early motion planning [13], phase erosion [8], and delayed events [2].This paper assigns local speed, destination, and timing to geometry, prompt outcome, and clip length, respectively.Source: §2 · p. 3

3. Same Law, Different Geometry

The study defines a world by its visible geometry, local law, and initial state, then holds law and state fixed while varying matched geometries. It compares generated motion with simulator references using controlled interventions and measures spanning tracks, contacts, outcomes, and timing.

Object

  • A world is W = (Ω, L, x0): visible geometry, local law, and initial state; the study varies Ω while holding L and x0 fixed.Within each family, variants share global statistics and use the same prompt, so the first frame alone conveys the variation.Source: §3 · p. 3

Two families

  • The two matched families are undulating tracks and flat deflectors, with geometry variants matched on length, transit time, drop, endpoints, or mean angle.The track family includes straight, single-frequency, and broadband profiles; deflector courses include one or three contacts.Source: §3 · p. 3

Paired interventions

  • Paired interventions vary one factor at a time, including a local track edit, ramp angle, barrier height, prompt outcome, clip length, photographed first frame, or regeneration.The local edit is 15 mm; barriers range from 0.70 to 1.20 of the release drop, and clip lengths are 3, 5, and 8 seconds.Source: §3 · p. 3

Reference and readings

  • The simulator supplies a tolerance-banded reference, while trajectory readings measure track speed response, contact direction and order, tray arrival, and ramp height.Track gain and trend are normalized by tempo; Table 1 reports model-level medians and identifies the physical oracle as its first row.Source: §3 · p. 3, Table 1 · p. 4

Models

  • Nine image-to-video models are evaluated, with three seeds per scene unless otherwise stated; paired-by-seed interventions use open-weight models.Videos are assessed for scene integrity and readability before dynamics are read.Source: §3 · p. 4

4. Results

Across the tested models, visible geometry shapes local motion, but the resulting dynamics differ from motion under a fixed physical law. Text controls destination, clip length controls timing in the open-weight models tested, and the pattern also appears with photographed first frames.

4.1. How does visible geometry modulate motion?

  • Generated speed follows track undulation, while mean slope contributes little; first-contact responses also diverge from the prescribed restitution.The gain at 3 cycles per metre is 0.54–1.24 of the physical gain, and eight models lead the physical phase by 15°–41°; at first contact, closed models have restitution 0.67–0.74 against 0.85, while some open-weight models slide.Source: §4.1 · pp. 4–5, Figure 3 · p. 5

4.2. Does the modulation form a local dynamics?

  • Edits can alter motion before the ball arrives: in three open-weight models, pre-arrival path changes exceed those from equal-size off-track edits.MiniMax-H3 slows at a bump by 2.4%, a fifth of the physical change, while LTX-2.5 reaches either edit 3–6% sooner and slows at a dip where physics speeds up.Source: §4.2 · p. 5, Figure 5 · p. 7

4.3. What organizes the global trajectory?

  • Naming the tray as the outcome raises tray arrival to 98–100% of trackable videos for seven models, even when contacts are incorrect.With a neutral prompt, arrival falls by 33–96 percentage points across eight models; the drawn tray alone barely attracts the ball.Source: §4.3 · p. 6
  • For three open-weight models, generated event tempo scales with clip length at an exponent γ of 0.85–1.04.The scene, prompt, and seed are fixed; unlike physical event duration, generated tempo changes with clip length.Source: §4.3 · p. 6

4.2. Does the modulation form a local dynamics?

  • Across three-deflector scenes, the physical contact order appears in only 12–24% of closed-model videos and none of the open-weight videos.Three open-weight models seldom reach a second contact, while Seedance models show independent deviations at successive contacts; calibrating a contact law improves prediction for only one model.Source: §4.2 · p. 5, Figure 5 · p. 7

4.4. Photographed first frames and regeneration

  • With photographed first frames, six models’ readings remain within their render seed-to-seed spread, and the pattern from the earlier sections is reproduced.Specific differences include camera movement for LTX-2.5, larger exit residuals for MiniMax-H3, and higher gain for Seedance 2.0.Source: §4.4 · p. 7
  • On regeneration, models mostly return their own dynamics rather than correcting altered tempo or phase toward physics.For slowed, constant-speed, and phase-shifted sources, λ stays below 0.1 except at the highest noise level for distilled LTX-2.5; violated contacts are corrected, but the resulting trajectory retains model-specific errors.Source: §4.4 · p. 7

4.2. Does the modulation form a local dynamics?

  • The ball exceeds its release height in 63 of 72 readable videos and crosses 43 of 49 physically impassable barriers.Six models cross every tested barrier; the physical oracle crosses barriers below release height and none above it.Source: §4.2 · p. 5, Figure 6 · p. 7

5. Discussion

The discussion distinguishes geometry’s local influence on motion from text and clip length as global conditions, contrasting these roles with state-based evolution under a fixed law. It also explains how paired interventions address evaluation and identifies the study’s scope.

5. Discussion

  • Geometry is preserved and locally modulates motion, while text names the destination and clip length sets timing; fixed-law motion instead updates state event by event.Source: §5 · pp. 7–8
  • Figure 7 contrasts named versus neutral prompts, arrival time across clip lengths, and normalized-time trajectories at 3, 5, and 8 seconds.Source: Figure 7 · p. 8
  • Table 2 records changes in readings between rendered and photographed frames, plus regenerated-motion displacement toward physics by source and noise level.Source: Table 2 · p. 8
  • Outcome-based scores can be satisfied by naming the destination, while tempo-normalized scores absorb clip-length effects; paired input changes use the law as a reference.Source: §5 · p. 8
  • The study covers one rigid ball in two planar geometry families, nine models, and 3–8 second clips; photographed first frames test the visual domain.Source: §5 · p. 8

Supplementary Material

The supplement defines matched geometry interventions, a simulator-and-ensemble reference, and a measurement pipeline for evaluating generated motion. It covers probes of shape response, contact composition, state dependence, destination, timing, and visual domain.

A.2. Track family

  • Matched track levels vary the drawn profile while holding length, release rule, prompt, and transit time fixed, testing predicted unit-gain, zero-phase speed response and mean-slope acceleration.The family isolates how speed responds to drawn shape across spatial frequencies.Source: §A.2 · pp. 11–12

A.3. Deflector family

  • Deflector scenes vary contact geometry and layout to test predicted exit angles, three-contact composition, and the contrast between physical paths and matched zigzag templates.Paired layouts share the launch ramp, tray position, total drop, and mean angle.Source: §A.3 · p. 12

A.4. Local edits and shared-front tracks

  • Local edits and shared-front tracks test physical-direction speed changes, effects of edits ahead of the ball, and whether later motion follows the drawn phase or changes over shared geometry.The intervention set also includes a null edit and reruns to assess unrelated changes and sampler variation.Source: §A.4 · pp. 12–13

A.5. Ramp pairs, barriers and chutes

  • Ramp pairs test release-height-bounded climbs, humps test a release-height threshold, and chutes vary curvature while holding exit state fixed despite law-predicted identical flights.The ramp prediction includes rolling-resistance effects; the hump ensemble is designed to split near the predicted threshold.Source: §A.5 · p. 13

A.6. Goal interventions; A.7. State controls

  • Tray and prompt interventions test destination following, while near-miss and permuted-deflector controls test whether geometry attracts contact or determines contact order.Prompt pairs preserve the first frame, ensemble, and seed; near misses are compared with a hit control.Source: §A.6 · p. 13, §A.7 · p. 14

A.8. Clip length; A.9. Photographed first frames

  • Clip-length pairs test whether timing changes with duration; photographed-frame controls hold geometry fixed while changing the first frame’s visual domain.The clip test compares 3-, 5-, and 8-second versions; photographed scenes are compared with measured-geometry simulator ensembles and rendered controls.Source: §A.8 · p. 14, §A.9 · p. 14

A.10. Regeneration sources

  • Regeneration sources probe which parts of motion persist when models re-render scenes and whether replacements move toward the stated law or the model’s own scene version.Six pilot-set scenes—three tracks and three deflector layouts—serve as sources, each with an exact render.Source: §A.10 · pp. 14–15, Table A.7 · p. 15

B. The reference

  • A simulator applies the stated law to first-frame geometry, with a 64-member ensemble defining scene tolerance bands; all physical comparisons use this oracle.The reference includes rolling tracks, ramps and chutes, free flight between contacts, and prescribed deflector and tray interactions.Source: B. The reference · p. 15
  • A 64-member simulator ensemble provides a geometry-specific reference, with paired intervention arms sharing keys so their differences come from changed geometry alone.Scenes are included only when the ensemble remains sufficiently consistent; readings use the exact render of the nominal trajectory, and barrier comparisons account for the ensemble’s split pass rate.Source: Table B.1 · p. 16, B. The reference · p. 16

C. Measurement

  • Video readings map trajectories and drawn geometry to board coordinates, then compare measurements with exact-render baselines.Per-frame homographies absorb camera motion, while ball segmentation and track or deflector geometry extraction yield the position and shape measurements.Source: C. Measurement · p. 16, §C.1 · p. 17

C.2. Readings

  • Track readings compare speed-undulation gain and phase with tempo-rescaled physical motion, while trend ratios distinguish physical acceleration from preferred-speed motion.The supplement also defines balanced accuracy and kinematic gain to assess downhill acceleration and whether the ball stays on the drawn rails.Source: §C.2 · p. 17
  • Deflector readings test contact sequence, exit-law residuals, and downstream steering; intervention readings quantify locality, response fronts, climbs, barriers, landings, clip-length scaling, and regeneration.The stated law is calibrated on single-deflector contacts and then evaluated on three-deflector contacts; intervention measures include pre-edit path changes, landing shifts, and motion’s dependence on clip duration.Source: §C.2 · pp. 17–18

C.3. Validation

Validation checks show that the readings distinguish simulated and deliberately altered motions, while measurement floors set when model readings are interpretable. The integrity rule separates videos suitable for dynamics analysis from those with apparatus or other changes.

C.3. Validation

  • Synthetic mechanisms and known-error motions produce distinct readings, including recovered gain, phase, restitution, and contact-order errors.Considering gain, phase, trend ratio, and b together avoids misreading several mechanisms; calibrated contact laws also predict multi-deflector contacts more accurately for a model with a consistent but wrong law.Source: §C.3 · p. 18

D. Integrity

  • The integrity rule leaves exact renders unflagged and detects injected perturbations, while recurring apparatus changes are treated as findings about model behavior.The rule defines intact and readable videos; dynamics are read only on readable videos, where apparatus changes begin after the ball’s last use of the affected part.Source: §C.3 · p. 18, D. Integrity · pp. 18–19, §D.1 · p. 20

C.3. Validation

  • Photographed-scene twins set tracking-error floors of 1.3–1.4 mm on tracks, 2.4 mm on the broadband scene, and 2.1–2.2 mm on deflectors; model readings count only when intervals clear matched floors at the model’s rate and size.Pose-level floors match nominal scenes except on two track scenes at 16 fps, where gain floors reach 0.31 and phase floors 25°.Source: §C.3 · p. 18, §C.4 · p. 18

D.1. The rule

  • A video is readable when all non-apparatus flags are clear and every apparatus change begins after the ball’s last use of that part.The intact share is the integrity statistic; readable videos supply the dynamics analysis.Source: §D.1 · p. 20

D.2. Shares per model and experiment

Integrity varies across models and experiments: several preserve track scenes well, while deflector scenes more often involve apparatus changes. Recurring failure forms differ by model and include moving parts, camera motion, and object-count changes.

D.2. Shares per model and experiment

  • Six models keep 96–100% of track videos intact, while deflector scenes cost every model more and some models rarely preserve them.LTX-2.5 moves its camera in 64 of 72 deflector videos; Wan 2.2 (TI2V-5B) keeps too few videos intact for any dynamics reading.Source: §D.2 · p. 20

D.3. Recurring failure forms

  • Recurring failures include struck deflectors or trays moving, camera motion, duplicated or vanishing balls, and changes that grow with clip length.Examples vary by model: LTX-2.3 treats deflectors as loose objects, while LTX-2.5 (distilled) rotates the launch ramp mostly after the ball leaves it.Source: §D.3 · p. 20

E. Models and generation settings

  • The study uses nine image-to-video models and documents generation settings and per-model experiment coverage to support reproducibility.The settings include frame rate, length, sampler, prompts, and seeds; Table D.1 reports intact and readable shares by model and experiment.Source: E. Models and generation settings · pp. 20–21, Table D.1 · p. 21

E.1. Models

The experiments use nine image-to-video models with documented generation settings and controlled variations. Prompts are fixed within scene families, and repeatability differs between open-weight and closed models.

E.1. Models

  • Open-weight models use packaged workflows at their 480p-class settings, while first frames are letterboxed for those models and sent unchanged to closed models.Prompt rewriting is off, and generated soundtracks are not used.Source: §E.1 · p. 21
  • Clip-length comparisons vary duration while holding other settings equal, and regeneration probes encode, noise, and denoise source videos at model-specific levels.Closed models run the main sets, selected interventions, and photographed-frame rows; their intervention subsets are specified in the passage.Source: §E.1 · pp. 21–23

E.2. Prompts

  • Within a family, prompts stay fixed, with placeholders for ball colour and consistent names for deflectors and the launch ramp..Source: §E.2 · p. 23

E.3. Seeds and repeatability

  • Open-weight models are generated with seeds 0, 1, and 2; closed-model generations are replicates because they ignore or do not reproduce seeds.Reruns of most open-weight models reproduce decoded frames exactly, and the remaining reported variation leaves the measured trajectory unchanged.Source: §E.3 · p. 23

F. Results by question

Appendix F gives per-model results behind the main paper’s questions, with tables detailing geometry measurements and the results’ statistical summaries.

F. Results by question

  • Appendix F reports per-model results for geometry modulation, locality, global trajectory organization, photographed first frames, and regeneration.Source: F. Results by question · p. 23
  • Table F.1 measures intact videos and retained geometry, including track amplitude and on-track fraction, and deflector angle and position.Source: Table F.1 · p. 23
  • Unless stated otherwise, values are medians over readable, estimable videos with scene-bootstrap 95% intervals, and n counts videos.Source: F. Results by question · p. 23

F.1. Response on the track family

The models preserve the drawn tracks and modulate speed with their undulations, but depart from the physical law’s response to slope and fail to fit a single consistent dynamics.

F.1. Response on the track family

  • At 3 cycles/m, speed gain is 0.54–1.24 times physical, and eight models lead physical phase by 15–41° while preserving the drawn track.Source: §F.1 · pp. 23–24, Table F.2 · p. 25
  • On straight tracks, trend ratio is −0.10 to 0.65 versus 1 for the stated law, and speed relaxes toward a preferred value within 0.07–0.74 s.Source: §F.1 · p. 24, Table F.3 · p. 26
  • All models are slower than simulated motion at f = 3, with α = 1.5–3.2.Source: §F.1 · p. 25
  • Two preferred-speed mechanisms fit five models, while the time-rescaled stated law fits none, with χ2/n of 6.5–27.1.Source: §F.1 · pp. 25–26

F.2. Contacts and composition on the deflector family

Contact errors do not compose into the physical sequence across deflectors, although named-outcome prompts can still guide the ball to the tray.

F.2. Contacts and composition on the deflector family

  • At first contact, closed models’ apparent restitution is 0.67–0.74 versus the prescribed 0.85, while three open-weight models slide along the deflector.Source: §F.2 · p. 26, Table F.5 · p. 27
  • On three deflectors, physical contact order appears in 12–24% of closed-model videos and none of the open-weight videos; exact renders reproduce it every time.Source: §F.2 · p. 26, Table F.6 · p. 28
  • Fitting a single-deflector contact law improves three-deflector predictions only for Seedance 2.0.Source: §F.2 · p. 26, Table F.6 · p. 28
  • With named-tray prompts, seven models reach the tray in 98–100% of videos, while model arrival exceeds simulator arrival by 16–87 percentage points on wrong-route videos.Source: §F.2 · pp. 26–27, Table F.7 · p. 28

F.3. Locality: local edits and shared-front tracks

Local-edit and shared-front tests reveal that generated motion may respond before reaching an edit and that track geometry does not yield a uniform response across models.

F.3. Locality: local edits and shared-front tracks

  • Only MiniMax-H3 changes speed in the physical direction at an edit, by a fifth of the physical change; three open-weight models also change path before reaching an edit.Source: §F.3 · p. 28, Table F.8 · p. 29
  • In closed models, Seedance 2.0 and Seedance 2.0 mini speed up at the dip by +9.3% and +12.3%, respectively, versus the simulator’s +7.4%.Source: §F.3 · p. 28
  • On shared-front tracks, several models follow the drawn back-section phase, but their phase leads can exceed the front-section leads by 17–25°.Source: §F.3 · pp. 28–29

F.4. Energy: ramp pairs, barriers and chutes

Generated motion violates the physical energy threshold on ramps and barriers, while its response to chute curvature is limited; prompting strongly steers destination, but the route and tray capture remain unreliable.

F.4. Energy: ramp pairs, barriers and chutes

  • 63 of 72 readable ramp ascents rise above release height, and 43 of 49 crossings succeed at barriers physics says are impassable.The mean height ratio is 1.15–2.36 across models, versus a physical oracle of 0.96; six models cross every barrier tested.Source: §F.4 · p. 29, Table F.10 · p. 31, Table F.11 · p. 32
  • No model shows a physical crossing threshold: ensemble crossing probability falls from 1.00 at barrier heights 0.70 and 0.85 to zero at 1.05 and 1.20.Over barriers higher than the release drop, crossing balls in eight models retain 0.33–0.87 of their speed at the foot, while physics predicts a turn-around.Source: §F.4 · p. 29, Table F.11 · p. 32
  • Only Wan 3.0’s landing follows chute curvature; MiniMax-H3’s exit direction steepens, but its landing order does not reliably track curvature.Wan 3.0’s landing shifts −2.95 mm per unit of κ; its exit direction steepens −2.36° per unit. MiniMax-H3’s landing order remains within the spread between chutes.Source: §F.4 · p. 29, Table F.12 · p. 32
  • Neither fitted preferred-speed mechanism reproduces a model’s behavior across the undulating track, local edit, and ramp pair together.The slope-target rule crosses every barrier, while smoothed cruise turns back on the 60° ascent; locality and energy require more than these track-fit mechanisms.Source: §F.4 · p. 30

F.5. Outcome: prompt pairs and tray interventions

  • With the same first frame, leaving the outcome unnamed reduces tray arrival by 33–96 percentage points in matched prompt pairs.The neutral prompt also slows seven models, and the drop remains large for several models even when neutral-prompt motion is complete.Source: §F.5 · p. 30
  • Under the neutral prompt, the drawn tray alone has weak capture, and adding a second tray rarely sends the ball into it.Capture contrasts are 0.42 for Seedance 2.0 and 0.10 for Seedance 2.0 mini; models place balls in the second tray in 0–3 videos.Source: §F.5 · p. 31
  • Near-miss contacts occur, but no trackable video reproduces either permuted contact order across 61 trials.With three seeds, the reported near-miss counts establish paths within 10 mm of the deflector end.Source: §F.5 · p. 32

F.6. Timing: clip length

Longer clips stretch motion and place events at similar fractions of the clip, with model-specific timing behavior. Most readings persist on photographs of the built scenes, though some changes or failures remain.

F.6. Timing: clip length

  • From 3 to 8 seconds, the same event stretches nearly in proportion, occurs at a fixed fraction of the clip, and leaves extra time for rest or repetition.Both prompts in this experiment name the outcome.Source: §F.6 · pp. 32, 34
  • On tracks, duration exponents are 0.85–1.04 in three models, near the clip-scaled value of 1 rather than the fixed-rate value of 0.MiniMax-H3’s exponent is 1.04 [0.95, 1.14], LTX-2.3’s is 0.85 [0.53, 1.04], and LTX-2.5 (distilled)’s is 0.91 [0.90, 0.92].Source: §F.6 · p. 32, Table F.17 · p. 35
  • Timing responses vary by model: Wan 2.2 (A14B) runs about twice as fast at 3 seconds as at 5 seconds, then keeps its 5-second pace at 8 seconds.Its tempo ratios are 0.49 [0.38, 0.53] for 3 s over 5 s and 0.85 [0.70, 1.12] for 8 s over 5 s.Source: §F.6 · p. 33
  • Across clip lengths, the track-family undulation response largely holds, while the relaxation rate in video time varies most.The physical-time relaxation rate matches at 5 and 8 seconds for both LTX models; the 3-second estimates depart, possibly because short clips are truncated.Source: §F.6 · p. 34, Table F.18 · p. 35
  • Longer clips do not consistently improve outcomes: some models repeat events, lose the ball, or leave it at rest during the added time.Wan 2.2 (A14B) lands in 12/12 videos at both 3 and 8 seconds, then the ball returns to the launch point in 7 of 8 long clips.Source: §F.6 · p. 34

F.7. Photographed first frames

  • Photographed first frames leave the main readings of six models within their seed spread, and the broad patterns hold for every readable model.On photographs, three-deflector contact order appears in 0 or 1 of 6 videos per model; track gains are 0.59–1.36 and trend ratios remain far from 1.Source: §F.7 · pp. 34–35
  • Three photograph-related changes remain: LTX-2.5 shifts the camera, MiniMax-H3 has larger contact errors, and Seedance 2.0 shows a higher track gain.LTX-2.5 shows fiducial drift in 9/12 photograph videos versus 0/12 twins; MiniMax-H3’s contact error rises by 17.5° and Seedance 2.0’s gain by 0.66.Source: §F.7 · p. 34

F.8. Regeneration probe

Regeneration tends to restore each model’s own motion patterns rather than the physical dynamics. The appendix also documents how its visual summaries, paired comparisons, uncertainty intervals, and decision floors are constructed.

F.8. Regeneration probe

  • At the lowest noise levels, regeneration mostly copies the source, but even then it adds measurable deviation.Outputs stay within 4–15% of the source-to-physics distance (41% for one transparent-deflector case), while an exact source gains 17–21 mm of deviation, ten times the floor.Source: §F.8 · p. 35
  • At higher noise levels, regenerated motion moves away from the physical source and toward each model’s own version or other model-specific behavior.For the restitution-0.3 source, Wan 2.2 (A14B) regenerations move 0.66 toward its own video and 0.10 toward physics; contact order remains wrong and restitution stays 0.16–0.45 against 0.85.Source: §F.8 · p. 36

G. Case grids and per-model charts

  • The case grids show stroboscopic ball positions against dashed simulator paths, with representative model videos chosen by stated rules for each scene level.The per-model charts collect readings across experiments; altered-scene examples are used when a model has no readable video.Source: G. Case grids and per-model charts · pp. 36–37

H. Statistics

  • The unit of analysis is a scene with its seeds, and model properties are reported only when readings clear frame-rate and output-size floors.Intervals come from scene resampling; per-video readings are summarized by medians, while binary outcomes are summarized by their share.Source: H. Statistics · p. 43, §H.1 · p. 43

H.1. Units and intervals

  • Intervals use scene-level resampling, drawing a scene’s seeds together so that between-scene variation enters each interval.Gain and phase use regression coefficients with Newey–West covariance; coefficient ratios use Fieller intervals.Source: §H.1 · p. 43

H.2. Paired designs

  • Open-weight intervention arms share scene and seed, so paired videos differ only in the changed element; closed-model arms use independent samples.Prompt and clip-length comparisons are paired by scene and seed, while photographed frames are compared with their stated controls.Source: §H.2 · p. 43

H.3. Permutation and stratified resampling

  • For chute landing slopes, curvature labels are permuted within each open-weight seed; ramp and barrier intervals resample seeds within scenes.The chute interval omits between-chute spread, making the permutation p-value the decision measure.Source: §H.3 · p. 43

H.4. Reading intervals against floors

  • A reading counts as a model property only when its interval clears the model’s measurement floor; exploratory mechanism predictions carry no claim on their own.The null-edit rule flags none of 120 noise-only runs and all 120 runs where the null arm carries the bump response.Source: §H.4 · p. 43
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