The capture point.

Push a standing humanoid and something has to decide, in about a tenth of a second, whether it can hold its ground or has to step. The thing that decides is one number.

Take where the center of mass is, add how fast it is moving times sqrt(h/g), and you get a point on the floor called the capture point: the spot where, if the robot planted a foot right now, it would come to rest balanced. While that point stays inside the foot it already has on the ground, ankle torque is enough. Push harder and the hips fold and the arms windmill, buying a little angular momentum. Push harder still and the capture point escapes the foot entirely, and the only correct answer left is to step on it. Not near it. On it.

I built a small demo of this with the real link lengths from the Unitree G1 URDF, thigh 194 mm and shin 300 mm, and what surprises people is how little math there is: one point, one polygon, and a rule about which side of the line you are on.

The part that stays with me from commissioning real humanoids is that falling is not the failure mode. Falling is in the spec. The failure mode is falling without a plan, which is exactly what the capture point exists to prevent. A robot that knows where to step when shoved is a robot you can put in a room with people.