Can a humanoid run all of its models on board?

No, and the reason is in the body itself. A humanoid has room for the models that keep it upright and keep it safe: balance, reflexes, stops, speed and motion limits. It does not have room for perception at the scale of a whole floor, for decisions that weigh many tasks at once, or for a language model large enough to take an instruction from a supervisor and act on it. Those models are too large to carry and too urgent to send to a cloud on the far side of a long network path. Element 31 serves them from a pool inside the building instead.

What stays on the robot

The on-board model is the robot's own. It runs balance and gait, it enforces stops and speed limits, and it holds the motion envelope the vendor shipped. Nothing about the pool changes that. The vendor's safety behavior is the vendor's, and it stays on the machine exactly as the vendor delivered it.

This matters for a plain reason. A reflex that depends on a network round trip is not a reflex. The robot has to be able to stop, slow, and hold position with no help from anything outside its own body, and a humanoid on a shared floor is judged by how it behaves when things go wrong rather than when they go right.

What the pool serves

The pool, a Czar in the building's own rack or several Czars joined as a Czar Grid, serves the models that will not fit. Perception that recognizes the whole floor, not just the robot's immediate reach. Decisions that account for the other robots, the people, and the work queue. Language models that let a lead on the floor say what needs doing in ordinary words.

Because the pool sits on the facility's own network, the round trip is short enough to be useful inside a task. Because it is shared, the same perception that helps a humanoid helps the mobile robots and pick arms on the same floor. Substrate holds each robot's latency budget so that a humanoid waiting on a decision is served within the time it can afford to wait.

When the pool cannot answer

The pool will sometimes be slow or unreachable. A switch fails, a node is taken out for an update, a cable is pulled. In every one of those cases the robot keeps its on-board model and falls back to it. It does what it can do alone, which is move carefully, finish a simple motion, or stop and wait.

That is the design. The pool makes the robot more capable while it is reachable and never makes the robot less safe when it is not. A pool that fails leaves a robot that stops, not one that guesses.

So the honest answer to the title is that a humanoid runs everything it must run on board and borrows everything else from the building. The division is deliberate, and it is what lets a fleet of humanoids from more than one vendor work a floor without each one carrying a data center on its back. The use cases page shows what that looks like for each kind of facility.