Open questions

Coherence horizon

Finish the ladder. Train the painter on Rules 184, 170, 110 and 90, then sweep the number of sampling steps. That scores the seven open predictions, including P9, v(90) > v(30) > v(170), which was written before those rules were trained.
Longer training. With four times the training on Rule 30, does the painter's mistake rate fall, and does its horizon then follow ε^−1/2, as the exchange rate says?
A flat painter. Twelve residual blocks at full resolution, with no downsampling. Is the U-Net's six-row exact zone set by how much of its depth runs at full resolution?
Attention and information topology. A patch-attention painter with no built-in locality or arrow of time, against a runner that writes cells in raster order like a language model.
A prediction for video models. From the exchange rate: failures of persistence (paint, number plates, identity; D = 1) should shrink with scale much faster than failures of smoke, fire and water (D ≈ 4). Successive generations of public video models can check it.

An anticipating driver. The model humans collide because their main law acts on what they saw one lag ago, with no extrapolation. Add temporal anticipation (Treiber, Kesting and Helbing, 2006), compute the new boundary, and then run. How much of its lag does anticipation give back, and do the contacts vanish?
A fair re-test of P3. The registered stop threshold (0.5 m/s) fails on Sugiyama's dense ring, where long margins mean crawling speeds. Register a criterion that does not depend on it, such as the speed spread relative to the uniform-flow speed, or contacts, or use a less dense ring.
Intersections. A four-way stop is mutual exclusion and gridlock is deadlock. What margin does an intersection need, and whose margin does a cautious automated driver spend there?
Blind driving. Senders and colleagues (1967) put drivers in a visor that lifted only when they asked for a glance. A browser version would measure how long a driver can run with no input, which joins margin to the coherence horizon.

Pictures with more bits. One bit per block leaves 19 classes of elementary worlds without a closed picture; any alphabet leaves 4 (Rules 30, 45, 106 and 154, by Israeli and Goldenfeld's search). For each world, what is the fewest bits per block at which a picture closes? That curve is the exchange rate between compression and physics.
The optimal denoiser on these worlds. Run the locally optimal denoiser on pictures of Rules 30, 110 and 90. Its receipts are exact and associative, and the census knows the causal answer. How often does its invented next frame agree with the world, and does a closed picture make its receipts causal?
A real model's noise against the floor. Train a small video model on pictures of Rule 110, where history helps, and Rule 30, where it does not, and compare its per-cell entropy with the measured noise floors.

Continuing flips. Let reality flip bits at a steady rate. The information needed is at least the entropy of the flips; how close does a model that knows the law come to it while new flips keep arriving, and how does that compare with a model that copies?
A gas without the extra invariants. Add rest particles or alternate the collision's handedness so the diagonal counts are no longer conserved. Does the disk's ghost vanish and its entropy reach the uniform value, and does the causal order still give three dimensions?
A model that must learn the law. How many observed bits does a model need to learn the collision table as well as the state, against the 14 questions a model that already has the law needs?
The copying threshold. It lies between 0.26 and 0.28 of the world per step, below the mean-field 0.308. Is it a directed-percolation transition? Its exponents would say.