The champion
Its tape, its head, and its state, read off the universal machine's tape after every step.
State w is a prelude, not part of the champion: the universal machine's tape for the machine it runs is one-way, so w walks right over a strip of 0s, erasing them, and hands over to A with exactly as much room on its left as the champion ever uses.
The whole run
Time runs left to right: each column is the tape after one step, filled where it holds a 1. The marked cell is the head.
Why this is a hard test
A busy beaver is the halting machine of a given size that runs longest from a blank tape (Radó, 1962). Whether a given machine ever halts cannot be decided in general, so these numbers are found one size at a time, by ruling out every other machine. Two states: 6 steps. Four: 107 steps, 13 ones (Brady, 1983). Five: 47,176,870 steps, settled only in 2024 by a collaborative, computer-checked proof.
The champion sweeps back and forth across a growing block of 1s, as the picture above shows, and then halts. The network never saw it: it trained on random machines, with tapes of up to six cells. With its prelude the champion has five states, and its tape reaches 14 cells.
The network is the one from the first page: one transformer layer, two attention heads, 211,270 parameters, trained only on the steps of a universal Turing machine while it ran random machines. The champion is written on the universal machine's tape as data:
Every configuration above is read from the universal machine's own tape after each step, and is
checked against the champion run directly. The same check runs in plain Python in
machines/lag5.