World first

Three frames of a discrete lattice gas show particles spreading through time.

The question

The world and the models

Results

Post hoc

What this says about video first and world first

Checkpoint

Limits

World first

A world model that starts from video matched a reversible world frame by frame and lost it across frames. One that holds the world's state kept it, could be steered, and ran back to its start bit for bit.

The world is the HPP lattice gas on a 128 × 128 torus, filmed as smoke: each frame counts the particles in 4 × 4 blocks. The same first frames go to five models:

the world (its state and its law);
the world from a picture (the law, with a state guessed from the first frame);
a rule learned from the training particles;
recall, the frame that followed the nearest training pair;
a mosaic, each block drawn from training blocks with the same surroundings.

Recall and the mosaic see only frames. Each is the optimum of its training objective on 200 training films, so neither is held back by training or capacity.

One frame at a time the models are alike. Every array of counts is the picture of some state. The mosaic's counts match the world's distribution to a total variation of 0.056.
The mosaic leaves the world after about five frames, on the films it was built from as much as on new ones. Its correlation with the world averages 0.17 on its own training films against 0.78 for the world from a picture. By frame 29 it is anti-correlated (−0.30), because its smoke stays where it started while the world's gas leaves.
Recall is a recording. It replays a training film exactly, and on a new film it copies one other training film from its first frame on (20 of 20 runs). It ignored the hole in 20 of 20 films and froze at the end of its film in 19 of 20.
Matter and consequences. The mosaic changes the particle count in 99.8% of its steps. After a hole is punched, the particles it still lacks at frame 20 range from −0.04 to 2.1 times what it removed; the world keeps exactly what was removed, at every frame.
Only the world returns. Run back from its own state, the world returns the word WORLD bit for bit. Recall and the mosaic trained on reversed films do not (−0.09 and −0.05), and neither does the true law started from a picture of the last frame (0.28).
Learning made a world once, where the model's state was the world's. The rule learned from particles saw all 65,536 neighbourhoods, reproduced 20 of 20 new films and the unseen word bit for bit, and walked through walls it never met.

Status, 28 September 2026. Of twelve predictions written before any lattice code existed, eight held and four failed (P3, P6, P8, P10).

The question

Compare a world model that starts from video with one that starts from the world and renders it. On a one-off basis both can give pictures of the same quality. The claim: a video-first world can be neither steered nor audited for its training data reliably, while a world-first model gives reversibility, control and quality. The trade-off is in perceived computational steps: most people want a lossy world with a polished look, and find out later what is wrong with it as a world. And a model that starts in pixel space can never reach an emergent world outside its training data, and in most cases not even within it.

pictorial-form gave the condition a picture must meet to have physics of its own, π ∘ F^N = G ∘ π. This piece builds a world whose picture does not meet it, and asks what that costs models of pictures when they are steered, reversed, audited and taken outside their data.

The world and the models

The predictions define everything; this is the short version.


World	HPP lattice gas (Hardy, de Pazzis and Pomeau, 1973): four bits per site, one particle per direction. A micro-step turns two head-on particles by 90° when they are alone at a site, then moves every particle one site; a particle facing a wall reverses in place. Every micro-step is a bijection that conserves particles.
Reversal	turn (collide once, reverse every velocity), run the ordinary law, turn again: the state returns bit for bit (Loschmidt), and the film plays backward frame by frame on the way.
Camera	particles per 4 × 4 block: a 32 × 32 frame, values 0–64, every 2 micro-steps. It cannot see velocities, so the picture does not close.
Training	200 films of 30 frames: a background of 0.04–0.12 particles per direction and one to three round blobs at 0.5–0.8. No walls, letters or holes. Filming them took 190,054,400 site updates of the world.

Model	Given	Next frame
world (W)	the state and the law	run 2 micro-steps, render
world from a picture (W′)	frame 0 and the law	guess a state (each block's particles placed at random among its 64 bits), then as the world
learned rule (V3)	the state	a table from a site's four neighbours (16 bits) to its next state, learned from every training micro-step; blind to walls
recall (V1)	frames 0 and 1	the training frame that followed the nearest training pair of frames: the optimum of the whole-frame objective, which returns training frames
mosaic (V2)	frames 0 and 1	each block's next count drawn from training examples with the same context: its 3 × 3 neighbourhood in eight levels and its own level one frame earlier, backing off to shorter contexts when unseen. This is the n-gram model of video, a locally consistent patch mosaic in the sense of Kamb and Ganguli (arXiv 2412.20292). The full context was found for 91.5% of blocks.

Recall and the mosaic trained on the films played backward (V1b, V2b) run time back.

Results

One frame at a time

A held-out film run by the five models

At frame 0 all five agree by construction, and at frame 2 the mosaic and the world from a picture both correlate with the world at 0.92. Recall's frames are real training frames, so each is a true picture of some world. The mosaic's block counts over the held-out films match the world's histogram to a total variation of 0.056 (P2). No test on a single frame separates these models, because the camera is onto: every array of counts is the picture of some state.

Across frames

Correlation with the world and particles shown, frame by frame

The world from a picture stays with the world: 0.92 at frame 2, a plateau near 0.74 from frame 12. It has the law but not the velocities, so it tracks the world's large-scale flow and not its particles. The mosaic falls below 0.5 at frame 10, crosses zero at frame 17 and ends at −0.30, and it does the same on the films it was built from (dashed): a mean of 0.17 against 0.78 for the world from a picture (P4). Recall on a new film starts at 0.58 and holds near 0.35 from frame 10, the level of two different films of the same kind; it rises to 0.47 by frame 29.

The particles shown say the same thing another way. The world, the learned rule and the world from a picture conserve them exactly. Recall jumps to a film with 15.3% fewer particles at its first frame and keeps that film's count. The mosaic changes its count in 99.8% of its steps and ends 7.3% light on average, more than 2% off in 19 of 20 films (P5).

Outside the data: a word and a wall

The word WORLD run forward and back

The word WORLD is written in gas, one 4 × 4 block per pixel of a 5 × 7 font. By frame 3 the image has inverted (−0.53 inside the word's box): particles fly out of the strokes into the gaps between them. The mosaic follows the word for a frame (0.83 at frame 2) and recall does not (0.37) (P6). The learned rule reproduces the whole run bit for bit (P11).

A wall with a slit

A wall with a slit, dense gas on the left. The world and the world from a picture keep every wall block empty for all 30 frames and pass a jet through the slit: 625 particles on the right at frame 0, 1,271 at frame 29. Recall, the mosaic and the learned rule all put gas into all 60 wall blocks by frame 3 (P7, P11). The learned rule, exact everywhere else, lets 9,079 particles into the right side, because a wall was a local case it had never met.

Steering: a hole

A hole punched at frame 10

At frame 10, a disk of radius 16 sites at the centre is emptied: particles deleted in the world and the world from a picture, the same disk erased from the pictures of recall and the mosaic. The world's deficit then stays at exactly the number removed at every later frame, although the hole itself refills in a few frames; so does the deficit of the world from a picture. Recall drops the hole at the next frame in 20 of 20 held-out films, and on the replayed training films its frame 11 is the film's own frame 11 in 20 of 20.

The mosaic neither keeps nor forgets the hole. The particles it still lacks at frame 20 range from −0.04 to 2.1 times what it removed. The prediction was that it would lose at least half in 10 or more films; it did in 3 (P8 failed). In some films the emptiness spreads. A likely cause, not tested: a block next to vacuum matches the sparsest training gas, which stays sparse. The spatial effect correlates with the true effect at 0.49 at frame 14, against 0.83 for the world from a picture.

The way back

Turned at frame 29 and run 29 frames more, the world returns to the word bit for bit and passes back through every earlier frame in order (P1). The others end far from it, measured inside the word's box (P9):

Run back from frame 29	Correlation with the word at frame 0
the world, from its own state	1, bit for bit
the true law, from a state guessed from frame 29's picture	0.28
recall trained on reversed films	−0.09
mosaic trained on reversed films	−0.05

The world from a picture does return to its own start exactly when it runs back from its own state (40 of 40 runs, P12). What it cannot do is reverse a picture. At frame 29 the word is still in the world's state, carried by velocities, and gone from its picture.

Receipts

Recall's receipt is exact and trivial: one training frame per output frame. On a new film it copies a single training film from its first frame to its last in all 20 runs. It joins that film 0 to 7 frames late (see post hoc), so in 19 of 20 runs it reaches the end of the film and repeats the last frame (P10 failed on this). The mosaic's receipt is a crowd. A frame draws its blocks from 195 of the 200 training films on average (never fewer than 169). The median block shares its context and its drawn count with 6 training examples, any of which could have been the one drawn, and 22% of blocks have exactly one (P10 predicted a median of at least 10). The world's receipt is its own state two micro-steps earlier: every particle traces back through the law, and the turned run recovers it.

Scored predictions

These were fixed before any lattice code existed.

ID	Prediction	Verdict	Evidence
P1	the world reverses the WORLD run bit for bit; the world and the world from a picture conserve particles and keep walls empty; recall replays 20 of 20 training films exactly	held	all checks
P2	the mosaic's count histogram within total variation 0.10 of the world's	held	0.056
P3	recall's frame 2 under 0.5 on new films; the world from a picture over 0.8	failed	recall 0.579; world from a picture 0.924
P4	on training films, the mosaic's mean correlation at least 0.1 below the world from a picture's; recall exact	held	0.172 against 0.781
P5	at least 90% of the mosaic's steps change the count; its count off by over 2% at frame 29 in half the new films	held	99.8%; 19 of 20
P6	on the word, recall's frame 2 under 0.3 and the mosaic's over 0.6	failed	recall 0.371; mosaic 0.828
P7	by frame 3 of the slit, gas in half the wall blocks for the mosaic, a third for recall; none for the world and the world from a picture	held	60, 60, 0 and 0 of 60
P8	the world keeps the hole's deficit; recall drops it in 80% of films; the mosaic loses half of it by frame 20 in half the films	failed	the first two held (every frame; 20 of 20); the mosaic in 3 of 20
P9	run back from frame 29, recall, the mosaic and the world from a picture end under 0.3 with the word; the world returns it	held	−0.09, −0.05, 0.28 (narrowly); 1
P10	recall consecutive from frame 4 in 90% of films; the mosaic draws on at least 50 films per frame, median block at least 10 equal sources	failed	1 of 20 (the rest froze at the end of their film); at least 169 films; median 6
P11	the learned rule exact on new films and the word, wrong on the slit	held	20 of 20, exact, gas in walls from the first micro-step
P12	the world from a picture under 0.9 at frame 29, conserving, and exact on its own reversal	held	0.735; conserved; 40 of 40

P3 and P6 failed in the same direction: recall's first frame is closer to the world than expected (0.58 and 0.37). Among 5,600 training pairs there is usually a film whose blobs overlap the new ones. P8 and P10 failed because they predicted the wrong kind of wrongness. The mosaic does not forget the hole; it holds a deficit with no law behind it. Recall does not stay a clean recording to the end; it joins a film late and runs out of film.

Post hoc

Written after scoring; none of this was predicted.

Recall prefers blurrier, lighter frames. In all 20 new films, the training frame recall matched had lower contrast than the frame it was matching: its variance was 0.53 of it on average. It also had 0.85 of the particles, and came 3.5 frames later in its film on average (0 to 7). Squared distance penalises a sharp blob in the wrong place twice, so an older, more spread-out frame with less in it wins. Matching only against the training films' first frames would have given the same frame-2 correlation (0.587 against 0.579). The late start costs nothing at first; it runs recall out of film later.
The mosaic's smoke stays where it started. The world's frames decorrelate from its own frame 0 and turn negative: 0.24 at frame 10, −0.31 at frame 20, −0.26 at frame 29. The gas leaves the blobs along the four axes, and the regions it left end below the average. The world from a picture does the same (−0.27 at frame 29). The mosaic's frames stay correlated with frame 0 (0.64 at frame 10, 0.39 at frame 29). Its smoke spreads in place, and where it keeps mass the world has emptied. That is the anti-correlation at the end of the run.
Time per frame. The world takes 0.18 ms, the learned rule 0.17 ms, the mosaic 0.74 ms and recall 15.9 ms, on one processor core. The world does 32 site updates for every block the camera shows, and is still the fastest, because the lattice gas is a cheap world.

What this says about video first and world first

Three kinds of model. Recall is a recording: perfect frames of a real world that is not this one, exact attribution, no response to anything done to it, and no future past the end of its film. The mosaic is a collage: locally plausible, responsive in appearance, attributable only to a crowd, and without conservation, so an edit's consequences drift at random and the world's own matter drains away. The world holds a state the camera never shows. Its frames are no better one at a time, but they follow from one another: particles are conserved, a hole's deficit persists, walls stay walls and time runs back.

Why frames are not enough. The camera counts particles and cannot see where they are going, so two states with the same picture have different futures. A model whose state is the picture must supply the missing part at every step. Recall supplies it by copying another world's continuation, the mosaic by sampling what followed similar patches. Neither can carry the consequence of an edit, because the consequence lives in the velocities. This is pictorial-form's non-closure at work, measured as steering, conservation and reversal instead of noise.

A lawful model of pictures carries a hidden state. The world from a picture receives exactly what the video models receive and adds the law acting on a guessed state. That is enough to conserve particles, keep the hole's deficit, respect walls and return exactly to its own start. It is still not the world. It stays near 0.74 and cannot reverse a picture back to the word. So a model that starts from video reaches a lawful world only by holding a state finer than its pictures and a law on that state: by becoming world first with a guessed world. Whether a trained video model's latent state closes, π ∘ F = G ∘ π, is the question to put to each one.

Where learning makes a world. The learned rule generalised perfectly to the word, an arrangement no training film had, because every local case in it was one it had seen, and its state was the world's state. It failed at walls, a local case it had not seen. In this world, the ability to go outside the training data is the ability to recombine known local laws in a state space that closes. A picture space does not close, so a model of pictures cannot do even that.

The trade in computational steps. Per frame, the world does 32,768 site updates (32 for every block shown), none of them visible. The mosaic makes one draw per block (1,024 draws, about 46,000 index probes). Recall compares the frame against every training pair (11.9 million operations, growing with the data). Here the world is also the fastest, but only because the lattice gas is cheap; the micro-state of a real scene is far too large to run. That is the honest appeal of video first: it skips the world. The skip is paid in advance, because the training films are the world's own work (190 million site updates to film these 200), and the video models can only replay or recombine it. What the skip costs shows up later: frames as polished as the world's, whose consequences do not follow from what happened.

What is not shown. "Never" is shown here for one world and for the optima of two architectures. Trained networks sit between recall and mosaic, with biases of their own; a network with a latent state is a different case, and the argument above says what it would need. The failures are structural (the picture does not close), which is why they are expected to carry over, but that is an argument, not a measurement.

Checkpoint

Check	Answer
What did the subject force to change?	Three things. The steering test moved from where the hole is to whether the missing particles stay missing, once it was clear, before the predictions were written down, that a mosaic keeping a hole in place would pass a spatial test. Recall latched late and froze, which P10 did not anticipate. The letters inverted at frame 3, a property of HPP's particle flights that nothing in the framing predicted.
What does the compelling result leave unestablished?	The anti-correlated mosaic and the exact reversal are properties of these optimal models in this world. They do not establish how any trained video network behaves, or "never" in general.
Can a stranger enter?	The page shows five screens of smoke. "Hide the names" shuffles them and asks which is the world, with no caption.
Can a participant change the terms?	The viewer writes their own word, empties gas anywhere, turns time at any frame, and picks the training set size (50, 100 or 200 films).
Global verdicts?	8 of 12 held, 4 failed. The failure that bears on the claim is P8: the mosaic's response to an edit is erratic rather than forgetful.

World first?

The question?

The world and the models?

Results?

Post hoc?

What this says about video first and world first?

Checkpoint?

Limits?

World first

The question

The world and the models

Results

Post hoc

What this says about video first and world first

Checkpoint

Limits